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Calculus 1 / AB Q&A Archive of September 28, 2024

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September 28 of 2024

Question 1 Given A = e^{-2v} (\hat{x} sin 2x + \hat{y} cos 2x), find $\nabla \cdot A$. e^{-2v} (sin 2x + cos2x) e^{-2v} 2 cos 2x 0 e^{-2v} cos 2x 1 pts
Practice score: 0/31 Answered: 0/31 Question 3 Let $f(x) = 4x + 4$ and $g(x) = 4x^2 + 2x$. After simplifying, $(f + g)(x) =$ Question Help: Video Submit Question
Compute the average rate of change of the function over the indicated interval. f(x) = 7x^3 + 2x^2 - 7 [5, 6] 1577 6 659 659 6 1577
1. Find the partial fraction expansion of the following rational expressions. x+1 a) x³+x²-6x b) x²-6x+7 (x²-4x+5)²
3. Linear First Order Integrating Factor: The population of a wolf species is given by y'-0.2xy=4x. Solve and check with initial condition y(0) = 8 x= #weeks since the start In addition, find the number of wolves in the population after 4 weeks. General Solution Particular Solution y(4) wolves
\lim_(u->-1)(u+1)/(u^(3)+1) $$\lim_{u \to -1} \frac{u + 1}{u^3 + 1}$$
7. A particle has an initial position vector $\vec{r_0}$ = 2.3$\hat{i}$ + 1.9$\hat{j}$ m and an initial velocity of $\vec{v_0}$ = 4.2$\hat{i}$ + 0.9$\hat{j}$ m/s. If its constant acceleration is $\vec{a}$ = 0$\hat{i}$ + 2.4$\hat{j}$ m/s², determine its position (x,y coordinates) and velocity…
\int (x)/(\sqrt(3-2x-x^(2)))dx
- Definition: the slope of the line tangent to the curve of y = f(x) at a point (a, f(a)) is
2. (2 pts) Find the average rate of change of the function f(x) = 2x² over the interval [1,3]. Done
3. If D is the differential operator, then the general solution to (D + 2)²y = 0 is: (A) C₁e-4x (B) C₁e-2x (C) e-4x (C₁ + C₂x) (D) e-2x (C₁ + C₂x)
Consider the following. $$f(x) = \frac{1}{4}x^4 - \frac{1}{3}x^3 - 3x^2$$ Find the critical numbers. (Enter your answers as a comma-separated list. If an a x = Find the open intervals on which the function is increasing or decreasing. Use a g increasing decreasing
Problem 1. Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ be defined by $$f(x, y, z) = \frac{1}{e^x + e^y + e^z}.$$ Answer the following true/false questions. You only need to write the answers (true or false). You do not need to show your work in this problem. (a) True or false: $f(0,0,0) =…
e\int_(-1)^1 x[3-e^(x)]dx
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. (Do this on paper. Your instructor may ask you to turn in this graph.) y=3sin(x), y = x = 0, x = π/2 Then find the area S of…
Use elimination to find the solution of the system. 3x+9y=33 -10x-6y=-14 $3x + 9y = 33$ $-10x - 6y = -14$
Use compositions of functions to decide whether or not the functions are inverses of each other. 5) f(x) = 2x^2 + 1, g(x) = \sqrt{\frac{x-1}{2}}
(7) Find the constants a and b such that the function f(x) is continuous on the entire real line. $$f(x) = \begin{cases} \frac{x^2-4}{x-2} & \text{if } x < 2; \\ ax^2-bx+1 & \text{if } 2 \le x < 3; \\ 4x-a+b & \text{if } x \ge 3. \end{cases}$$
Evaluate the indefinite integral $$\int \frac{6dr}{r \ln(3r)} = $$ To enter absolute values, do not use the bars, but the function "abs(x)".
4. [-/14.28 Points] DETAILS MY NOTES SCALCET9 3.1.082. Find the value of c such that the line y = x + 9 is tangent to the curve y = c√x. 9 4 c = Need Help? Read It Submit Answer
Find the domain of the vector-value function $$r(t) = \begin{pmatrix} -t^5, 5t^3, \frac{1}{(t+3)^7} \end{pmatrix}$$
1. Differentiate the following given functions. a. h(t) = −4(9 – 3t – t4)5 b. y = √x4 + 2x c. p(y) = sin7 (5y – 6y3) d. y = ln(2x4 – 5x² + 8x) e. f(x) = ln(7x4(5 – 3x)²) f. y = ln(4x² / 3x² - 8x) 2. Find the tangent line to f(x) = (2 - 4x²)3 at x = 1.
(c) Find a series $a_0 + a_1x + a_2x^2 + a_3x^3 + ...$ whose sum is $\frac{x^2 + 5}{1-x}$. Make the pattern for $a_n$ clear. HINT: Foil the product $(x^2 + 5)(1 + x + x^2 + x^3 + ...)$.
f(x, y) = 4xysin(x + y); π π 44 First, find fxπ and ππ 4'4 fy =
(10 pts): Compute the following integral. \int (1)/(t\sqrt(4t^(2)-9))dt 2. (10 pts): Compute the following integral. $$\int \frac{1}{t\sqrt{4t^2-9}} dt$$
\int 15z^(3)e^(z)dz eveluate the integral
Question 15 Which of the following functions is a solution to the DE? $$y'' + 16y' + 64y = 0$$ A. $$y = e^t$$ B. $$y = te^{-8t}$$ C. $$y = 6e^{-8t}$$ D. $$y = e^{-8t}$$ E. $$y = t^2e^{-8t}$$ B, C, and D only A, C, and D only B and D only B, C, D, and E only A and E only
Solve the following differential equation: (dy)/(dx)=(3x\sqrt(1+y^(2)))/(y) Solve the following differential equation: $\frac{dy}{dx} = \frac{3x\sqrt{1+y^2}}{y}$
2. Find the following limit. Fully justify your answer (e.g. if you use a limit law or other fact about limits, indicate this). $$\lim_{x \to 1} \left( \frac{x-1}{\sin(x-1)} + 3x - e^{x-1} + 2 \right)$$
Determine the derivative of f(x) = (4x + 3)5. f'(x) = 20(4x + 3)4 f'(x) = (4x + 3)4 f'(x) = 4(4x + 3)4 f'(x) = 5(4x + 3)4
Question 1 Evaluate the integral $$\int \tan^3x\sec^6x dx$$ 1 1 A sec⁸x-sec⁶x+c 8 6 1 1 B - sec⁶x-sec⁴x+c 6 4 1 C 10 -sec¹⁰x-sec⁸x+c 1 8 1 1 D sec⁴x-sec²x+c
Find the angle between the planes 6x + 9y = 5 and 6x + 9y + 2z = - 12. The radian measure of the acute angle is θ = 9 (Round to the nearest thousandth.)
21-22 Find, correct to the nearest degree, the three angles of the triangle with the given vertices. 21. A(1,0), B(3,6), C(-1,4)
Consider the following iterated integral $$\int_R \int f(x, y) dA.$$ 30 $$\int_0^{30} \int_{y/2}^{15} (x + y) dx dy$$ Evaluate the iterated integral $$\int_R \int f(x, y) dA.$$ $$\int_R \int f(x, y) dA = \boxed{}$$
Find the magnitude of the torque in foot-pounds at point P for the following lever. 45° F Q |PQ| = 5 in and |F| = 30 lb 1225 O A. 24 √2 ft-lb 35 OB. 24√2 ft-lb 25 OC.√2 ft-lb 25 OD. -√2 ft-lb
Problem #8: By changing the order of integration, the following integral $$\int_{\arctan x}^{1} \int_{0}^{\pi/4} f(x, y) dy dx$$ can be written in the form $$\int_{a}^{b} \int_{g(y)}^{h(y)} f(x, y) dx dy$$ (a) Enter the functions g(y) and h(y) (in that order) into the answer box below,…
9. [0/1 Points] DETAILS MY NOTES CALCETQC1 2.4.015A. Let $h(x) = \frac{f(x)}{1 + g(x)}$. Given $f(2) = 3$, $f'(2) = -5$, $g(2) = 1$, and $g'(2) = -4$, evaluate $h'(2)$. $h'(2) = $
3. (8 points) Find an equation of the plane that passes through the points (a, 0, 0), (0, a, 0), and (0, 0, a). 4. (10 points) Determine whether the following lines intersect, are parallel, or are skew. $$L_1: \frac{x-3}{2} = \frac{y-1}{-1} = \frac{z-4}{1}$$ and $$L_2: \frac{x+2}{3} =…
5) Find $f(g(x))$ and $g(f(x))$. Given: $f(x) = 3x$; $g(x) = x^2 - 2x$ $f(g(x)) = $ $g(f(x)) = $ a. $3x^2 - 6x$ b. $9x^2 - 6x$ c. $9x^3 - 6x^2$ d. $3x^3 - 6x$ e. $3x^3 - 6x^2$
Q A field is a rectangle with a perimeter of 1140 feet. The length is 300 feet more than the width. Find the width and length of the rectangular field.
Find all values of x such that the distance between (x,1) and (-2,-3) is 5 units
It takes Eugene 15 hours to pick forty bushels of apples. Ashley can pick the same amount in 9 hours. How long would it take them if they worked together?
For the equation y=x^(2)+1, which of the following would represent this function being translated up two units?
the position of a particle along a straight line is s= t^3/3 -3t^2+5t
Compute the volume obtained by revolving R Region with boundary y=sinx,x-axis, and x= pi. about x-axis
Find the centroid x y of the region bounded by: y= 4x^(2) +2x y=0 and x=3
State the order of the differential equation: y' +4y' - y =sinx
Jlve Quadratic Use factoring to solve the quadratic equation. Check by sub 5x^(2)+10x=0
consider the function f(x,y) = (e^x -3x)cos(y) suppose S is surface z=F(x,y)
13 Use your knowledge of reference points to write a function for a unique parabola that satisfies the given information. If it is not possible to write a function, state why not. Given: Exactly one x-intercept (-3,0) y-intercept (0,6)
find the equation of a line through the point (-1,2,-1) that is perpendicular to the plane 2x-4y+2z=3
a projectile is fired from the top of a 30ft tall building at an angle of 45 degrees with an inital velocity of 40 ft/sec. Determine the vector valued function that descibes the position of the projectile
\lim_(x->\infty )(x-3)/(x-2) Evaluate the limit. If the limit can be described with \infty or -\infty , do so.
G(x)=8x^(2) Find all antiderivatives of F(use C for the constant of intergation)
Is mathematics under GKM consistent an(d)/(o)r complete? Consistant Complete Neither consistant nor complete Both consistant and complete It's a bit more complicated than that.
Find the percentage of t a. 2% of 7 e. 2% of 5 minutes i. 5% of 500g Find the total quantity
0.0000345 0.0345 0.00345 Question 6 Change the following scientific notation number into standard notation: 9.865x 10^(6) 986500 9865 9,865,000 98,650,000 Question 7 1 pts
The parabola passes through the origin, and the 2 points (-1,-6),(2,0).
If the above is not filled out 10 points will be taken off. Find the distance between each pair of points. (5,-4),(8,-5)
Find the critical values for the following functions. Use the second order conditions to determine if this point is a maximum, minimum, inflection point or saddle point. z=7x^2-78x-6xy-48y+4y^2-23
F(x)=3x^2-2. If x=4 and h=12, what is the average rate of change?
the function y=100(1.05)x represents the cost per a night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opene
What is the point slope form of the line with slope (2)/(6) that passes through the point (-4,-7) ?
Show All Work 17. Vanessa throws a tennis ball in the air. The function h(t)=-16t^(2)+45t+7 represents the distance, in feet, that the ball is from the ground at any time t. At what time, to the nearest tenth of a second, is the ball at its maximum height?
Use the limit definition to find the derivative of the function f(x)=x^(3)-2x at [1,-1]
I'm thinking of a number. When i double it and take the result away from 25, the answer is less than 13
Give the slope and the y-intercept of the line y=2x+3. Make sure the y-intercept is written as a coordinate.
62 decreased by twice Vidya's score Use the variable v to represent Vidya's score.
Calculate Area and Volume 8. A piece of cardboard measures 30cm by 30cm. An open-topped box is to be constructed by removing a square with side length of 10cm from each corner and foldin: up the edges. a
((2+2x)^2/(2-x)^2)=115 solve for x and show what you put in for a,b and c in the quadratic equation and how you found a, b, and c.
Q is a region bounded by f(x)= (6 − 3x) and f(x)=e^(-x) Find the volume of the solid of revolution formed by rotating the region Q about y= −2. (Round to 3 decimals)
f(x)= b-2x if x<-4 -96/x-b if x is > or equal -4 find the two values of b for which f is continuous function at -4
Find d(y)/(d)x by differentiating implicitly. When applicable, express the result in terms of x and y. y+5xy-4=0
Rewrite with a ce Add to tops with Simplify your an Try these: -(2)/(5)+(3)/(4)
Find the coordinates of point S on bar (QR) such that the ratio of QS to SR is 1:3.
Find a possible formula for the exponential function through the points (-1,6) and (2,(2)/(9))
Perform the multiplication. If possible, reduce the answer to its lowest terms. (2(2)/(7))(4(3)/(8))
Given y =x^3-9x^2+ 2x + 30, what is the infection point
Consider the given line. a. Use a slope triangle to find the slope of the line.
I need the second derivative of G(r) = square root of r + ninth root of r
Find the direction of the vector B⃗ = (1.6 m ) x^ + (5.1 m ) y^
For this item, enter the answer in the space provided. An equilateral triangle with side lengths of 10 units is translated 4 units to the right. What is the length of one side of the triangle after translation, in units?
Mark Question for Use Let f(x)=5x-2 and g(x)=x^(2). Find and simplify (f*g)(x) O f(x)g(x)
When the product of 8 and 8 is divided by the sum of 8 and 8 , what is the quotient?
One side of a triangle is one-third the longest side. The third side is 10 feet less than the longest side. The perimeter is 88 . Find all three sides.
O^(24) WEB Dr Ellen Brook Lines and Question 5, 1. Part 1 of 2 Find a linear function h, given h(4)=-3 and h(-2)=9. Then find h(1). h(x)=h
Find the digits in the hundreds place, in the tenths place, and in the thousandt 140.2583 hundreds: tenths: thousandths:
FInd the equation of the oscilating circle to y=e^(x) at the point (0,1)
Use the power rule to find the first-order partial derivatives of the function: z=(8x-5y)(3x+4y)
If the sum of four consecutive even integers is 108 , what is the smallest of the four integers
If n=27,bar (x)(x- bar )=30, and s=5, find the margin of error at a 99% confidence level
x^(2)-5x-14=(x+a)(x-b), where a and b are whole numbers. What are the values of a and b ?
Question Find the equation of a line perpendicular to y=-3x-4 that contains the point (3,0). Write the equation in slope-intercept form.
a wheel has a 7cm radius if a wheel rotats 300 degrees how far has the motorcycle move
the sum of andy and Bretts ages is 44. Andys age is 8 more than twice Bretts age. How old is Brett.
Find the expression that represents the value of p. pr=t Solve the equation for g. 3(g-h)=14 Solve for x. ax-5=10 Find the expression that represt value of e. 5e-8=2e+f
Slope 0; through left parenthesis negative 6 comma negative 4 right parenthesis
Writing an equation for the parabola with given vertex and y-intercept
obtain \int \int_R (2-x-2y) dy dx, where R is the region bounded by the lines x= 2y,x + 2y= 2 and x=0
determine the points in the interval (0,5) at which the function has a discontinuity. At each point of discontinuity state the comditions in the
Which shows the rational expression written using the least common denominator? (x+1)/(4x^(2))+(x+1)/(x^(2))
1 point Two cars A and B are racing. The distribution of their speeds at 5 second intervals are
Find the vertex, focus, and directrix of the parabola w y^(2)=-8x
When the function f, of , xf(x) is divided by 2, x, minus, 12x-1, the quotient is x, squared, minus, 6, x, minus, 1x 2 -6x-1 and the remainder is minus, 6-6. Find the function f, of , xf(x) and write the result in standard form.
f(x) = x+3, for x less than or equal to -3 f(x) = 1, for -3
a. Use the given zeros: (11)/(7) and 7 to write the factored form of ,f(x)=2x^(2)-25x+77 f(x)
Find the particular solution using undetermined coefficients y''-2y - 3y = -3te^(-t)
what is the domain of f ( x ) = √ x + 4
Alex is evaluating the expression 12.75-:w+4w when w=2.55. Explain each step he should follow.
uestion list What is the slope of the line through (-3,7) and (4,8) in the
Evaluate the expression. Write fractional answers in simplest form. (If an answer 15 undefined, enter UNDEFINED. ) (3+[18-:(-3)])/(12)
Suppose that a fourth order differential equation has a solution y=-4e^(4x)xsin(x) . Find the initial conditions that this solution satisfies. y(0) = y′(0) = y′′(0) = y′′′(0) =
x^(3)+7x^(2)-36 The polynomial has zeros at -6 and 2 . If the remaining zero is z, then what is the value of -z ?
Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '\infty ' or '-\infty ', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x->−1/2 8x − 2 8x2 + 9
The standard helix has parameterization . Find the curvature of the helix. Does the result agree with your intuition?
use implicit differentiation to find d/dx of log base 10 root x
The cost of a thirty second Super Bowl ad in 1970 was $42000. In 2013 the cost of a thirty second Super Bowl ad was $4 million. What is the percent increase?
Find two numbers whose sum is 51 and whose product is 494
h=48t-16t^(2) When will the rocket be exactly 32 feet above the ground?
Consider the pair of functions. f(x) = x , g(x) = x + 7 (a) Find (f ∘ g)(x). Simplify the results. (f ∘ g)(x) =
For the following algebraic expressions, determine which are terms, like terms, and coefficients. 5x^(2)+3+8x-7x^(2)
A circle has diameter 18 cm. What angle is subtended at the center of the circle by an arc of 12 cm? Note: Write the exact answer but not the approximate value (For example write 45 or 4/5 but not 0.8)
Find a parametric equation for the tangent line to the curve x=t^2+1, y=8sqrt t, z=e^(t^2-1) to the curve
find a function that models the simple harmonie motion amplitude 24 ft period 2 min
ln(x)+ln(x-3)=ln(x+21) r(s), separated by commas and using fractions and radicals as necessary
what is the width of a ractangle with a leng of (5)/(6)and a area of 9 write an equation
Nora and Luna are standing at two different points on a flat field. Nora is standing at point (-2,5) and Luna is standing at point (6,5).
Question 7 (2.5 points ) A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. Note that the two triangles are proportional to one another.
Find the slope-intercept form for the line passing through (6,3) and parallel to the line passing through (2,6) and (-8,2).
writ the equation in general form. y-intercept: 3; parallel to y=3x-4
A plane can fly 650 miles in the same time as it takes a car to go 250 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.
Part 1 of 2Find an equation of the tangent plane to the surface at the given point.f(x, y) = (x + y)cos(8xy) + 10; 2, 2First, find fx2, 2 and fy2, 2.fx2, 2 = fy2, 2 =
A solid has a base that is bounded by the parabola y= - x^2+ 3 and the x-axis. The slices perpendicular to the base and x-axis are squares. Find the volume of the solid.
In 2016, the world population was about 7.42 billion. During the next 8 years, the world population increased by about 1.05% each year. Write an exponential model that represents the population y (in billions ) t years after 2016.
find equation for a circle with a dimaeter whose endpoints are (3,-5) and (-2,2)
For time 0<=t<=4, a particle moves along the x-axis with position given by f(t)=(1)/(3)t^(3)-5t-2. During what time interval (s) is the speed of the particle increasing. Justify your answer.
What is the degree of the expression that represents the perimeter of the triangle?
How old is a bone that contains 25% of its original carbon - 14 that was present in the living animal. (The half-life of carbon -14 is 5730 years. )
evaluate each complex number. you may need to simplyfy the radical as well (5i)(-i)(11)
Solve the equation (1)/(3)y+3=(1)/(10)y. Enter your answer as an integer or reduced fraction. Do not use decimals
Write a positive sine function. 7 0.5 points y=asin(b(x-c))+d What is a? type your answer...
the gilliam family wants to save for a big vactaion that costs 11,200. they now have 5,100 to invest in an interest bearing account. Determing what the APR would be if compounded monthly for 3 years.
If the cost to mail a letter is 48 cents for mail weighing up to one ounce and 25 cents for each additional ounce or fraction of an ounce, find the cost of mailing a letter that weighs 82 grams.
f corresponding sides of similar triangles are in a 3:5, then what is the ratio of the areas of these triangles
Directions: Determine the linear equation from the following information. 14. Through (2,-5) and (-3,5)
The straight line 4 has equation 4x+y=7 Find an equation of the straight line perpendicular to L that passes through (-8,3).
Find an explicit particular solution of the following initial value problem. (dy)/(dx)=9e^(2x-3y), y(0)=0
e the guadratic equation by x^(2)-2x-6=0 , choose the appropriate form n, solve the equation. Simplify here is more than one solution
Use a. the Trapezoidal Rule, b. the Midpoint Rule, and c. Simpson's Rule to approximate the given integral with the specified value of n. \int_1^3 (\sin t)/(t) dt , n=4
Factor out the GCF. In this problem, the GCF should include a negative -12x^(7)-20x^(6)-44x^(4)
on 8.1 Question 15, 8.1.59 Find the equation of the line. Through (8,-1); parallel to the line 2x+7y=4
if 38% of a substance had decayed away by 1998 and 49% was left in 2014, when will only 35% be left? when did the substance start to decay?
a curve f(x)=x^(3)-10x+9 is line through (2,-3) the equation of the tangent line is
solve the initial value problem with piecewise right hand side dy/dx + y = f(x) , y(0)=-8. Where f(x) = -1 if 0<=x<3 , 1 if 3<=x. y(x) = ? for 0<=x<3, y(x)=? for x>=3. Hint your sol should be continuos at x=3
Write an equation for the line that passes through (3, 4) and (-3, 0).
omework Question 11,0.3.63 Part 1 of 3 Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function. R(x)=(9x^(2)+15x-14)/(3x-2)
kaitlin earns 51 dollars each week working part tie at a bookstore she earns an additional dollars for each book that she sells Let A be the amount (in dollars ) that kaitlin earns in a week is she sells B books write equation if she sells 12 books
If z = x2 xy + 2y2 and (x, y) changes from (3, 1) to (2.96, 1.05), compare the values of z and dz. (Round your answers to four decimal places.)dz= z=
The hypotenuse of a right triangle measures 13cm. One leg of the triangle measures 12cm. Find the length of the other leg of the triangle cm Need Help? Read it Watch it
Calculate the exterior dimensions that an open rectangular box should have, for which the wall thickness \delta and the (interior) capacity V are given; so that doing so uses the least possible amount of material.
uations Test What is the slope of the line passing through (0,-2) and (5,-4) ?
square for the following equation? -6x^(2)-48x=-384 Answer Attempt 2 out of 2
Find the limit of the vector valued function <(3t^2) +1, (t-1)/(t+1), (2t+1)/(t+1)>
what is the slope intercept form of a line that passes through the (-8,6) and has a slope of -3
Knowledge Check Question 12 bonsider the line y=(4)/(5)x+7. Find the equation of the line that is parallel to this line and passes through the point (-8,-2). Find the equation of the line that is perpendicular to this line and passes through the point (-8,-2). Equation of parallel line:…
Identify the standard form for and the leading coefficient of the polynomial. 9h^(4)+15h^(5)-3h^(2)+40
Evaluate the expression for h=10.4. Write your answer as a decimal or whole number. h -12.2
Fine the linear equation that's parallel to: y=-(5)/(2)x+1 and goes through (-10,3)
The area of the region outside the circle r equals 2 and inside the circle r equals 4 sin theta is equal to
The population of Town N, currently at 102,000 , decreased 15% from a year ago. What was the population of Town N a year ago?
Evaluate ∫ ∫ D  y dA, where D is the triangular region with vertices (0, 0), (3, 9), and (12, 0)
Measure the length of each leg and the hypotenuse of this triangle: AF= units AG= units FG= units
Consider the first pair of terms and th 6xt+10x|+9t+15| Factor out the GCF from the first two
erimeter of a square is siven by P=45, wheres represents the length of a side
What is the correct meaning of 60% ? 60 out of 10 60 out of 1,000 60 out of 60 60 out of 100
The cross sections of a solid are semicircles perpendicular to y-axis, with diameters from the parabola x = 2 to theparabola x = 9- 2. The solid is between the intersections of both curves. Find the volume of the solid.
Consider the planes 𝑥 + 𝑦 − 𝑧 = 2 and 2𝑥 − 𝑦 + 3𝑧 = 1. a) Find the angle between the planes. b) Find the line of intersection, l, between the planes. c) Use your answer from part a) to find the equation of a plane that passes through the origin and contains the line of intersection. d) Find the…
ertically compressed by a factor of (1)/(9), horizontal asymptote y=31, vertical asymptote of x=5, reflected across the x-axis
Bookwork code: 6A 48 people can unload a ship in 5 hours. 48 people started unloading at 1pm. After 3 hours, 32 people had to leave. The remaining people kept working to finish unloading the ship. How many hours after 6m did the remaining people each have to work?
The equation of line f is y = (2)/(3)x + 6 Line g is parallel to line f . What is the slope of line g ?
find an equation of the plane that contains the given vector equation: r(t)=
Use a. the Trapezoidal Rule, b. the Midpoint Rule, and c. Simpson's Rule to approximate the given integral with the specified value of n. \int_0^1 \sqrt(x+x^(3)) dx , n=10
Given the function f ( x ) = 1 6 x − 2 and the function g ( x ) = 2 x 2 + 9 x + 7 determine each of the following. Give your answer as an integer or a simplified fraction. Evaluate Evaluate f ( f ( 1 ) ) f ( f ( 1 ) ) =
Assume that lim x->1 x f(x) = 1 and lim x->1 g(x) x + 1 = −1. Evaluate lim x->1 f(x)g(x) f(x) − g(x
Two-thirds of a number is negative six. Find the number. -4 -9 -8
x^(2)+16x complete the square and factor the resulting percent square trinomial
Find equation of circle that have endpoints of a diameter with P(-2, 2) and Q(4, -6)
Find the derivative of y using an implicit differential equation:4 cos x sin y = 1
Malcolm deposits $2,500 in a bank that is paying 9% interest continuously. Identify the function P that represents the amount of money Malcolm will have after t years.
Let f(x)=6x^1/5 (x^3)-11 evaluate the following specific values of f' f'(3) and f(4)
write the equation in general form. passes through (-4,2); perpendicular to y=5x-3
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt.
Simplify and leave your answer as a proper fraction or a mixed number. 2(9)/(10)+3(4)/(5)
write a equasion for which every real number is a solution
e Rate of Change Practic 2. Find average rate of change over the interval 0,1
If sinA=16 and tanB=25 where A and B are in the interval [/2,3/2] , What are the exact values of the following trigonometric functions? (Matching problem)
Consider the following limit \lim_(x->a)((x-7)(x-5)(x+6))/((x-5)(x-6)(x+4)). For which values of a (the value that x is approaching) does the limit NOT exist? Select ALL correct answers. A. a=5. B. a=6. C. a=7. D. a=-4. E. a=-6. F. a=-5.
To find the area at this point, we evaluate the area function, A, for x=2,50
what is the point slope form of the line passing through 4,-2 and has a slope of -(2)/(7)
A box is dropped from rest from height h and lands on the ground after atime interval t.if another box is dropped from a balcony at height 3h
Question 1 Given A = e^{-2v} (\hat{x} sin 2x + \hat{y} cos 2x), find $\nabla \cdot A$. e^{-2v} (sin 2x + cos2x) e^{-2v} 2 cos 2x 0 e^{-2v} cos 2x 1 pts
Practice score: 0/31 Answered: 0/31 Question 3 Let $f(x) = 4x + 4$ and $g(x) = 4x^2 + 2x$. After simplifying, $(f + g)(x) =$ Question Help: Video Submit Question
Compute the average rate of change of the function over the indicated interval. f(x) = 7x^3 + 2x^2 - 7 [5, 6] 1577 6 659 659 6 1577
1. Find the partial fraction expansion of the following rational expressions. x+1 a) x³+x²-6x b) x²-6x+7 (x²-4x+5)²
3. Linear First Order Integrating Factor: The population of a wolf species is given by y'-0.2xy=4x. Solve and check with initial condition y(0) = 8 x= #weeks since the start In addition, find the number of wolves in the population after 4 weeks. General Solution Particular Solution y(4) wolves
\lim_(u->-1)(u+1)/(u^(3)+1) $$\lim_{u \to -1} \frac{u + 1}{u^3 + 1}$$
7. A particle has an initial position vector $\vec{r_0}$ = 2.3$\hat{i}$ + 1.9$\hat{j}$ m and an initial velocity of $\vec{v_0}$ = 4.2$\hat{i}$ + 0.9$\hat{j}$ m/s. If its constant acceleration is $\vec{a}$ = 0$\hat{i}$ + 2.4$\hat{j}$ m/s², determine its position (x,y coordinates) and velocity…
\int (x)/(\sqrt(3-2x-x^(2)))dx
- Definition: the slope of the line tangent to the curve of y = f(x) at a point (a, f(a)) is
2. (2 pts) Find the average rate of change of the function f(x) = 2x² over the interval [1,3]. Done
3. If D is the differential operator, then the general solution to (D + 2)²y = 0 is: (A) C₁e-4x (B) C₁e-2x (C) e-4x (C₁ + C₂x) (D) e-2x (C₁ + C₂x)
Consider the following. $$f(x) = \frac{1}{4}x^4 - \frac{1}{3}x^3 - 3x^2$$ Find the critical numbers. (Enter your answers as a comma-separated list. If an a x = Find the open intervals on which the function is increasing or decreasing. Use a g increasing decreasing
Problem 1. Let $f: \mathbb{R}^3 \rightarrow \mathbb{R}$ be defined by $$f(x, y, z) = \frac{1}{e^x + e^y + e^z}.$$ Answer the following true/false questions. You only need to write the answers (true or false). You do not need to show your work in this problem. (a) True or false: $f(0,0,0) =…
e\int_(-1)^1 x[3-e^(x)]dx
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. (Do this on paper. Your instructor may ask you to turn in this graph.) y=3sin(x), y = x = 0, x = π/2 Then find the area S of…
Use elimination to find the solution of the system. 3x+9y=33 -10x-6y=-14 $3x + 9y = 33$ $-10x - 6y = -14$
Use compositions of functions to decide whether or not the functions are inverses of each other. 5) f(x) = 2x^2 + 1, g(x) = \sqrt{\frac{x-1}{2}}
(7) Find the constants a and b such that the function f(x) is continuous on the entire real line. $$f(x) = \begin{cases} \frac{x^2-4}{x-2} & \text{if } x < 2; \\ ax^2-bx+1 & \text{if } 2 \le x < 3; \\ 4x-a+b & \text{if } x \ge 3. \end{cases}$$
Evaluate the indefinite integral $$\int \frac{6dr}{r \ln(3r)} = $$ To enter absolute values, do not use the bars, but the function "abs(x)".
4. [-/14.28 Points] DETAILS MY NOTES SCALCET9 3.1.082. Find the value of c such that the line y = x + 9 is tangent to the curve y = c√x. 9 4 c = Need Help? Read It Submit Answer
Find the domain of the vector-value function $$r(t) = \begin{pmatrix} -t^5, 5t^3, \frac{1}{(t+3)^7} \end{pmatrix}$$
1. Differentiate the following given functions. a. h(t) = −4(9 – 3t – t4)5 b. y = √x4 + 2x c. p(y) = sin7 (5y – 6y3) d. y = ln(2x4 – 5x² + 8x) e. f(x) = ln(7x4(5 – 3x)²) f. y = ln(4x² / 3x² - 8x) 2. Find the tangent line to f(x) = (2 - 4x²)3 at x = 1.
(c) Find a series $a_0 + a_1x + a_2x^2 + a_3x^3 + ...$ whose sum is $\frac{x^2 + 5}{1-x}$. Make the pattern for $a_n$ clear. HINT: Foil the product $(x^2 + 5)(1 + x + x^2 + x^3 + ...)$.
f(x, y) = 4xysin(x + y); π π 44 First, find fxπ and ππ 4'4 fy =
(10 pts): Compute the following integral. \int (1)/(t\sqrt(4t^(2)-9))dt 2. (10 pts): Compute the following integral. $$\int \frac{1}{t\sqrt{4t^2-9}} dt$$
\int 15z^(3)e^(z)dz eveluate the integral
Question 15 Which of the following functions is a solution to the DE? $$y'' + 16y' + 64y = 0$$ A. $$y = e^t$$ B. $$y = te^{-8t}$$ C. $$y = 6e^{-8t}$$ D. $$y = e^{-8t}$$ E. $$y = t^2e^{-8t}$$ B, C, and D only A, C, and D only B and D only B, C, D, and E only A and E only
Solve the following differential equation: (dy)/(dx)=(3x\sqrt(1+y^(2)))/(y) Solve the following differential equation: $\frac{dy}{dx} = \frac{3x\sqrt{1+y^2}}{y}$
2. Find the following limit. Fully justify your answer (e.g. if you use a limit law or other fact about limits, indicate this). $$\lim_{x \to 1} \left( \frac{x-1}{\sin(x-1)} + 3x - e^{x-1} + 2 \right)$$
Determine the derivative of f(x) = (4x + 3)5. f'(x) = 20(4x + 3)4 f'(x) = (4x + 3)4 f'(x) = 4(4x + 3)4 f'(x) = 5(4x + 3)4
Question 1 Evaluate the integral $$\int \tan^3x\sec^6x dx$$ 1 1 A sec⁸x-sec⁶x+c 8 6 1 1 B - sec⁶x-sec⁴x+c 6 4 1 C 10 -sec¹⁰x-sec⁸x+c 1 8 1 1 D sec⁴x-sec²x+c
Find the angle between the planes 6x + 9y = 5 and 6x + 9y + 2z = - 12. The radian measure of the acute angle is θ = 9 (Round to the nearest thousandth.)
21-22 Find, correct to the nearest degree, the three angles of the triangle with the given vertices. 21. A(1,0), B(3,6), C(-1,4)
Consider the following iterated integral $$\int_R \int f(x, y) dA.$$ 30 $$\int_0^{30} \int_{y/2}^{15} (x + y) dx dy$$ Evaluate the iterated integral $$\int_R \int f(x, y) dA.$$ $$\int_R \int f(x, y) dA = \boxed{}$$
Find the magnitude of the torque in foot-pounds at point P for the following lever. 45° F Q |PQ| = 5 in and |F| = 30 lb 1225 O A. 24 √2 ft-lb 35 OB. 24√2 ft-lb 25 OC.√2 ft-lb 25 OD. -√2 ft-lb
Problem #8: By changing the order of integration, the following integral $$\int_{\arctan x}^{1} \int_{0}^{\pi/4} f(x, y) dy dx$$ can be written in the form $$\int_{a}^{b} \int_{g(y)}^{h(y)} f(x, y) dx dy$$ (a) Enter the functions g(y) and h(y) (in that order) into the answer box below,…
9. [0/1 Points] DETAILS MY NOTES CALCETQC1 2.4.015A. Let $h(x) = \frac{f(x)}{1 + g(x)}$. Given $f(2) = 3$, $f'(2) = -5$, $g(2) = 1$, and $g'(2) = -4$, evaluate $h'(2)$. $h'(2) = $
3. (8 points) Find an equation of the plane that passes through the points (a, 0, 0), (0, a, 0), and (0, 0, a). 4. (10 points) Determine whether the following lines intersect, are parallel, or are skew. $$L_1: \frac{x-3}{2} = \frac{y-1}{-1} = \frac{z-4}{1}$$ and $$L_2: \frac{x+2}{3} =…
5) Find $f(g(x))$ and $g(f(x))$. Given: $f(x) = 3x$; $g(x) = x^2 - 2x$ $f(g(x)) = $ $g(f(x)) = $ a. $3x^2 - 6x$ b. $9x^2 - 6x$ c. $9x^3 - 6x^2$ d. $3x^3 - 6x$ e. $3x^3 - 6x^2$
Q A field is a rectangle with a perimeter of 1140 feet. The length is 300 feet more than the width. Find the width and length of the rectangular field.
Find all values of x such that the distance between (x,1) and (-2,-3) is 5 units
It takes Eugene 15 hours to pick forty bushels of apples. Ashley can pick the same amount in 9 hours. How long would it take them if they worked together?
For the equation y=x^(2)+1, which of the following would represent this function being translated up two units?
the position of a particle along a straight line is s= t^3/3 -3t^2+5t
Compute the volume obtained by revolving R Region with boundary y=sinx,x-axis, and x= pi. about x-axis
Find the centroid x y of the region bounded by: y= 4x^(2) +2x y=0 and x=3
State the order of the differential equation: y' +4y' - y =sinx
Jlve Quadratic Use factoring to solve the quadratic equation. Check by sub 5x^(2)+10x=0
consider the function f(x,y) = (e^x -3x)cos(y) suppose S is surface z=F(x,y)
13 Use your knowledge of reference points to write a function for a unique parabola that satisfies the given information. If it is not possible to write a function, state why not. Given: Exactly one x-intercept (-3,0) y-intercept (0,6)
find the equation of a line through the point (-1,2,-1) that is perpendicular to the plane 2x-4y+2z=3
a projectile is fired from the top of a 30ft tall building at an angle of 45 degrees with an inital velocity of 40 ft/sec. Determine the vector valued function that descibes the position of the projectile
\lim_(x->\infty )(x-3)/(x-2) Evaluate the limit. If the limit can be described with \infty or -\infty , do so.
G(x)=8x^(2) Find all antiderivatives of F(use C for the constant of intergation)
Is mathematics under GKM consistent an(d)/(o)r complete? Consistant Complete Neither consistant nor complete Both consistant and complete It's a bit more complicated than that.
Find the percentage of t a. 2% of 7 e. 2% of 5 minutes i. 5% of 500g Find the total quantity
0.0000345 0.0345 0.00345 Question 6 Change the following scientific notation number into standard notation: 9.865x 10^(6) 986500 9865 9,865,000 98,650,000 Question 7 1 pts
The parabola passes through the origin, and the 2 points (-1,-6),(2,0).
If the above is not filled out 10 points will be taken off. Find the distance between each pair of points. (5,-4),(8,-5)
Find the critical values for the following functions. Use the second order conditions to determine if this point is a maximum, minimum, inflection point or saddle point. z=7x^2-78x-6xy-48y+4y^2-23
F(x)=3x^2-2. If x=4 and h=12, what is the average rate of change?
the function y=100(1.05)x represents the cost per a night at a hotel that cost $100 when the hotel opened and has been increasing by 5% every year since the hotel opene
What is the point slope form of the line with slope (2)/(6) that passes through the point (-4,-7) ?
Show All Work 17. Vanessa throws a tennis ball in the air. The function h(t)=-16t^(2)+45t+7 represents the distance, in feet, that the ball is from the ground at any time t. At what time, to the nearest tenth of a second, is the ball at its maximum height?
Use the limit definition to find the derivative of the function f(x)=x^(3)-2x at [1,-1]
I'm thinking of a number. When i double it and take the result away from 25, the answer is less than 13
Give the slope and the y-intercept of the line y=2x+3. Make sure the y-intercept is written as a coordinate.
62 decreased by twice Vidya's score Use the variable v to represent Vidya's score.
Calculate Area and Volume 8. A piece of cardboard measures 30cm by 30cm. An open-topped box is to be constructed by removing a square with side length of 10cm from each corner and foldin: up the edges. a
((2+2x)^2/(2-x)^2)=115 solve for x and show what you put in for a,b and c in the quadratic equation and how you found a, b, and c.
Q is a region bounded by f(x)= (6 − 3x) and f(x)=e^(-x) Find the volume of the solid of revolution formed by rotating the region Q about y= −2. (Round to 3 decimals)
f(x)= b-2x if x<-4 -96/x-b if x is > or equal -4 find the two values of b for which f is continuous function at -4
Find d(y)/(d)x by differentiating implicitly. When applicable, express the result in terms of x and y. y+5xy-4=0
Rewrite with a ce Add to tops with Simplify your an Try these: -(2)/(5)+(3)/(4)
Find the coordinates of point S on bar (QR) such that the ratio of QS to SR is 1:3.
Find a possible formula for the exponential function through the points (-1,6) and (2,(2)/(9))
Perform the multiplication. If possible, reduce the answer to its lowest terms. (2(2)/(7))(4(3)/(8))
Given y =x^3-9x^2+ 2x + 30, what is the infection point
Consider the given line. a. Use a slope triangle to find the slope of the line.
I need the second derivative of G(r) = square root of r + ninth root of r
Find the direction of the vector B⃗ = (1.6 m ) x^ + (5.1 m ) y^
For this item, enter the answer in the space provided. An equilateral triangle with side lengths of 10 units is translated 4 units to the right. What is the length of one side of the triangle after translation, in units?
Mark Question for Use Let f(x)=5x-2 and g(x)=x^(2). Find and simplify (f*g)(x) O f(x)g(x)
When the product of 8 and 8 is divided by the sum of 8 and 8 , what is the quotient?
One side of a triangle is one-third the longest side. The third side is 10 feet less than the longest side. The perimeter is 88 . Find all three sides.
O^(24) WEB Dr Ellen Brook Lines and Question 5, 1. Part 1 of 2 Find a linear function h, given h(4)=-3 and h(-2)=9. Then find h(1). h(x)=h
Find the digits in the hundreds place, in the tenths place, and in the thousandt 140.2583 hundreds: tenths: thousandths:
FInd the equation of the oscilating circle to y=e^(x) at the point (0,1)
Use the power rule to find the first-order partial derivatives of the function: z=(8x-5y)(3x+4y)
If the sum of four consecutive even integers is 108 , what is the smallest of the four integers
If n=27,bar (x)(x- bar )=30, and s=5, find the margin of error at a 99% confidence level
x^(2)-5x-14=(x+a)(x-b), where a and b are whole numbers. What are the values of a and b ?
Question Find the equation of a line perpendicular to y=-3x-4 that contains the point (3,0). Write the equation in slope-intercept form.
a wheel has a 7cm radius if a wheel rotats 300 degrees how far has the motorcycle move
the sum of andy and Bretts ages is 44. Andys age is 8 more than twice Bretts age. How old is Brett.
Find the expression that represents the value of p. pr=t Solve the equation for g. 3(g-h)=14 Solve for x. ax-5=10 Find the expression that represt value of e. 5e-8=2e+f
Slope 0; through left parenthesis negative 6 comma negative 4 right parenthesis
Writing an equation for the parabola with given vertex and y-intercept
obtain \int \int_R (2-x-2y) dy dx, where R is the region bounded by the lines x= 2y,x + 2y= 2 and x=0
determine the points in the interval (0,5) at which the function has a discontinuity. At each point of discontinuity state the comditions in the
Which shows the rational expression written using the least common denominator? (x+1)/(4x^(2))+(x+1)/(x^(2))
1 point Two cars A and B are racing. The distribution of their speeds at 5 second intervals are
Find the vertex, focus, and directrix of the parabola w y^(2)=-8x
When the function f, of , xf(x) is divided by 2, x, minus, 12x-1, the quotient is x, squared, minus, 6, x, minus, 1x 2 -6x-1 and the remainder is minus, 6-6. Find the function f, of , xf(x) and write the result in standard form.
f(x) = x+3, for x less than or equal to -3 f(x) = 1, for -3
a. Use the given zeros: (11)/(7) and 7 to write the factored form of ,f(x)=2x^(2)-25x+77 f(x)
Find the particular solution using undetermined coefficients y''-2y - 3y = -3te^(-t)
what is the domain of f ( x ) = √ x + 4
Alex is evaluating the expression 12.75-:w+4w when w=2.55. Explain each step he should follow.
uestion list What is the slope of the line through (-3,7) and (4,8) in the
Evaluate the expression. Write fractional answers in simplest form. (If an answer 15 undefined, enter UNDEFINED. ) (3+[18-:(-3)])/(12)
Suppose that a fourth order differential equation has a solution y=-4e^(4x)xsin(x) . Find the initial conditions that this solution satisfies. y(0) = y′(0) = y′′(0) = y′′′(0) =
x^(3)+7x^(2)-36 The polynomial has zeros at -6 and 2 . If the remaining zero is z, then what is the value of -z ?
Use properties of limits and algebraic methods to find the limit, if it exists. (If the limit is infinite, enter '\infty ' or '-\infty ', as appropriate. If the limit does not otherwise exist, enter DNE.) lim x->−1/2 8x − 2 8x2 + 9
The standard helix has parameterization . Find the curvature of the helix. Does the result agree with your intuition?
use implicit differentiation to find d/dx of log base 10 root x
The cost of a thirty second Super Bowl ad in 1970 was $42000. In 2013 the cost of a thirty second Super Bowl ad was $4 million. What is the percent increase?
Find two numbers whose sum is 51 and whose product is 494
h=48t-16t^(2) When will the rocket be exactly 32 feet above the ground?
Consider the pair of functions. f(x) = x , g(x) = x + 7 (a) Find (f ∘ g)(x). Simplify the results. (f ∘ g)(x) =
For the following algebraic expressions, determine which are terms, like terms, and coefficients. 5x^(2)+3+8x-7x^(2)
A circle has diameter 18 cm. What angle is subtended at the center of the circle by an arc of 12 cm? Note: Write the exact answer but not the approximate value (For example write 45 or 4/5 but not 0.8)
Find a parametric equation for the tangent line to the curve x=t^2+1, y=8sqrt t, z=e^(t^2-1) to the curve
find a function that models the simple harmonie motion amplitude 24 ft period 2 min
ln(x)+ln(x-3)=ln(x+21) r(s), separated by commas and using fractions and radicals as necessary
what is the width of a ractangle with a leng of (5)/(6)and a area of 9 write an equation
Nora and Luna are standing at two different points on a flat field. Nora is standing at point (-2,5) and Luna is standing at point (6,5).
Question 7 (2.5 points ) A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. Find the height of the tree. Note that the two triangles are proportional to one another.
Find the slope-intercept form for the line passing through (6,3) and parallel to the line passing through (2,6) and (-8,2).
writ the equation in general form. y-intercept: 3; parallel to y=3x-4
A plane can fly 650 miles in the same time as it takes a car to go 250 miles. If the car travels 80 mph slower than the plane, find the speed of the plane.
Part 1 of 2Find an equation of the tangent plane to the surface at the given point.f(x, y) = (x + y)cos(8xy) + 10; 2, 2First, find fx2, 2 and fy2, 2.fx2, 2 = fy2, 2 =
A solid has a base that is bounded by the parabola y= - x^2+ 3 and the x-axis. The slices perpendicular to the base and x-axis are squares. Find the volume of the solid.
In 2016, the world population was about 7.42 billion. During the next 8 years, the world population increased by about 1.05% each year. Write an exponential model that represents the population y (in billions ) t years after 2016.
find equation for a circle with a dimaeter whose endpoints are (3,-5) and (-2,2)
For time 0<=t<=4, a particle moves along the x-axis with position given by f(t)=(1)/(3)t^(3)-5t-2. During what time interval (s) is the speed of the particle increasing. Justify your answer.
What is the degree of the expression that represents the perimeter of the triangle?
How old is a bone that contains 25% of its original carbon - 14 that was present in the living animal. (The half-life of carbon -14 is 5730 years. )
evaluate each complex number. you may need to simplyfy the radical as well (5i)(-i)(11)
Solve the equation (1)/(3)y+3=(1)/(10)y. Enter your answer as an integer or reduced fraction. Do not use decimals
Write a positive sine function. 7 0.5 points y=asin(b(x-c))+d What is a? type your answer...
the gilliam family wants to save for a big vactaion that costs 11,200. they now have 5,100 to invest in an interest bearing account. Determing what the APR would be if compounded monthly for 3 years.
If the cost to mail a letter is 48 cents for mail weighing up to one ounce and 25 cents for each additional ounce or fraction of an ounce, find the cost of mailing a letter that weighs 82 grams.
f corresponding sides of similar triangles are in a 3:5, then what is the ratio of the areas of these triangles
Directions: Determine the linear equation from the following information. 14. Through (2,-5) and (-3,5)
The straight line 4 has equation 4x+y=7 Find an equation of the straight line perpendicular to L that passes through (-8,3).
Find an explicit particular solution of the following initial value problem. (dy)/(dx)=9e^(2x-3y), y(0)=0
e the guadratic equation by x^(2)-2x-6=0 , choose the appropriate form n, solve the equation. Simplify here is more than one solution
Use a. the Trapezoidal Rule, b. the Midpoint Rule, and c. Simpson's Rule to approximate the given integral with the specified value of n. \int_1^3 (\sin t)/(t) dt , n=4
Factor out the GCF. In this problem, the GCF should include a negative -12x^(7)-20x^(6)-44x^(4)
on 8.1 Question 15, 8.1.59 Find the equation of the line. Through (8,-1); parallel to the line 2x+7y=4
if 38% of a substance had decayed away by 1998 and 49% was left in 2014, when will only 35% be left? when did the substance start to decay?
a curve f(x)=x^(3)-10x+9 is line through (2,-3) the equation of the tangent line is
solve the initial value problem with piecewise right hand side dy/dx + y = f(x) , y(0)=-8. Where f(x) = -1 if 0<=x<3 , 1 if 3<=x. y(x) = ? for 0<=x<3, y(x)=? for x>=3. Hint your sol should be continuos at x=3
Write an equation for the line that passes through (3, 4) and (-3, 0).
omework Question 11,0.3.63 Part 1 of 3 Find the vertical, horizontal, and oblique asymptotes, if any, for the given rational function. R(x)=(9x^(2)+15x-14)/(3x-2)
kaitlin earns 51 dollars each week working part tie at a bookstore she earns an additional dollars for each book that she sells Let A be the amount (in dollars ) that kaitlin earns in a week is she sells B books write equation if she sells 12 books
If z = x2 xy + 2y2 and (x, y) changes from (3, 1) to (2.96, 1.05), compare the values of z and dz. (Round your answers to four decimal places.)dz= z=
The hypotenuse of a right triangle measures 13cm. One leg of the triangle measures 12cm. Find the length of the other leg of the triangle cm Need Help? Read it Watch it
Calculate the exterior dimensions that an open rectangular box should have, for which the wall thickness \delta and the (interior) capacity V are given; so that doing so uses the least possible amount of material.
uations Test What is the slope of the line passing through (0,-2) and (5,-4) ?
square for the following equation? -6x^(2)-48x=-384 Answer Attempt 2 out of 2
Find the limit of the vector valued function <(3t^2) +1, (t-1)/(t+1), (2t+1)/(t+1)>
what is the slope intercept form of a line that passes through the (-8,6) and has a slope of -3
Knowledge Check Question 12 bonsider the line y=(4)/(5)x+7. Find the equation of the line that is parallel to this line and passes through the point (-8,-2). Find the equation of the line that is perpendicular to this line and passes through the point (-8,-2). Equation of parallel line:…
Identify the standard form for and the leading coefficient of the polynomial. 9h^(4)+15h^(5)-3h^(2)+40
Evaluate the expression for h=10.4. Write your answer as a decimal or whole number. h -12.2
Fine the linear equation that's parallel to: y=-(5)/(2)x+1 and goes through (-10,3)
The area of the region outside the circle r equals 2 and inside the circle r equals 4 sin theta is equal to
The population of Town N, currently at 102,000 , decreased 15% from a year ago. What was the population of Town N a year ago?
Evaluate ∫ ∫ D  y dA, where D is the triangular region with vertices (0, 0), (3, 9), and (12, 0)
Measure the length of each leg and the hypotenuse of this triangle: AF= units AG= units FG= units
Consider the first pair of terms and th 6xt+10x|+9t+15| Factor out the GCF from the first two
erimeter of a square is siven by P=45, wheres represents the length of a side
What is the correct meaning of 60% ? 60 out of 10 60 out of 1,000 60 out of 60 60 out of 100
The cross sections of a solid are semicircles perpendicular to y-axis, with diameters from the parabola x = 2 to theparabola x = 9- 2. The solid is between the intersections of both curves. Find the volume of the solid.
Consider the planes 𝑥 + 𝑦 − 𝑧 = 2 and 2𝑥 − 𝑦 + 3𝑧 = 1. a) Find the angle between the planes. b) Find the line of intersection, l, between the planes. c) Use your answer from part a) to find the equation of a plane that passes through the origin and contains the line of intersection. d) Find the…
ertically compressed by a factor of (1)/(9), horizontal asymptote y=31, vertical asymptote of x=5, reflected across the x-axis
Bookwork code: 6A 48 people can unload a ship in 5 hours. 48 people started unloading at 1pm. After 3 hours, 32 people had to leave. The remaining people kept working to finish unloading the ship. How many hours after 6m did the remaining people each have to work?
The equation of line f is y = (2)/(3)x + 6 Line g is parallel to line f . What is the slope of line g ?
find an equation of the plane that contains the given vector equation: r(t)=
Use a. the Trapezoidal Rule, b. the Midpoint Rule, and c. Simpson's Rule to approximate the given integral with the specified value of n. \int_0^1 \sqrt(x+x^(3)) dx , n=10
Given the function f ( x ) = 1 6 x − 2 and the function g ( x ) = 2 x 2 + 9 x + 7 determine each of the following. Give your answer as an integer or a simplified fraction. Evaluate Evaluate f ( f ( 1 ) ) f ( f ( 1 ) ) =
Assume that lim x->1 x f(x) = 1 and lim x->1 g(x) x + 1 = −1. Evaluate lim x->1 f(x)g(x) f(x) − g(x
Two-thirds of a number is negative six. Find the number. -4 -9 -8
x^(2)+16x complete the square and factor the resulting percent square trinomial
Find equation of circle that have endpoints of a diameter with P(-2, 2) and Q(4, -6)
Find the derivative of y using an implicit differential equation:4 cos x sin y = 1
Malcolm deposits $2,500 in a bank that is paying 9% interest continuously. Identify the function P that represents the amount of money Malcolm will have after t years.
Let f(x)=6x^1/5 (x^3)-11 evaluate the following specific values of f' f'(3) and f(4)
write the equation in general form. passes through (-4,2); perpendicular to y=5x-3
A brine solution of salt flows at a constant rate of 8 L/min into a large tank that initially held 100 L of brine solution in which was dissolved 0.2 kg of salt.
Simplify and leave your answer as a proper fraction or a mixed number. 2(9)/(10)+3(4)/(5)
write a equasion for which every real number is a solution
e Rate of Change Practic 2. Find average rate of change over the interval 0,1
If sinA=16 and tanB=25 where A and B are in the interval [/2,3/2] , What are the exact values of the following trigonometric functions? (Matching problem)
Consider the following limit \lim_(x->a)((x-7)(x-5)(x+6))/((x-5)(x-6)(x+4)). For which values of a (the value that x is approaching) does the limit NOT exist? Select ALL correct answers. A. a=5. B. a=6. C. a=7. D. a=-4. E. a=-6. F. a=-5.
To find the area at this point, we evaluate the area function, A, for x=2,50
what is the point slope form of the line passing through 4,-2 and has a slope of -(2)/(7)
A box is dropped from rest from height h and lands on the ground after atime interval t.if another box is dropped from a balcony at height 3h
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