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February 2024
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Precalculus Q&A Archive of February 1, 2024

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February 1 of 2024

A wheel with diameter 34 in. is rotating 19°/sec. Find the linear speed and round to 3 decimal places.

A sector of a circle has a central angle of 135 degrees . Find the area of the sector if the radius of the circle is 11 cm.

Find the length of an arc that subtends a central angle of 238° in a circle of radius 11 cm.

Slope-Intercept Applications $ (y=m x+b) $ 1. A music app charges $ \$ 2 $ to download the app plus $ \$ 1.29 $ per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs. \[ m=1.29 \$ \] \[ y=1.29 .(30)+2 \] \[ y=38.7+2 \] \[ y=40.70 \$ \]

$ \frac{2}{\sqrt{x y}} $

evaluation of water quality of a given place, the water sample was collected and laboratory analysis was made. By which the following constituents were found. Ca = 50 mg/l; Mg = 15 mg/l; Na = 80 mg/l; CO3 = 20 mg/l, and HCO3 = 245 mg/. Determine, following parameters: a.Sodium absorption ratio…

d. Rp $ 4.700 .000,00 $ c. $ \operatorname{Rp} 4.800 .000,00 $ 15. PD ARJUNA mempunyai data per 31 Desember 2016 sebagai berikut: - Pembelian barang dagang Rp $ 120.000 .000,00 $ - Penjualan Rp $ 150.000 .000,00 $ - Persediaan barang dagang per 1 Jan 2016 Rp 30.000.0000,00 - Beban…

(1) Potatoes are dried from $ 14 \% $ total solid to $ 93 \% $ total so Did What is the product yield from each $ 1000 \mathrm{~kg} $ of raw potatos assuming that $ 8 \% $ weight of the original potatoe is lost in peating, assume that yourbasis is $ 1000 \mathrm{~kg} $.

A cannonball is launched at an angle of 75° with the ground at a speed of 40 meters per second. Find the magnitudes of the vertical and horizontal components of its velocity.

19. A pontoon boat is traveling 25 miles per hour in the direction of S 65° W. If it hits a current traveling at 6 miles per hour in the N 15° W direction, find the resultant magnitude and direction of the boat. A. 22.73 mph; N 80.32° W B. 21.45 mph; S 73.77° W C. 23.09 mph; N 72.48° W D. 24.68…

19. A pontoon boat is traveling 25 miles per hour in the direction of S 65° W. If it hits a current traveling at 6 miles per hour in the N 15° W direction, find the resultant magnitude and direction of the boat.

1. Complete the suggested table of valu a. $ y=x+3 $ b. $ y= $ \begin{tabular}{|c|c|} \hline$ x $ & $ y $ \\ \hline 2 & \\ \hline 1 & \\ \hline 0 & \\ \hline-1 & \\ \hline-2 & \\ \hline \end{tabular}

$ \begin{array}{l}\frac{12 n^{5}}{36 n} \\ \frac{a^{3} b^{5}}{a b^{2}} \\ \frac{-21 w^{5} x^{2}}{7 w^{4} x^{6}} \\ \left(\frac{4 p^{7}}{7 r^{2}}\right)^{2} \\ 8^{-2} \\ \left(\frac{a}{11}\right)^{4} \\ k\left(1 k^{4}\right)\left(k^{-6}\right)\end{array} $

3. Find the curl and divergence for the following vector field \[ \vec{F}(x, y, z)=\frac{3 y}{z} \hat{\imath}+\sqrt{x z} \hat{\jmath}+x \cos y \hat{k} \]

In $ \triangle A B C, A P \perp B C, B Q \perp A C B-P-C, A- $ $ \mathrm{Q}-\mathrm{C} $ then prove that, $ \triangle \mathrm{CPA} \sim \triangle \mathrm{CQB} $. If $ A P=7, B Q=8, B C=12 $ then Find $ A C $.

12. A velocity field is given as \[ u=\operatorname{ar} y+t^{2}, v=n+f^{2} \text { and } w=1-s t^{2} \] Determine local, convective asel total accelerations of a fisid particle at the spatial position $ (3,1,2,10) $.

Simplificar: \[ (\sqrt[4]{x}+1)(\sqrt[4]{x}-1)(x+1)(\sqrt{x}+1)\left(x^{4}+x^{2}+1\right) \]

Example 2 Compute curl $ \vec{F} $ for \[ \vec{F}(x, y, z)=x^{2} y \hat{\imath}+(3 x-y z) \hat{\jmath}+z^{3} \hat{k} \] Solution:

The internal diameter of a swimming pool is $ 42 \mathrm{~m} $. The depth is $ 5 \mathrm{~m} $. Calculate the cost of tiles using round the wall at the rate of Rs 100 per $ \mathrm{m}^{2} $.

Find the quotient and remainder using long division for (2x^2-6x-4)/(x-4) The quotient is The remainder is

Fig. 4.27

19. A pontoon boat is traveling 25 miles per hour in the direction of S 65° W. If it hits a current traveling at 6 miles per hour in the N 15° W direction, find the resultant magnitude and direction of the boat. A. 22.73 mph; N 80.32° W B. 21.45 mph; S 73.77° W C. 23.09 mph; N 72.48° W D. 24.68…

27. Write p as the sum of two orthogonal vectors, one of which is the projection of p onto q. p = <-7, -6>; q = <4, 2> A. p = <-, -> + <-, -> B. p = <, -> + <-, -> C. p = <, > + <-, -> D. p = <, -> + <-, -> 28. A 525-pound piano is sitting on a loading dock with a 20° incline. What amount of…

25. Find the projection of c onto d: c = <-6, -1>; d = <-2, 8> 26. Find the projection of u onto v: u = -8i - j; v = 4i + 4j

15. Write the vector below in trigonometric form. m = -10i + 10j A. m = 4?5?cos 135°, sin 135°? B. m = 4?5?cos 315°, sin 315°? C. m = 10?2?cos 135°, sin 135°? D. m = 10?2?cos 315°, sin 315°? 17. A bird is flying at a true bearing of 75° at a speed of 40 miles per hour. Write the velocity of the…

13. Given v = <1, -7>, find a unit vector u in the same direction as v. A. <u221a2/17, -7u221a2/17> C. <u221a7/10, -2u221a7/10> B. <u221a7/17, -2u221a7/17> D. <u221a2/10, -7u221a2/10>

19. Calculate interest on Capital and on Current Accounts @ $ 5 \% $ p.a. from the following Balance Sheet as at 31st March, 2023 of Anu and Bobby: BALANCE SHEET as at 31st March, 2023 \begin{tabular}{lr|r|l|r} \hline \multicolumn{6}{c}{ BALANCE SHEET as at 31st March, 2023 } \\ \hline…

1. Describe the mathematical statements in each set. 2. Differentiate $ 5 x-1 $ from $ y=5 x-1 $. How about $ 5 y-10 $ and $ 5 y-10=2 x $ ? 3. Differentiate mathematical expressions from mathematical equations. 4. Which of the given sets is the set of mathematical equations? How about…

Suppose there is a point $ (2,-5,7) $ on the surface $ z=f(x, y) $ of an unknown differentiable function $ f $ where $ f_{x}(2,-5)=0.5 $ and $ f_{y}(2,-5)=-6 $ . Find the equation for the tangent plane to the surface at the given point. \[ z= \]

BALANCING Three ropes are tied to a small metal ring. At the end of each rope, three engine crew are pulling, each trying to move the ring in their direction. If we look down from above, the forces and directions they are applying are shown on the image. Find the net force on the ring due to…

d) $ 12 \mathrm{~km} $

5. Experiment: Record the number of hours one watehes IV from $ 7 \mathrm{pm} $ to $ 11 \mathrm{pm} $ for the past trve niphts, Random Variable: The number of hours spent watehing TV from 7 pm to $ 1.1 \mathrm{pm} $

5. Experiment: Record the number of hours one watches TV from $ 7 \mathrm{pm} $ to $ 11 \mathrm{pm} $ for the past five nights.; Random Variable: The number of hours spent watching TV from $ 7 \mathrm{pm} $ to $ 11 \mathrm{pm} $

of the egg in grams 5. Experiment: Record the mumber of hours one watches TV from $ 7 \mathrm{pm} $ to $ 11 \mathrm{pm} $ for the past five nights, Random Variable: The number of hours spent watching TV from $ 7 \mathrm{pm} $ to $ 11 \mathrm{pm} $

If $ x=25 $ and $ y=-2 $, what is $ \frac{\sqrt[y]{x^{y}} x^{3 / 2}}{\sqrt{x}} ? $

Home Dashboard My courses Time left 0.21:54 Find $ \frac{d y}{d x} $ by using implicit differentiation for the function $ 3 x+2 y=\sin y $.

Time left 0:23:12 Given $ z=3 x^{2} y-4 x y, x=2 t $ and $ y=2 t^{2} $. Use the Chain Rule to find $ \frac{d z}{d t} $.

6. Find the $ 30^{\text {th }} $ derivative of $ y $ if $ y=x^{50} $

QUESTION ONE Eagle, Heron \& Sparrow On 1 October 2016 Eagle plc acquired, for Tzs 316,000,000; 80,000 Tzs 1,000 ordinary shares in Heron Ltd. The profit and loss reserves at the date of acquisition totalled Tzs $ 250,000,000 $. On 30 September 2010 Eagle plc acquired, for Tzs 47,000,000;…

1. $ 24: 56=3 $ 2. $ 44: 20= $ $ -: 5 $

9. An antique clock has an hour hand and minute hand 6 inches and 9 inches long. fast is the tip of the hands separating/approaching at 4 o'clock?

12. Each of two sides of a triangle are increasing at the rate of $ 1 / 2 $ foot per second, and the included angle is decreasing $ 2^{\circ} $ per second. Find the rate of change of the area when the sides and included angle are respectively 5 feet, 8 feet, and $ 60^{\circ} $.

Find the partial derivative of $ Z $ with respect to $ x $ and $ y $ 14. $ Z $ \[ \begin{array}{c} Z=\frac{x^{2}-y^{2}}{x y} \\ Z x= \\ Z y= \end{array} \]

9. An antique clock has an hour hand and minute hand 6 inches and 9 inches long. How fast is the tip of the hands separating/approaching at $ 40^{\prime} $ clock?

Exercises 1. Mark on the Argand diagram, the radius vectors corresponding to d) $ 3-4 i $ a) $ 1+1 $ b) $ -3+2 i $ c) $ -3-2 i $ p) $ \cos 60^{\circ}+i \sin 60^{\circ} $ Write down the moduli of these complex numbers and give the principal values of th arguments.

$ \frac{g(x)}{r(x)}=\frac{x^{2}-9}{x-3} $

a.) reflected over the $ y $-axis and vertically shifted up 2 amits. $ y=\sqrt{(5)}+2 $ b.) reflocted over the $ x $-axis and horizontally shifled right 7 units. $ y=-\sqrt{(x-7)} $ 2. Complete the table assuming its displaying the entire domain of the function, /. Place a diagonal line…

Can you find a rational function f(x)=P(x)/Q(x), where P(x) is a polynomial of degree 1, Q(x) is a polynomial of degree 2, such that the domain of f(x) contains all real numbers.

Consider the function f(x)= 5x+7 and g(x) = square root x+3 Give the domain of f o g (x) g o f(x) Give the domain of g o f(x)

Q. 20 If $ A $ be a finite set having $ n $ elements and $ P(A) $ is its power set, then total number of subsets of $ P(P(A) $ ) is: (1) $ 2^{n} $ (2) $ 4^{n} $ (3) $ 2^{2^{n}} $ (4) $ 2^{2 n} $

Given $ z=5+3 i $

$ f(x)=-x^{2}+7 $

28. $ x^{2}+7 x y+6 y^{2} $

Find the volume $ V $ of the solid obtained by rotating the region bounded by the given curves about the specified line. \[ y=x^{2}, x=y^{2} ; \quad \text { about } y=1 \] \[ V= \] Sketch the region.

,Find all zeros of the function f(x)=12 x^3-23 x^2-3 x+2 Enter the zeros separated by commas.

Find all zeros of the function f(x)=12 x^3+7 x^2-14 x-5 Enter the zeros separated by commas.

Tutorial Exercise Find the volume $ V $ of the solid obtained by rotating the region bounded by the given curves about the specified line. $ y=6 x^{2}, \quad y=6 x, \quad x \geq 0 ; $ about the $ x $-axis Step 1

EXAMPLE 1. Evaluate the integral \[ \iint_{R} \cos \left(\frac{x-y}{x+y}\right) d x d y \] where $ R $ is the triangular region with vertices $ (0,0),(1,0),(0,1) $.

Find the volume $ V $ of the solid obtained by rotating the region bounded by the given curves about the specified line. \[ 2 x=y^{2}, x=0, y=5 ; \text { about the } y \text {-axis } \] \[ v= \] Sketch the region.

Find the volume $ \mathrm{V} $ of the solid obtained by rotating the region bounded by the given curve.. Find the volume $ \mathrm{V} $ of the solid obtained by rotating the region bounded by the given curves about the specified line. \[ \begin{array}{c} y=6 x 2, \quad y=6 x, \\ x \geqslant…

$ 3 6 \longdiv { 6 0 0 } $

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Consider the parabola given by the equation: f(x) =-4 x^2 -14 x -9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas: …

A wheel with diameter 34 in. is rotating 19°/sec. Find the linear speed and round to 3 decimal places.

A sector of a circle has a central angle of 135 degrees . Find the area of the sector if the radius of the circle is 11 cm.

Find the length of an arc that subtends a central angle of 238° in a circle of radius 11 cm.

A cannonball is launched at an angle of 75° with the ground at a speed of 40 meters per second. Find the magnitudes of the vertical and horizontal components of its velocity.

19. A pontoon boat is traveling 25 miles per hour in the direction of S 65° W. If it hits a current traveling at 6 miles per hour in the N 15° W direction, find the resultant magnitude and direction of the boat. A. 22.73 mph; N 80.32° W B. 21.45 mph; S 73.77° W C. 23.09 mph; N 72.48° W D. 24.68…

19. A pontoon boat is traveling 25 miles per hour in the direction of S 65° W. If it hits a current traveling at 6 miles per hour in the N 15° W direction, find the resultant magnitude and direction of the boat.

Find the quotient and remainder using long division for (2x^2-6x-4)/(x-4) The quotient is The remainder is

19. A pontoon boat is traveling 25 miles per hour in the direction of S 65° W. If it hits a current traveling at 6 miles per hour in the N 15° W direction, find the resultant magnitude and direction of the boat. A. 22.73 mph; N 80.32° W B. 21.45 mph; S 73.77° W C. 23.09 mph; N 72.48° W D. 24.68…

27. Write p as the sum of two orthogonal vectors, one of which is the projection of p onto q. p = <-7, -6>; q = <4, 2> A. p = <-, -> + <-, -> B. p = <, -> + <-, -> C. p = <, > + <-, -> D. p = <, -> + <-, -> 28. A 525-pound piano is sitting on a loading dock with a 20° incline. What amount of…

25. Find the projection of c onto d: c = <-6, -1>; d = <-2, 8> 26. Find the projection of u onto v: u = -8i - j; v = 4i + 4j

15. Write the vector below in trigonometric form. m = -10i + 10j A. m = 4?5?cos 135°, sin 135°? B. m = 4?5?cos 315°, sin 315°? C. m = 10?2?cos 135°, sin 135°? D. m = 10?2?cos 315°, sin 315°? 17. A bird is flying at a true bearing of 75° at a speed of 40 miles per hour. Write the velocity of the…

13. Given v = <1, -7>, find a unit vector u in the same direction as v. A. <u221a2/17, -7u221a2/17> C. <u221a7/10, -2u221a7/10> B. <u221a7/17, -2u221a7/17> D. <u221a2/10, -7u221a2/10>

Can you find a rational function f(x)=P(x)/Q(x), where P(x) is a polynomial of degree 1, Q(x) is a polynomial of degree 2, such that the domain of f(x) contains all real numbers.

Consider the function f(x)= 5x+7 and g(x) = square root x+3 Give the domain of f o g (x) g o f(x) Give the domain of g o f(x)

,Find all zeros of the function f(x)=12 x^3-23 x^2-3 x+2 Enter the zeros separated by commas.

Find all zeros of the function f(x)=12 x^3+7 x^2-14 x-5 Enter the zeros separated by commas.

help fast

help fast!

Consider the parabola given by the equation: f(x) =-4 x^2 -14 x -9 Find the following for this parabola: A) The vertex: B) The vertical intercept is the point C) Find the coordinates of the two x intercepts of the parabola and write them as a list, separated by commas: …