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Precalculus Q&A Archive of June 5, 2024

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June 5 of 2024

10. Determine \( B \) such that \( 3 x+2 y-7=0 \) is perpendicular to \( 2 x-B y+2=0 \) ?
Write the left side in terms of sine and cosine. \[ \frac{\cos \theta}{-1-\frac{\sin \theta}{\cos \theta}}+\frac{\sin \theta}{1+\frac{\cos \theta}{\sin \theta}} \] Write each term from the previous step as one fraction. \[ \frac{\cos ^{2} \theta}{\square}+\frac{\sin ^{2} \theta}{\sin…
ho wcan teaching degree can bring value to society and create worth living world
4. Calcula el valor del ángulo \( { }^{\circ} \theta^{\prime \prime} \)
2 Observa el grafico y determina por extensión cada operación. a.) \( 4-3 \) \( b-C \) \( =2-B+4 \) Ten en cuers: Enladterencacecantrit commata Es Eacr \[ A-3=8-x \]
\( \int \tan ^{3} x \sec ^{4} x d x \)
18. Write the complex number in trigonometric form \[ 5-5 i \]
17. Write the complex number in rectangular form \[ 14\left(\cos 300^{\circ}+i \sin 300^{\circ}\right) \]
12. Give the exact value of the expression without using a calculator. \[ \cos \left(\tan ^{-1} 7\right) \]
Solve the equation. \[ \tan \theta=2 \sin \theta \] What is the solution in the interval \( 0 \leq \theta<2 \pi \) ?
1. Determine \( d y / d x \) and \( \frac{d^{2} y}{d x^{2}} \) in each of the following cases. Simplify your Answers. \( 1.1 \quad x=2 \sin t, \quad y=\cos ^{2} t \) \( 1.2 \quad x=e^{2 t}, \quad y=e^{t} \sin t \) \( 1.3 x=\sin ^{2} \theta, \quad y=\sin \theta \) 1.4 \( y=t-\cosh t, \quad…
\( \int_{1}^{2}\left(3 x^{2}-2 x+1\right) d x \)
4. Find the remaining five trigonometric functions \[ \sin \theta=\frac{12}{13}, \theta \text { in quadrant } I I \]
\( \left\{\begin{array}{l}\frac{x}{6}+\frac{y}{4}=\frac{x+y-1}{3} \\ \frac{2 x-y}{8}-\frac{3}{2}=\frac{x^{2}+2 y}{2}\end{array}\right. \)
5. Solve the following equations using quadratic formula a) \( 4 x^{2}-11 x+6=0 \) b) \( x^{2}-5 x-2=0 \) c) \( 7 x^{2}=6-19 x \) d) \( 16 x-x^{2}=0 \) e) \( \frac{3}{x-2}=\frac{1}{x}+1 \)
12. The point \( \left(\frac{\pi}{4}, 1\right) \) is on the tangent wave. a) Where is this point translated if the tangent wave becomes \( y=-3 \tan \left(2 \theta-\frac{\pi}{2}\right)-1 \) ? \[ \begin{array}{lll} \left(2 x+\frac{\pi}{4},-3 y-1\right) & \\ x=45^{\circ} & \rightarrow & 135…
22. \( f(x)=108 x-x^{4} \) on \( [-1,5] \). 2. \( f(x)=4 x^{3}-3 x^{4}+4 \) on \( (-1,2) \). 24. \( f(x)=x^{4}-4 x^{3}+30 \) on \( (-2,4) \).
Find particular integral(PI) of the following differential equation: \[ \left(D^{2}+4\right) y=e^{x}+\sin 2 x+3 \]
how many children did the prophet has with khadija
Convert \( 186^{\circ} \) to radians. A. \( 31 \pi \mathrm{rad} \) B. \( 31 \pi \) \( \qquad \) rad C. \( 31 \pi \) \( \qquad \) rad 60 D. \( 31 \pi \) \( \qquad \) rad
Q3. Draw the graph, tree and its co-tree for the following circuit
5. \( \int_{0}^{\pi} \sin \left(\frac{x}{2}\right) d x \)
- Razonamiento 2. Determina si la afirmación es verdadera o falsa. Justifica tu respuesta. - El número mil quinientòs cuarenta y ocho unidades, trescientos noventa y siete milésimas se escribe 1548,0397 . Comunicación 3. Escribe un número decimal comprendido entre las parejas dadas.
8.7 PROBLEM SET 8-3 1. A rectangular warehouse is to have 3,300 square feet of floor area and is to be divided into two rectangular rooms by an interior wall. Cost per running foot is $125 for exterior walls and $80 for the interior wall. a) What dimensions will minimize total wall cost? b)…
Question 1 Solve the equation. \[ 10^{-2 \mathrm{x}}=10^{-3 \mathrm{x}} \] \( \frac{5}{7} \) \( -7 \) 1 0
(a) Determine the Fourier coefficients \( a_{0} \) and \( a_{n} \) of the 2 periodic function \[ f(x)=\left\{\begin{array}{l} -1 \text { if }-\Pi<x<0 \\ 1 \text { if } 0<x<\Pi \end{array}\right. \] page 1 of 4
Pate \[ I=\int \frac{\sqrt{y} \cdot(y+1)}{y} d y \]
express as a. olumn vector
5. (a) A three-phase, fully-controlled converter is connected to the \( 415 \mathrm{~V} \) supply, which has a reactance of \( 0.25 \Omega / \) phase and resistance of \( 0.05 \Omega / \) phase. The converter is operating in the inverter mode with \( \alpha=150 \) o and a continuous 50 A load…
21. El plano que pasa por el punto \( (1,-1,1) \) y tiene vector nor\( \mathrm{mal} \mathbf{i}+\mathbf{j}-\mathbf{k} \)
21. El plano que pasa por el punto \( (1,-1,1) \) y tiene vector nor\( \mathrm{mal} \mathbf{i}+\mathbf{j}-\mathbf{k} \) 22. El plano que pasa por el punto \( (-2,8,10) \) y es perpendicular a la recta \( x=1+t, y=2 t \) y \( z=4-3 t \) 23. El plano que pasa por el origen y es paralelo al plano…
4. Repeat Problem 3 for a rod of length \( l \) with density varying uniformly from 2 to 1 . 5. For a square lamina of uniform density, find \( I \) about (a) a side, (b) a diagonal, (c) an axis through a corner and perpendicular to the plane of the lamina. Hint: See the perpendicular axis…
4. Repeat Problem 3 for a rod of length \( l \) with density varying uniformly from 2 to 1 .
3. A thin rod \( 10 \mathrm{ft} \) long has a density which varies uniformly from 4 to \( 24 \mathrm{lb} / \mathrm{ft} \). Find (a) \( M \), (b) \( \bar{x} \), (c) \( I_{m} \) about an axis perpendicular to the rod, (d) \( I \) about an axis perpendicular to the rod passing through the heavy…
Vectors \( \overrightarrow{\boldsymbol{A}} \) and \( \overrightarrow{\boldsymbol{B}} \) are shown in the figure. Vector \( \overrightarrow{\boldsymbol{C}} \) is given by \( \overrightarrow{\boldsymbol{C}}=\overrightarrow{\boldsymbol{B}}-\overrightarrow{\boldsymbol{A}} \). The magnitude of…
9. Coffee / People / enjoy / drinking / most.
5. Construct an Euler circuit if one exists. If no Euler circuit exists, determine whether the directed graph has an Euler path. Construct an Euler path if one exists.
19. The Coot of fencing a field @ ? 5 per metre cm find its area \& ale sides.
Q2. Use Green`s function, solve the boundary value problem \[ u^{\prime \prime}(x)-u(x)=x, u(0)=u(1)=0 \]
Convert \( \frac{d^{2} y}{d x^{2}}+x y=1, y(0)=0, y(1)=1 \) into an integral equation
Prove that if \( E \) is a countable subset of \( \mathbb{R} \) then \( m^{*}(E)=0 \).
24 The table shows information about the surface area of each of the world's oceans. \begin{tabular}{|l|c|} \hline \multicolumn{1}{|c|}{ Ocean } & \begin{tabular}{c} Surface area in \\ square kilometres \end{tabular} \\ \hline Pacific & \( 1.56 \times 10^{8} \) \\ \hline Indian & \( 6.86…
Consider a \( 10 \% \) debenture, redeemable at par (TZS 1,0000 in four years' time and whereby investors require a \( 12 \% \) return. Calculate the current market value.
6. For \( n \geq 1 \), and positive integers \( a \) and \( b \), show the following: (a) If \( (a, b)=1 \), then \( \left(a^{n}, b^{n}\right)=1 \) (b) The relation \( a^{n} \mid b^{n} \) implies \( a \mid b \).
2. Find the ordinary and exact interest on P53,000 at \( 4.5 \% \) using actual and approximate time from February 1, 2016 to March 16, 2016 (leap year).
\( \frac{\sin x \tan x}{1-\cos x} \equiv 1+\frac{1}{\cos x} \)
The following particulars relate to a manufacturing company which the three department \( \mathrm{A}, \mathrm{B}, \mathrm{C} \) and two service department \( \mathrm{X} \) and \( \mathrm{Y} \). \[ \begin{array}{l} \text { Department } \\ \text { A } \quad \text { B } \quad \text { C } \quad…
find derivative of \( \frac{x}{5.76+0.0036 x^{2}} \)
6) Find a vector perpendicular to both \( \hat{i}-3 \hat{j}+2 \hat{k} \) and \( 5 \hat{i}-\hat{j}-4 \hat{k} \)
a) Find the permutations of the following words ABRACADABRA LOKICHOGIO BURUKENGE KIZUNGUMKUTI
If \( \phi \) is a scalar Function show that CurL grad \( \phi=0 \)
If \( \vec{F} \) ls a vector Form show \( \operatorname{Curl} \) curl \( \vec{F}=\operatorname{grad} \operatorname{div} \vec{F}-\nabla^{2} F \)
5. When a 3-ton truck is driven at a speed of \( x \) miles per hour, it travels \( m(x) \) miles per aallon of fuel consumed, where \[ m(x)=\frac{x}{5.76+0.0036 x^{2}} \] at what speed should a truck be driven if \( m(x) \) is to be maximized.
Differentiate ?((x-2)³+x)
5. The exact value of \( \cos 210^{\circ} \) is: A) \( \frac{\sqrt{3}}{2} \) B) \( -\frac{(\sqrt{3})}{2} \) C) \( \frac{1}{2} \) D) \( -\frac{1}{2} \)
12) Solve the following equation over the interval 0 < θ ≤ 2π. 15 cos² θ + cos θ - 2 = 0
3. The professor says sometimes that logs can't be simplified, and all we can do without a calculator is estimate what integers they like between. What's different about these- why don't they simplify nicely? And, how do I determine what integers these logs are between? log$_2$(12) log(40)
Determine all of the complex zeros of the polynomial function P(x) = x⁴ + 2x³ - 9x² - 10x - 24. x = -4, x = 3, x = -1±i√7 / 2 x = 4, x = -3, x = -1±√7 / 2 x = -1±i√7 / 2 only x = -4, x = 3 only
Divide and simplify. √45 √5 √45 √5 = (Simplify your answer. Type an exact answer, using radicals as m
Find the exact values for the six trigonometric functions of the angle $\theta$ in the figure. A 16 $5\sqrt{17}$ B 13 C Complete the table by using the names of the sides to express each trigonometric function as a ratio. sin $\theta$ = csc $\theta$ = cos $\theta$ = sec $\theta$ = tan $\theta$…
6. The point (5, 12) lies on the graph of y = g(x). If the function is transformed to the one below, a point on the graph of the transformed function will by (n, 24). The value of n will be y = g(x - 2) + 12
If $f(\theta) = 2 \cos \theta - \cos 2\theta$, find $f\left(\frac{\pi}{8}\right)$. Do not use a calculator and express each exact value as a single fraction. (Type an integer or a simplified fraction. Type an exact answer, using radicals as needed. Rationalize the denominator.)
Let p and q represent the following simple statements. p: It is snowing outside. q: I get an A. Write the symbolic statement ~ (qVp) in words.
Find (a) the future value of the given principal P and (b) the interest earned in the given period. P = $3800 at 7.5% compounded annually for 17 years (a) The future value of the principal after 17 years is $ (Round to the nearest cent as needed.)
Graph the equation $y = 1.5 \csc(2\pi x - 5\pi) + 2$. Use the blue diamond to shift the graph horizontally and vertically, the yellow triangle to stretch the graph vertically, and the red circle to stretch the graph horizontally. Reset
Use the value of $csc \theta = \frac{6}{5}$ for the acute angle $\theta$ to find the following trigonometric function values. a. $sin \theta$ b. $cos \theta$ c. $tan \theta$ d. $tan (90^\circ - \theta)$ a. $sin \theta = $ (Simplify your answer, including any radicals. Use integers or fractions…
13. [-/3.33 Points] Solve the absolute-value inequality. Express the answer using interval notation. $|5x-4| < 11$ Graph the solution set.
The graph above is a transformation of the function $f(x) = |x|$. Write an formula for the function graphed above: $g(x) = a|x + 2| - 1$ using an incorrect one.
Solve the exponential equation and write your answer in exact form. 11^x = 101 log11/log101 log101/log11 log112 log1.925
Objective 1: Identify Specific and General Terms of a Geometric Sequence For Exercises 9-18, determine whether the sequence is geterms of a Geometric Sequencente) 9. 6, 18, 54, 162, 13. 3, 12, 60, 360, 4 8 16 17. 2. 10. 4, 20, 100, 500, 177 5 12. 5. 14. 7, 14, 42, 88, ... 18. 5 15 45 135 15. 5,…
Sketch the graph of the function by first making a table of values. (If an answer is undefined, enter UNDEFINED.) $f(x) = -x + 4$, $-4 \le x \le 4$ X $f(x) = -x + 4$ -4 -3 0 1 3 4
Solve the nonlinear inequality. Express the solution using interval notation. (x + 4)^2(x - 7)(x + 6) ≥ 0 (-∞, -6] U [-4, ∞) (-∞, -7] U {4} U [6, ∞) (-∞, -6] U [7, ∞) (-∞, -4] U [7, ∞) (-∞, -6] U {-4} U [7, ∞) Graph the solution set
Find a formula for the inverse of the following function, if possible. $$A(x) = \frac{-3}{3x + 2}$$
Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate $\theta=$ $\sqrt{2}sin(\theta)+1=0$ rad
Question 33 Simplify the expression. $$\frac{1 - sin^2x}{cos(-x)}$$ cos x -sin x -cos x
Score on last try: 0 of 6 pts. See Details for more. Get a similar question You can retry this question below Consider the right triangle shown below that has an interior angle measure of $\theta$ radians. 4 cm 2.12 cm $\theta$ 3.39 cm a. The vertical leg of the triangle is how many times as…
A C b B a Note: Triangle may not be drawn to scale. Suppose A = 69 degrees and b = 8. Find: a = C = B = degrees C
Try It #6 Write an explicit formula for the nth term of the sequence. {; 2,5,5,5,2,.. Enter the exact answer. Include a multiplication sign between symbols. For example, 3 * n. an =
Find the distance between the points P₁ = (5,-2) and P2 = (9,8) Give an exact answer. Simplify any radicals. Distance =
Use the triangle shown to the right to evaluate the following expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator. sin 30° sin 30° = (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in…
Express the absolute value function y = |x²-2x-15| as a piecewise function. Select one: a. y = { x²-2x-15 for -3 ≤ x ≤ 5 -x²+2x+15 for x < -3 or x > 5 b. y = { x²-2x-15 for x ≤ -3 or x ≥ 5 -x²+2x+15 for -3 < x < 5 c. y = { x²-2x-15 for x ≥ 0 -x²+2x+15 for x < 0 d. y = { x²-2x-15 for x ≤ -3 or x…
$\theta$ is an acute angle and $sin \theta$ and $cos \theta$ are given. Use identities to find $tan \theta$, $csc \theta$, $sec \theta$, and $cot \theta$. Where necessary, rationalize denominators. $sin \theta = \frac{20}{29}$, $cos \theta = \frac{21}{29}$ $tan \theta = $ (Simplify your answer,…
24. [0.66/3.33 Points] DETAILS MY NOTES S Evaluate the function at the indicated values. (If an answer is $$h(t) = t + \frac{2}{t}$$ $$h(-1) =$$ $$h(5) =$$ $$h(\frac{1}{2}) =$$ $$h(x-1) =$$ $$h(\frac{1}{x}) =$$
Find the inverse of the function: $f(x) = -4 \cdot log_8(x)$ $f(x)^{-1} = $
Find the 6th term of the binomial expansion of (3p - q)8.
Consider the following functions. $f(x) = x - 7$ and $g(x) = |x|$ Step 2 of 4: Find $(f - g)(-2)$.
6. Slippery Pete has stashed away $4320 into a Swiss account that earns 6%/a, compounded quarterly. To increase his wealth, he deposits $800 at the end of every three months for a period of five years. What will be his account balance after the five years?
Question Find the first 5 terms of the sequence $a_n$ defined below. $a_n = \begin{cases} 2n - 3 & \text{if n is odd} \\ 2n + 3 & \text{if n is even} \end{cases}$ Give your answer as a list separated by commas. For example, if you found that the terms were 2, 4, 6, 8, 10, you would enter 2, 4,…
For the quadratic function defined, write the function in the form $P(x)=a(x-h)^2+k$. $P(x)=x^2-2x-5$ $P(x)=\boxed{}$ (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Question 21 If -5 + 4log2(x + 1) = 1, then x = Round your answer to three decimal places. Do not enter fractions.
Simplify the expression. $$ \frac{5\sqrt{64}}{5\sqrt{-2}}$$ $$ \frac{5\sqrt{64}}{5\sqrt{-2}} = $$ (Simplify your answer.)
Express the absolute value function y = |-2x + 10| as a piecewise function. Select one: a. y = -2x+10 for x ≥ 0 2x-10 for x < 0 b. y = -2x+10 for x ≤ 5 2x-10 for x > 5 c. y = -2x+10 for x ≥ 5 2x-10 for x < 5 d. y = -2x+10 for x ≤ 5 2x + 10 for x > 5
Consider the following graph of two functions. 10 5 Step 2 of 4: Find (f-g)(-1). f y 10 5 5 10 g X 5 10
Given f(x), find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely .x. f(x) = $\sqrt{-5x^3 + 4} + 5$ Answer g(x) = h(x) =
The graph above is a transformation of the function $f(x) = |x|$. Write an formula for the function graphed above: $g(x) = |x + 1| - 2$
Question 9 Solve the absolute value equation |2x-5|=5-4x graphically. Answer saved Marked out of 1.00 Flag Select one: a. x = 0, question b. x = -3,0 5-35-2 c. x = 5-3 d. x = 0 Clear my choice
dical Expressions < Question 7, R.7.35 > Simplify the expression. Assume that all variables are positive. $$\sqrt[7]{\frac{7x}{y^6}} \cdot \sqrt[7]{\frac{y^6}{7x^8}}$$
The graph shows the consumer price index for a certain product during 2005-2021. The function f(t)=159-45 In t models these data, where t represents the number of years after 2004. So 2005 corresponds to t= 1. Complete parts (a)-(c). CPI of…
Back Question 11 Answer saved If the graph of y = f(x) is transformed to y = |f(x)|, an invariant point will never occur Marked out of Select one: 1.00 Flag question Previous page A. at the x-intercept B. at f(x) = |f(x)| C. below the x-axis D. at the y-intercept Clear my choice
Find all zeros of the polynomial. (Enter your answers as a comma-s P(x) = 16x^4 + 16x^3 + 20x^2 + 16x + 4
Select the answers that best complete the given statement. A function f has an inverse that is a function if there is no ✔line that intersects the graph of f at more than one point. Such a function is called a/an ✔function.
10. Find a quadratic function $f$ that has the vertex (3, -7) and x- intercept (-3, 0).
(b) For the functions from part (a) that do have 8 in their domain, find the value of the function at 8. (If 8 is not in the domain, enter UNDEFIN f(x) = x² - 3x g(x) = x-8 x h(x) = √x - 16
Find the following sum. Write your answer so that the numerator and denominator of your answer are in factored form. $$ \frac{3}{x + 7} + \frac{x}{x - 13} $$
Question 18 Find the partial sum $S_{14}$ for the arithmetic sequence with $a = 4$, $d = 3$. $S_{14} = $ 0/5 pts 2 19 Details
(b) Find the following. Use exact values and not decimal approximations. $$sin\left(-\frac{5\pi}{3}\right)=$$ $$sin\left(-\frac{5\pi}{3}-4\pi\right)=$$
Find the following for the given rational function. g(x) = $$ \frac{2x^2 - 9x - 5}{x^2 - 3x - 10} $$. a) Identify any vertical asymptotes and the coordinates of any holes in the graph. You will need to factor in order to answer this question. b) Identify the horizontal asymptote in the graph…
Graph the equation $y = 2.5 \csc(2 \pi x)$. Use the blue diamond to shift the graph horizontally and vertically, the yellow triangle to stretch the graph vertically, and the red circle to stretch the graph horizontally. Reset
Given the graph of the rational function below, evaluate each of the following limits. a) $$\lim_{x \to 2^+} f(x) =$$ b) $$\lim_{x \to 2^-} f(x) =$$
Question 1 (1 point) Convert the angle 176 degrees 24' 28" to radians. Please approximate your answer and round to three decimal places. radians Blank 1: Question 2 (1 point) Convert the angle 3.92 radians to degrees. Approximate your answer to three decimal places. degrees Blank 1:
Find the height of a pine tree that casts a 93-foot shadow on the ground if the angle of elevation of the sun is 26°35′. The height of the pine tree is approximately ft. (Round to the nearest integer as needed.)
Write the following equation in the standard form for an ellipse. 9y^2 + x^2 + 18y - 10x = 2
× Question 4 Score on last try: 0 of 3 pts. See Details for more. Get a similar question You can retry this question below 0/3 pts991 Details In many cases the Law of Sines works perfectly well and returns the correct missing values in a non-right triangle. However, in some cases the Law of…
The population (in thousands) of people of a city is approximated by the function P(t) = 1400(2)^0.1011t, where t is the number of years since 2010. a. Find the population of this group in 2018. o. Predict the population in 2028. a. The population of this group in 2018 is. (Round to the nearest…
Write an equation of the ellipse with the given characteristics and center at (0,0). Vertex: (3,0) Co-Vertex: (0, 2) Equation:
Click here to watch the video, Use $f(x)$ and $g(x)$ to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) Complete parts (a) through (c) below. $f(x)=x^2$, $g(x)=\sqrt{25-x}$ (a) $(f \circ g)(x)=\boxed{}$ (Simplify your answer)
: Radical Expressions Question 8, R.7.55 HW Score: 23.86%, Points: 0 of 1 Simplify the expression. Assume that all variables are positive and write your answer in radical notation. √2 ⋅ ³√2
5. And one more thing, if that's okay. The professor keeps taking about converting forms, and just can't remember how to do that either! I remember that maybe exponentials can be written as logs and logs can be written as exponentials, but I don't remember how. Can you show me how to convert…
Limits of the form $$\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$ occur frequently in calculus. Evaluate this limit for the given value of x and function f. $$f(x) = x^2, x = -9$$
2. Given $y = sec(2x - \frac{\pi}{2})$ a. Determine the Period and explain how you came about your answer. b. Is there a Phase Shift? If so, what is it? Discuss how you determined your answer. c. Determine the Asymptotes (if they exist) and explain how you arrived at your answer.
Aaron, a cross-country runner, trains all year round. He finds that the slippery road conditions in the winter cause him to slow down by 2 km/h, so that it takes him 2 hours longer to run to a 48 km course. Choose the correct expression for Aaron's time in the winter.
Use properties of exponents to determine which functions (if any) are the same. f(x) = 4^x + 12 g(x) = 2^(2x) + 5 h(x) = 32(4^x) O f(x) = g(x) O f(x) = h(x) O g(x) = h(x) All three functions are equal. None of the functions are equal.
Given the parametrically defined relation below, find the ordered pair (x, y) when t = 3. x = 3t + cos(πt) y = t² - sin (π/2 t)
Determine the equation of the vertical line through the point (-4, -7). Write your answer as an equation using the variables x and y. The equation of the line is:
8.7 PROBLEM SET 8-3 1. A rectangular warehouse is to have 3,300 square feet of floor area and is to be divided into two rectangular rooms by an interior wall. Cost per running foot is $125 for exterior walls and $80 for the interior wall. a) What dimensions will minimize total wall cost? b)…
Differentiate ?((x-2)³+x)
12) Solve the following equation over the interval 0 < θ ≤ 2π. 15 cos² θ + cos θ - 2 = 0
3. The professor says sometimes that logs can't be simplified, and all we can do without a calculator is estimate what integers they like between. What's different about these- why don't they simplify nicely? And, how do I determine what integers these logs are between? log$_2$(12) log(40)
Determine all of the complex zeros of the polynomial function P(x) = x⁴ + 2x³ - 9x² - 10x - 24. x = -4, x = 3, x = -1±i√7 / 2 x = 4, x = -3, x = -1±√7 / 2 x = -1±i√7 / 2 only x = -4, x = 3 only
Divide and simplify. √45 √5 √45 √5 = (Simplify your answer. Type an exact answer, using radicals as m
Find the exact values for the six trigonometric functions of the angle $\theta$ in the figure. A 16 $5\sqrt{17}$ B 13 C Complete the table by using the names of the sides to express each trigonometric function as a ratio. sin $\theta$ = csc $\theta$ = cos $\theta$ = sec $\theta$ = tan $\theta$…
6. The point (5, 12) lies on the graph of y = g(x). If the function is transformed to the one below, a point on the graph of the transformed function will by (n, 24). The value of n will be y = g(x - 2) + 12
If $f(\theta) = 2 \cos \theta - \cos 2\theta$, find $f\left(\frac{\pi}{8}\right)$. Do not use a calculator and express each exact value as a single fraction. (Type an integer or a simplified fraction. Type an exact answer, using radicals as needed. Rationalize the denominator.)
Let p and q represent the following simple statements. p: It is snowing outside. q: I get an A. Write the symbolic statement ~ (qVp) in words.
Find (a) the future value of the given principal P and (b) the interest earned in the given period. P = $3800 at 7.5% compounded annually for 17 years (a) The future value of the principal after 17 years is $ (Round to the nearest cent as needed.)
Graph the equation $y = 1.5 \csc(2\pi x - 5\pi) + 2$. Use the blue diamond to shift the graph horizontally and vertically, the yellow triangle to stretch the graph vertically, and the red circle to stretch the graph horizontally. Reset
Use the value of $csc \theta = \frac{6}{5}$ for the acute angle $\theta$ to find the following trigonometric function values. a. $sin \theta$ b. $cos \theta$ c. $tan \theta$ d. $tan (90^\circ - \theta)$ a. $sin \theta = $ (Simplify your answer, including any radicals. Use integers or fractions…
13. [-/3.33 Points] Solve the absolute-value inequality. Express the answer using interval notation. $|5x-4| < 11$ Graph the solution set.
The graph above is a transformation of the function $f(x) = |x|$. Write an formula for the function graphed above: $g(x) = a|x + 2| - 1$ using an incorrect one.
Solve the exponential equation and write your answer in exact form. 11^x = 101 log11/log101 log101/log11 log112 log1.925
Objective 1: Identify Specific and General Terms of a Geometric Sequence For Exercises 9-18, determine whether the sequence is geterms of a Geometric Sequencente) 9. 6, 18, 54, 162, 13. 3, 12, 60, 360, 4 8 16 17. 2. 10. 4, 20, 100, 500, 177 5 12. 5. 14. 7, 14, 42, 88, ... 18. 5 15 45 135 15. 5,…
Sketch the graph of the function by first making a table of values. (If an answer is undefined, enter UNDEFINED.) $f(x) = -x + 4$, $-4 \le x \le 4$ X $f(x) = -x + 4$ -4 -3 0 1 3 4
Solve the nonlinear inequality. Express the solution using interval notation. (x + 4)^2(x - 7)(x + 6) ≥ 0 (-∞, -6] U [-4, ∞) (-∞, -7] U {4} U [6, ∞) (-∞, -6] U [7, ∞) (-∞, -4] U [7, ∞) (-∞, -6] U {-4} U [7, ∞) Graph the solution set
Find a formula for the inverse of the following function, if possible. $$A(x) = \frac{-3}{3x + 2}$$
Find all solutions of the given equation. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to two decimal places where appropriate $\theta=$ $\sqrt{2}sin(\theta)+1=0$ rad
Question 33 Simplify the expression. $$\frac{1 - sin^2x}{cos(-x)}$$ cos x -sin x -cos x
Score on last try: 0 of 6 pts. See Details for more. Get a similar question You can retry this question below Consider the right triangle shown below that has an interior angle measure of $\theta$ radians. 4 cm 2.12 cm $\theta$ 3.39 cm a. The vertical leg of the triangle is how many times as…
A C b B a Note: Triangle may not be drawn to scale. Suppose A = 69 degrees and b = 8. Find: a = C = B = degrees C
Try It #6 Write an explicit formula for the nth term of the sequence. {; 2,5,5,5,2,.. Enter the exact answer. Include a multiplication sign between symbols. For example, 3 * n. an =
Find the distance between the points P₁ = (5,-2) and P2 = (9,8) Give an exact answer. Simplify any radicals. Distance =
Use the triangle shown to the right to evaluate the following expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator. sin 30° sin 30° = (Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in…
Express the absolute value function y = |x²-2x-15| as a piecewise function. Select one: a. y = { x²-2x-15 for -3 ≤ x ≤ 5 -x²+2x+15 for x < -3 or x > 5 b. y = { x²-2x-15 for x ≤ -3 or x ≥ 5 -x²+2x+15 for -3 < x < 5 c. y = { x²-2x-15 for x ≥ 0 -x²+2x+15 for x < 0 d. y = { x²-2x-15 for x ≤ -3 or x…
$\theta$ is an acute angle and $sin \theta$ and $cos \theta$ are given. Use identities to find $tan \theta$, $csc \theta$, $sec \theta$, and $cot \theta$. Where necessary, rationalize denominators. $sin \theta = \frac{20}{29}$, $cos \theta = \frac{21}{29}$ $tan \theta = $ (Simplify your answer,…
24. [0.66/3.33 Points] DETAILS MY NOTES S Evaluate the function at the indicated values. (If an answer is $$h(t) = t + \frac{2}{t}$$ $$h(-1) =$$ $$h(5) =$$ $$h(\frac{1}{2}) =$$ $$h(x-1) =$$ $$h(\frac{1}{x}) =$$
Find the inverse of the function: $f(x) = -4 \cdot log_8(x)$ $f(x)^{-1} = $
Find the 6th term of the binomial expansion of (3p - q)8.
Consider the following functions. $f(x) = x - 7$ and $g(x) = |x|$ Step 2 of 4: Find $(f - g)(-2)$.
6. Slippery Pete has stashed away $4320 into a Swiss account that earns 6%/a, compounded quarterly. To increase his wealth, he deposits $800 at the end of every three months for a period of five years. What will be his account balance after the five years?
Question Find the first 5 terms of the sequence $a_n$ defined below. $a_n = \begin{cases} 2n - 3 & \text{if n is odd} \\ 2n + 3 & \text{if n is even} \end{cases}$ Give your answer as a list separated by commas. For example, if you found that the terms were 2, 4, 6, 8, 10, you would enter 2, 4,…
For the quadratic function defined, write the function in the form $P(x)=a(x-h)^2+k$. $P(x)=x^2-2x-5$ $P(x)=\boxed{}$ (Simplify your answer. Use integers or fractions for any numbers in the expression.)
Question 21 If -5 + 4log2(x + 1) = 1, then x = Round your answer to three decimal places. Do not enter fractions.
Simplify the expression. $$ \frac{5\sqrt{64}}{5\sqrt{-2}}$$ $$ \frac{5\sqrt{64}}{5\sqrt{-2}} = $$ (Simplify your answer.)
Express the absolute value function y = |-2x + 10| as a piecewise function. Select one: a. y = -2x+10 for x ≥ 0 2x-10 for x < 0 b. y = -2x+10 for x ≤ 5 2x-10 for x > 5 c. y = -2x+10 for x ≥ 5 2x-10 for x < 5 d. y = -2x+10 for x ≤ 5 2x + 10 for x > 5
Consider the following graph of two functions. 10 5 Step 2 of 4: Find (f-g)(-1). f y 10 5 5 10 g X 5 10
Given f(x), find g(x) and h(x) such that f(x) = g(h(x)) and neither g(x) nor h(x) is solely .x. f(x) = $\sqrt{-5x^3 + 4} + 5$ Answer g(x) = h(x) =
The graph above is a transformation of the function $f(x) = |x|$. Write an formula for the function graphed above: $g(x) = |x + 1| - 2$
Question 9 Solve the absolute value equation |2x-5|=5-4x graphically. Answer saved Marked out of 1.00 Flag Select one: a. x = 0, question b. x = -3,0 5-35-2 c. x = 5-3 d. x = 0 Clear my choice
dical Expressions < Question 7, R.7.35 > Simplify the expression. Assume that all variables are positive. $$\sqrt[7]{\frac{7x}{y^6}} \cdot \sqrt[7]{\frac{y^6}{7x^8}}$$
The graph shows the consumer price index for a certain product during 2005-2021. The function f(t)=159-45 In t models these data, where t represents the number of years after 2004. So 2005 corresponds to t= 1. Complete parts (a)-(c). CPI of…
Back Question 11 Answer saved If the graph of y = f(x) is transformed to y = |f(x)|, an invariant point will never occur Marked out of Select one: 1.00 Flag question Previous page A. at the x-intercept B. at f(x) = |f(x)| C. below the x-axis D. at the y-intercept Clear my choice
Find all zeros of the polynomial. (Enter your answers as a comma-s P(x) = 16x^4 + 16x^3 + 20x^2 + 16x + 4
Select the answers that best complete the given statement. A function f has an inverse that is a function if there is no ✔line that intersects the graph of f at more than one point. Such a function is called a/an ✔function.
10. Find a quadratic function $f$ that has the vertex (3, -7) and x- intercept (-3, 0).
(b) For the functions from part (a) that do have 8 in their domain, find the value of the function at 8. (If 8 is not in the domain, enter UNDEFIN f(x) = x² - 3x g(x) = x-8 x h(x) = √x - 16
Find the following sum. Write your answer so that the numerator and denominator of your answer are in factored form. $$ \frac{3}{x + 7} + \frac{x}{x - 13} $$
Question 18 Find the partial sum $S_{14}$ for the arithmetic sequence with $a = 4$, $d = 3$. $S_{14} = $ 0/5 pts 2 19 Details
(b) Find the following. Use exact values and not decimal approximations. $$sin\left(-\frac{5\pi}{3}\right)=$$ $$sin\left(-\frac{5\pi}{3}-4\pi\right)=$$
Find the following for the given rational function. g(x) = $$ \frac{2x^2 - 9x - 5}{x^2 - 3x - 10} $$. a) Identify any vertical asymptotes and the coordinates of any holes in the graph. You will need to factor in order to answer this question. b) Identify the horizontal asymptote in the graph…
Graph the equation $y = 2.5 \csc(2 \pi x)$. Use the blue diamond to shift the graph horizontally and vertically, the yellow triangle to stretch the graph vertically, and the red circle to stretch the graph horizontally. Reset
Given the graph of the rational function below, evaluate each of the following limits. a) $$\lim_{x \to 2^+} f(x) =$$ b) $$\lim_{x \to 2^-} f(x) =$$
Question 1 (1 point) Convert the angle 176 degrees 24' 28" to radians. Please approximate your answer and round to three decimal places. radians Blank 1: Question 2 (1 point) Convert the angle 3.92 radians to degrees. Approximate your answer to three decimal places. degrees Blank 1:
Find the height of a pine tree that casts a 93-foot shadow on the ground if the angle of elevation of the sun is 26°35′. The height of the pine tree is approximately ft. (Round to the nearest integer as needed.)
Write the following equation in the standard form for an ellipse. 9y^2 + x^2 + 18y - 10x = 2
× Question 4 Score on last try: 0 of 3 pts. See Details for more. Get a similar question You can retry this question below 0/3 pts991 Details In many cases the Law of Sines works perfectly well and returns the correct missing values in a non-right triangle. However, in some cases the Law of…
The population (in thousands) of people of a city is approximated by the function P(t) = 1400(2)^0.1011t, where t is the number of years since 2010. a. Find the population of this group in 2018. o. Predict the population in 2028. a. The population of this group in 2018 is. (Round to the nearest…
Write an equation of the ellipse with the given characteristics and center at (0,0). Vertex: (3,0) Co-Vertex: (0, 2) Equation:
Click here to watch the video, Use $f(x)$ and $g(x)$ to find each composition. Identify its domain. (Use a calculator if necessary to find the domain.) Complete parts (a) through (c) below. $f(x)=x^2$, $g(x)=\sqrt{25-x}$ (a) $(f \circ g)(x)=\boxed{}$ (Simplify your answer)
: Radical Expressions Question 8, R.7.55 HW Score: 23.86%, Points: 0 of 1 Simplify the expression. Assume that all variables are positive and write your answer in radical notation. √2 ⋅ ³√2
5. And one more thing, if that's okay. The professor keeps taking about converting forms, and just can't remember how to do that either! I remember that maybe exponentials can be written as logs and logs can be written as exponentials, but I don't remember how. Can you show me how to convert…
Limits of the form $$\lim_{h \to 0} \frac{f(x + h) - f(x)}{h}$$ occur frequently in calculus. Evaluate this limit for the given value of x and function f. $$f(x) = x^2, x = -9$$
2. Given $y = sec(2x - \frac{\pi}{2})$ a. Determine the Period and explain how you came about your answer. b. Is there a Phase Shift? If so, what is it? Discuss how you determined your answer. c. Determine the Asymptotes (if they exist) and explain how you arrived at your answer.
Aaron, a cross-country runner, trains all year round. He finds that the slippery road conditions in the winter cause him to slow down by 2 km/h, so that it takes him 2 hours longer to run to a 48 km course. Choose the correct expression for Aaron's time in the winter.
Use properties of exponents to determine which functions (if any) are the same. f(x) = 4^x + 12 g(x) = 2^(2x) + 5 h(x) = 32(4^x) O f(x) = g(x) O f(x) = h(x) O g(x) = h(x) All three functions are equal. None of the functions are equal.
Given the parametrically defined relation below, find the ordered pair (x, y) when t = 3. x = 3t + cos(πt) y = t² - sin (π/2 t)
Determine the equation of the vertical line through the point (-4, -7). Write your answer as an equation using the variables x and y. The equation of the line is:
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