21 A particle travels along a horizontal line according to the function s(t) = 4 - 10t2 + 48t where t>0is measured in seconds and s is measured in feet. On what interval(s) is the particle slowing down? %3D (Enter your answer in interval notation. If entering more than one interval write the intervals as a union.) Provide your answer below:

Q: Use Green's Theorem to calculate (4z? - 3yz)dr + (3zy + Vy? + 6)dy, where Cis the circle (r – 1)2 + ...

A: Greens theorem

Q: a) Using an operator , solve the following differential equations d²y dy 20y = 0 dx dx2

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A: We have to find the form of the complete partial fraction of the function

Q: 3. Find all values of a, b, c so that the following function is continuous for all values of x x-1 s...

A: Please see the below picture for detailed solution. 

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Q: Replace the polar equation r= with an equivalent Cartesian equation. Then identify the graph. sin 0-...

A: r=7sinθ-3cosθ       ------1 x=rcosθ y=rsinθfrom 1 rsinθ-3rcosθ=7y-3x=7y=3x+7  

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Q: Find the tangent plane of the surface z = f(x, y) at (0,0, 0) in which 3y f(2, y) = || cos /3 t dt.

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Q: Given 2 cot- (esc) if – 3 3. a. Determine if f is continuous or discontinuous at r = 0 and at r = 3...

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Q: Express the area of the surface obtained by rotating the curve y=in cse(2x) between x= and x= about ...

A: surface area about y axis S=∫ab2πxds ....(1) where  ds=1+(dydx)2dx

Q: Evaluate the integral. NOTE: Enter the exact answer. cos(2x) da = + C %3D

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Q: Convert the point (-1,-V3) from Cartesian to polar coordinates. A) (-2,) B) (2.). c) (-2, ). D) (2,)...

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Q: Vx+11-4 (b) lim- x- 5 X-5

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Q: Given that f(x) = 7x + 4 and g(x) = 1 – x², calculate %3D - (a) f(9(0))= | (b) g(f(0))=

A: f(x) = 7x +4  g(x) = 1 -x2 f(g(0)) =? g(f(0)) = ? f(g(x)) = f(1-x2) = 7(1-x2) +4 = 7 -7x2 +4 = 11 -7...

Q: The solution to the initial-value problem 4y' = -8y, y(0) = -2 %3D is y = -2e-2x Select one: O True ...

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Q: The solution to the differential equation 2 - y = x cos(3x) is: Select one: x cos(3x) + cx? 3 O 3x s...

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Q: The sum of the series n-16) is: A) 1. B) 2. C) D) E) Diverges.

A: topic - series convergent and divergent

Q: Let a, = and b, n - 5 Calculate the following limit. an lim (Give an exact answer. Use symbolic nota...

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Q: 3 x2 dx 4

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Q: O g(x) = (3t+ 2) dl t %3D

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Q: Answer this question by showing all work and formulas used to solve: 2. a) If f(6) = 3, f'(6) = 6, g...

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Q: Find the distance between the points (distance formula) 1.(3, 2), (4, -3) 2.(-5, 1), (-7, -3)

A: Distance between two points are  √(x1-x2)^2+(y1hy2)^2  

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A: Given that for a certain ice cream company indicates that if the price per cup of ice cream is $50.0...

Q: II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D 5...

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Q: (a) Write one of the four vectors as a linear combination of some or all of the others. (b) Find a l...

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Q: 1. Find the domain of the following functions: х? - 3х-10 а. у- х-5 х+5 b. y=- Vx - 5

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Q: 5. The following data give approximations to the integral M = sin x dx. Jo ()- () N (h) = 1.570796, ...

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Q: Graph the set of points whose polar coordinates satisfy the equation 0 = r20. 5 Choose the graph tha...

A: Given that polar cuve equation θ=π5,r≥0Solution :π5<π4θ<π4r≥0

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A:

Q: Follow the steps to solve the initial value problem: 2ty – 2y = t5, y(1) = -1. a. Identify the integ...

A: Rewrite the differential equation into linear differential equation and then solve it.

Q: Determine whether the series converges, and if so find its sum. Enter the exact answer as an imprope...

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Q: Find the limit by rewriting the fraction first. ху — у — Зх + 3 lim х - 1 (x,y)>(1,4) x+1 ху — у — 3...

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Q: x - 36 lim X6 x+6 (a) Vx +11-4 (b) lim- x-5 (c) lim- X-2 2-x (d) x' +6x +9 lim x+3

A: a) limx→ -6 x2-36x+6 =limx→ -6 (x-6)(x+6)x+6                     ( using factorisation              ...

Q: 4.(a, b), (c, 0) 5.(2a+c, 2d), (2b-c, 2c)

A:

Q: Determine whether the given series is absolutely convergent, conditionally convergent or divergent. ...

A: The given series,       ∑n=1∞-1nn+1n2

Q: Using Figure 4, complete these functions. P(-20, 21) Figure 4 sine = -21/29 20/29 21/29 -20/29

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Q: Question Q is the region bounded by the graph of v(y) = 6y , x = 2, and y = 0. Find the volume of th...

A: Suppose that y=f(x) is a continuous non-negative function on the interval a,b.The Volume of the soli...

Q: Using the definition of derivative, find functions: a) y = xVx -2 .2 (b) y =- (x-1)

A: Given ,f(x)=xx2-2Therefore,f(x+h)=(x+h)(x+h)2-2We know that ,f'(x)=limh→0f(x+h)-f(x)hTherefore,f'(x)...

Q: Check that the point (−1,−1,1) lies on the given surface. Then, viewing the surface as a level surfa...

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Q: Using Figure 1, complete the following function. (-8, - 6) Figure 2 csce = 5/3 5/4 -5/3 -5/4

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Q: x In(2 + x³) dx

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Q: Find the solution of the following Differential Equations 2) y'+2xy = 0

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Q: Define Q as the region that is bounded by the graph of the function g(y) = 2/y+4, the y-axis, y = -3...

A: The volume of the given region, which is rotated about the y-axis, using the disk method is given by...

Q: Use any method to determine whether the series converges or diverges. (k!)° (9k)! O The series diver...

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Q: What is f'(x) given the integral function f(x) = cos Tud u? O f(x) = -2x cos( T) %3D O f(x) = -2x co...

A: The detailed solution is given below Thank you 

Q: Find the distance between the points (distance formula) 3.(-1, 1/2), (3/4, -4) 4.(a, b), (c, 0)

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Q: Write the first five terms of the sequence: ( +o0 S11 In n n=1 Determine whether the sequence conver...

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