A ball is launched into the air. 21 feet away from the launch site is a camera. If the ball is travelling vertically upwards at 13 feet per second, what is the rate of change of the angle of elevation (θ) from the camera to the ball when the ball is 41 feet off the ground? Submit an exact answer in fractional form.

Q: Which is the better base for working with exponents and logs : e or 10? Justify your answer.

A: log with base e is better for working with exponents.

Q: Consider the points A(1, –1, 2), B(2, –3,0), C(-1, –2,0), and D(2, 1, –1). (a) Find the volume of th...

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Q: Find the area of the triangle with vertices P(1, 4, –2), Q(0,0,0) and R(4,5, 1). NOTE: Enter the exa...

A: We can find the area as below.

Q: Find the volume of the following solid. The solid S between the surfaces z= ex-y and z = - 4 ex-Y, w...

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Q: 3. Evaluate each definite integral by using geometric formulas. (a) 14.x – 12| dr dr (b)

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Q: CSC r+ sec x Express in terms of sine and cosine. cot x + tanr

A: We know that  cscx=1sinx  , secx=1cosx  , cotx=cosxsinx  and tanx=sinxcosxSubsituting in cscx+secxco...

Q: Find all values of x and y such that f(x, y) = 0 and f(x, y) = 0 simultaneously. f(x, y) = x² + 4xy ...

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Q: |. Find the Taylor series of In(x) about a for a > 0. Your answer should be in sigma notation. You m...

A: Taylor's Series of f(x) about 'a' :     f(x) ≈ f(a) +f'(a)(x-a)+f''(a)2!(x-a)2 +f'''(a)3!(x-a)3+... ...

Q: P23.2. The population of Canada, as determined by the Canadian census, was as follows: year 2001 200...

A: t=year 2001 , X starts from 0.   X Y XY X2 Y2   0 30 0 0 900   5 31.6 158 25 998.56   10 33...

Q: The temperature at a point (x, y) is T(x, y), measured in degrees Celsius. A bug crawls so that its ...

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Q: Write an equation for the polynomial graphed below -5 -4 -3 -2- -3+ -4 -5+ y(x) = %3D

A: We see that the curve passing through the points 1, 4, -4.  

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

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Q: wo-period OLĠ model. Fc pose that preferences 3 In c2(t + 1) (2)

A: OLG MODEL : Overlapping Generations Model- 1) Time is discrete and runs to infinity. 2) Each individ...

Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

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Q: 11. S 8a'da = %3D

A: This is a problem related to integration. Based on the general formula of integration we will solve ...

Q: Find the indefinite integral. (Use C for the constant of integration.) sin3 40 v cos 40 d0

A: We can find the integral as below.

Q: dy +xy 1-y, y(1) = 0 dx

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Q: Find the volume of the following solid. The solid above the region R= {(x,y): 0<x<2, 0sy<4-x} and be...

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Q: Assume that x = x(t) and y = y(t). Find dt using the following information. dy x² +y? = 2.92; - 2 wh...

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Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid generate...

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Q: Find dy if y2T+4+ In(x+2)= xy3 dx y - 2Vx+4 2yvx+4 -3xy 2x+4 2yvx+ 4 y -2 2yvx +4 - 3xy- Vx +4 2yvx ...

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Q: Find the area of the region bounded by the curves, x = -6, x = 6, the x – axis and the parabola x2 –...

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Q: The density of oil in a circular oil slick on the surface of the ocean at a distance of r meters fro...

A: Mass

Q: (1) As x→ t0, the end behavior of the polynomial p(x) = 3x°(1 – 2x + x°) can be resembled as (A) p(x...

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Q: Biologists stocked a lake with 250 fish and estimated the carrying capacity (maximum pop- ulation fo...

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Q: Q3 : Evaluate the following integral. X4V9-x2

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j ...

A: I am attaching image so that you understand each and every step.

Q: . lim,0+ (1 + 2x)In(2z)

A: Solution :1∞  formif limx→0fx=1 limx→0gx=∞if the form limx→0 fxgx then elimx→0 fx-1gx

Q: 5. Which of the has a domain of (-o, +c0)? a. f(x) = x b. f(x) = x2 c. f(x) = x d. f(x) = x*

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Q: 5. S V16dy = 6. J 2 V8dc 7. J 3 27dx

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Q: Ssin (y)cos(y)/3+ sin° (y) + 5e" dy

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Q: 10 Which of the following is the derivative of g (x) = x2 -10 g (a) = x3 O g (2) = -10 d (x) -10 O g...

A: Question is solved.

Q: (2+x, x<2 15. Given the function g(x) = l6-x, x22 Find g(2). a 1 b. 2 C. 3 d. 4 16. (Refer to item #...

A: We have to choose correct option

Q: 3. For what value of x will the slope of the tangent to f(x) = 3*e* +5x +17 be equal to 5?

A: We can solve the given question as follows:

Q: Find the most general antiderivative or indefinite integral. 8/x dx

A: We have to find the indefinite integral.

Q: A rectangular box with a volume of 931 ft° is to be constructed with a square base and top. The cost...

A: Solution is given below:

Q: (2х + Зу — 5)dx + (3x — у — 2)dy — 0

A:

Q: Example 7: Determine whether the planes x- 3y + 6z = 4 and 5x+ y – z = 4 are orthogonal, parallel, o...

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Q: Express the following number as a reduced ratio of integers. 0.32 0.32323232...

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Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by par...

A: Given problem:- ∫ 3 tan-1(x) dx 

Q: Find the domain and range of the function graphed below. 5- 2 -5 4 -3 -2 I234 5 2 -4 -5- Domain: Ran...

A: From the given graph we can see that the given function exists for x belongs to [-1 , 2)  

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A:

Q: The first derivative of a continuous function y = f(x) is given. Find y" and then sketch the general...

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Q: Homing pigeonis avoid flying Suppose a homing pigeon is ed on an island at point C, which is 5 mi di...

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from ...

A: We know that vector equation of line passing through two points r¯=a¯+λ(b-a) Here a and b are positi...

Q: V -/1+/x - 1 1+/x +1 · IVx tan 2 tan dx 1+/x +1+//1+/x -1 -1

A:

Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

A: v=19, -12oppositely directed to v,(The angle between vectors with opposite direction is 180° and the...

Q: List the first four terms of each sequence. An = 2n + 6: 8 10 12 14 ,.... bn = (4)" : 4 16 64 256 ,....

A: We can find first four term of the given sequences . Put n=1,2 ,3 ,4 and find four terms of the sequ...

Q: Use the method of variation of parameters to find a particular solution of the following differentia...

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Q: dy sin: 8. x +2y = dx y(2) = 1

A: