1. The equation of motion of a particle is s = t3 + 6t2 – 63t + 9, where s is in meters and t is in seconds. Assume t > 0. a. Find the velocity and acceleration as functions of t. Clearly label which function is which. b. Find the acceleration when the velocity is 0. Label answer with units.

Q: Solve the following DE.

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Q: Find an approximation to 25 correct to within 10-4 using the Bisection Algorithm.

A: To find  x = 25(1/3) f(x) = x - 25(1/3) Bisection method First decide x = a and x =b so that f(a)*f(...

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A: Limit of the indeterminate form 1∞ can be solved as:

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A: Population A increases at a constant rate of 4%/yr. Population B increasesat a constant rate of 500 ...

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Q: . Differentiate the function: y = arccos(sin x)

A: Given:       y=arccossinx    

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Q: Please find vertex and write equation in standard form

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Q: 1. Differentiate the function: Y = arccos(sin x)

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A: The parametric equations are x = cos t, y = sin t; and the interval is 0 ≤ t < 2π

Q: Using substitution: Describe why Sæ(5 – 2²) dx ± fu*du where u = 5 – x2.

A: here we replace (5-x^2) with u then differentiate u, let us see

Q: The City Council proposed to utilize a government-owned land with an area of 9,600 square meters. On...

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Q: The City Council proposed to utilize a government-owned land with an area of 21,600 square meters. O...

A: Since you have asked multiple questions in a single request, we would be answering only the first qu...

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A: the given expression is: limx→elnlnxx-e we know that  logaa=1

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A: Given f(x)=x3+2

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A: General form of exponential growth or decay function is fx=abx .....1

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A: From, the graph Local maxima at x= -2, and x=1

Q: Solve and determine what type of DE.

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Q: Solve and determine what type of DE.

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Q: find the second derrivative

A: Consider the following formula: ddxxn=nxn-1 Consider the following function: fx=15x52 Differentiate ...

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A: Prove that, ∫eaxcosbxdx=eax(acosbx+bsinbx)a2+b2+c

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Q: Give a geometric description of the set of points (x, y, z) satisfying the pair of equations z = 0 a...

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Q: Solve the initial value problems for x as a functionof t. (3t4 + 4t2 + 1) dx/dt = 2√3, x(1) = -π√3/4

A:         dxdt(3t4+4t2+1)=23=>dx=23dt3t4+4t2+1=>dx=23dt(t2+1)(3t2+1)=>dx=23 [32(3t2+1)-12(t2+...

Q: What is the equation of Reciprocal Rule?

A: Suppose that f(x) is differentiable at x and fx≠0.

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Q: Use the numeric technique

A: Given Data The function is gx=x-1x2+x-6.   Evaluate the limit of the function gx=x-1x2+x-6 as x→∞, l...

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Q: Find the area bounded by the curve or line: the loop of y2=x4(3-x)

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Q: Find d^2 y/dx^2 in terms of x and y. y8 = x9   d^2 y/dx^2

A: Given expression is, y8=x9

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A: The area of horizontal surface is A=2 m2 And the height is h=4 m