A ball is dropped from the top of a lighthouse that is 145 feet above sea level. The height (position) of the ball after t seconds can be found using the function s(t) = -16t2 + 145 Write all answers in decimal form, rounded to three decimal places where appropriate. A. Find the average rate of change of the ball on the interval from 1 to 1.5 seconds. Include the units. B. Find the instantaneous rate of change of the ball 2 seconds after it is dropped. Include the units. C. Find the height of the ball 2 seconds after it is dropped. Include the units. Type your answers into the box below. Be sure to label your answers A, B, and C.

Q: An investment company pays 8% compounded semiannually. You want to have $23,000 in the future.…

A: given future value of investment=23000 $ interest rate=8%=0.08 time= 5 year n=2 (because interest…

Q: Evaluate; a.) Tim 6(x-2) = y(+x) x 3-8

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

Q: (It sinx) dx + #* HN (It sin x) dx

A:

Q: 3. Find the volume generated by revolving the area bounded above by y = ex, bound below by y=and x =…

A: The given curves are y=ex, y=11+x and x=1. From the given curves the bounded region is shown below;…

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, -6) +…

A:

Q: Find the derivate a) F(x) = 5-8x 1+ 2X f'(x)= 6) write all x-values (if any) at which the tangent…

A: (a) f(x)=5-8x1+2xd dx(ab)=bdadx-adbdxb2d dx(xn)=nxn-1

Q: Find dy/dx using the method of logarithmic differentiation In(x) (4+5 2)(a) when y = (4 + dy/dx =

A: y=(4+5x2)lnx  d dx(lnx)=1xd dx(xn)=nxn-1lnxn=nlnx

Q: Solve the following initial value problem using Laplace transform method: y"+3y'+2y=cos 2t y(0)=-1…

A:

Q: Find dy/dx by implicit differentiation and evaluate the derivative at the given point. x³ + y³ = 6xy…

A: given equation is x3 + y3 = 6xy – 1   Rule: ddxxn=n·xn-1

Q: Please show your work (i.e., provide an explanation of your final solution) to receive credit. If…

A:

Q: Find the cross product a x b. a =j + 6k, b = 5i - j + 4k Verify that it is orthogonal to both a and…

A:

Q: -9 dx (3x + 1)² 1

A: Solution: ∫1∞-9(3x+1)2dxTake the constant out=-9×∫1∞1(3x+1)2dx

Q: Part 1 Differentiate f(x) Answer: Part 2 df dx f'(x) = x³ - 4x + 5 x3 If f(x)=√x sinx, find f'(x).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The passcode for this gate is found by determining the domain of the derivative of f(x) and 45 then…

A:

Q: A function f is given, and the indicated transformations are applied to its graph (in the given…

A:

Q: 2 Find the average rate of change of g(x) = 7x² + on the interval [-3,4]

A: (1)  g(x)=7x2+2x4interval is [-3,4]

Q: Consider the function g(t) = = t 7+t²

A:

Q: The First Gate Upon arriving at the first gate, you ask your computer to translate the riddle.…

A:

Q: (x)) = main of f(g(x)). (Enter your answer using interval notation.) (x)) main of g(f(x)). (Enter…

A:

Q: Find fo go h. f(x) X g(x) = x³, h(x) = x + 6

A: Given :

Q: Make a substitution to express the integrand as a rational function and then evaluate the integral.…

A: The given integral ∫cos x7sin2x+8sin xdx. We have to find the solution to the integral. Formulas…

Q: 2. We want to find the dimensions of the rectangle of maximum perimeter that can be inscribed inside…

A:

Q: 0 8x dx x4 -8x² + 32 X

A: To evaluate the following integral. ∫028x dxx4-8x2+32

Q: Consider S, the curve segment of the curve y = sin(x) from x = 0 to x = π. (a) Complete the…

A:

Q: Find the area under one arch of the cycloid. x = 3a(t - sin t), y = 5a(1- cost)

A: The solution is shown below-

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-6, 0,…

A: Concept if a line passing through ( a, b , c ) whose direction ratio are ( l, m, n ) then equation…

Q: Find the derivative

A: Given: h(x)=(x-3)e5x-7x4

Q: Find the intervals on which the function is increasing or decreasing. (X) =283 - 6x2-48×+ 12 List…

A:

Q: Find all critical points of g(t) t = t = = This critical point is ---Select--- (smaller value)…

A:

Q: For each of the following, first write down a formula for the derivative that is asked for, in terms…

A:

Q: A class of fourth graders walks to a park on a field trip. The function y = f(t) graphed below gives…

A: The graph of function y=ft is given as ,

Q: Let f(x) = 8x³ + 1. Find the open intervals on which f is increasing (decreasing). Then determine…

A:

Q: "This passcode consists of the two below limits which include an Remember to type "infinity" for 0,…

A: For x approaching c from the left, x<c  ⇒  x-c5<0The denominator is a negative  approaching…

Q: Which of the following integrals gives the length of a semicircle of radius 5? ܐܢܘ 5 10 -5 25 - x²…

A: We have given the radius of the circle is 5.Equation of circle is x2+y2=25y=25-x2

Q: Solve the separable differential equation dx 1 x² + 25 dt and find the particular solution…

A:

Q: Revenue The following spreadsheet gives annual production costs and profits at Gauss-Jordan…

A: To find the revenue in each sector in each year.

Q: Use Gauss-Jordan row reduction to solve the given system of equations. (If there is no solution,…

A:

Q: Find the critical points for the function f(x,y)=32xy−(x+y)^4 and classify each as a local maximum,…

A: To solve the following problem

Q: Please show your work (i.e., provide an explanation of your final solution) to receive credit. If…

A: B=d dx(f(x)xg(x))d dx(xn)=nxn-1d dx(a.b)=a×dbdx+b×dadxd dx(ab)=b×d dx(a)-a×d dx(b)b2

Q: MATCHING LIST Question 8 Match each system of equation to the description of its solutions. 3x-9y+62…

A:

Q: Please show your work (i.e., provide an explanation of your final solution) to receive credit. If…

A: C=d dx(f(x4)g(x23))d dx(xn)=nxn-1d dx(a.b)=a×dbdx+b×dadx

Q: F) y= 4x³ In(8x)

A: y=4x3ln8xd dx(xn)=nxn-1d dx(lnx)=1xd dx(ab)=b×dadx-a×db dxb2

Q: Evaluate the integral Answer: z³ +66 x² + 6x + 8 S dx.

A: To evaluate the integral

Q: Please answer both. #1-The length of a rectangle is increasing at a rate of 6 cm/s and its width is…

A:

Q: y=x² R y=9

A:

Q: Find the derivative of the function at the given number. f(x) = x² - 9 at 0 f(0) =

A:

Q: Determine the truth set of the predicate: P(x): x € R/ x² − 3x + 1 = 0: 2 Solution: This is {x € R |…

A: Given Predicate: P(x) : x∈R ∧ x2-3x+1=0 To find: The truth set of P(x)

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A: Solving the following problem

Q: Find the linearization of the following function, at theta = pi/4  f(theta) = sin(theta) cos(theta)

A: The given function fθ=sinθ cosθ. We have to find the linearization of the function at θ=π4.

Q: Write out the form of the partial fraction decomposition of the function: - Sº A Determine the…

A: