The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object. r(t) = (3t, 4 cos(t), 4 sin(t)) v(t) (No Response) s(t) = (No Response) a(t) = (No Response)

Q: 1. Suppose that C is the top-half of the circle (x-a)² + y² = a², (a > 0) oriented in the…

A: Please see the below picture for detailed solution.

Q: At what point (x, y) is the function f(x) = 6x - 6 closest to the origin? Enter an exact answer.…

A:

Q: Given that the graph of f passes through the point (1,9) and that the slope of its tangent line at…

A: Slope of the  tangent line to the  curve  y = f(x) is f '(x)

Q: It f(x) = x² - 4x - 3, find f (x + 3). 10. If g(x) = 2x³ + 4x − 5, find g(x − m)

A: 9) The given function is: f(x)=x2-4x-3

Q: 5: Find the volume of the solid which is generated by rotating the region bounded by y=√x, y=x-2 and…

A:

Q: Complete the table, for the following investments, which shows the performance (interest and…

A:

Q: Exercises L- If H B =). 33" 3 14. BB+A-SI-D E A-

A: The answer is given below:

Q: Suppose the position function of a particle is given by r(t)=(√3 sin(t), t-2, √3 cos(t)). If the…

A:

Q: Find a formula for the inverse of the function. Select the correct answer. Or'(x)-(³²) ¹² 1/3 Of¹(x)…

A: Given problem :- fx=2-3x3 Find:- f-1x

Q: 1. 3 0 S 0-2 (x²y - 2xy)dydx

A:

Q: Find the mass and the center of mass of the lamina with density 8(x, y) = √y x² +1 the rectangular…

A: We have the following formulas(i)  Mass of a region m=∬δ(x,y)dA, where δ(x,y) is the density and dA…

Q: 4. √ (4x²–5x+6) dx

A:

Q: 1. (1) E (14) (1) Choose the correct option (Multiple Choice Questions): Which of the following is a…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: Find the arc length of the graph of the function over the given interval. y = In x, [1, 8]

A: Given that  function  y=fx=lnx,1,8The formula for arc length of a curve y=fx over thhe interval a,b…

Q: Show all your work to receive full credit. Write your answers as complete sentences. 1. Integrate…

A: Topic = Integration

Q: Say a candidate is running for mayor of a city. During the incumbent mayor's first year in office,…

A: Given that Say a candidate is running for mayor of a city. During the incumbent mayor's first year…

Q: 2A)Matrix A = 12 2₁ B = B = [₁ ²2₁ find AB. -21

A: Note:- Please repost part B because unable to understand  right side of differential equation…

Q: 2) Consider the DE: y" + 25y = 0 A) Verify that y = C₁ cos 5x + c₂ sin 5x is a solution of the given…

A:

Q: A department of roads and highways is doing a drive, a driver's rest area on the side of a highway.…

A: Ans=200 m  For detail...go through the solution...I have done solution in detail

Q: Use the remainder theorem to evaluate the polynomial for the given values of x. g(x) =…

A: According to our guidelines, we can answer only one question or three subparts of a question. Other…

Q: Use logarithmic differentiation to find the derivative of the function f(x) = (sin 7x)/x c) Coal is…

A:

Q: Find the distance between the pair of points (5.5,7.2) and (-0.5,4.2). If necessary, express the…

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

Q: Solve the following initial value problem. Provide your answer below: f(x) = ƒ"(x) = 36x² + 6x – 10,…

A:

Q: F(t) = 4(t+1)²

A: we have f(t) =4(t+1)2 =4(t2+2t+1)

Q: Find the arc length of the graph of the function over the given interval. y = In x, [1, 8]

A: We have to solve given Questions.

Q: Set-up and evaluate the triple integral for the mass of the box 1≤x≤2, 1≤ y ≤16, 0≤z≤ with density…

A:

Q: Evaluate the integral. Select the correct answer. 6 6 x In (19x) - 12/15 x + C none of these 16 x In…

A:

Q: If f '(x) = 0 and f"(x) <0, then the point (x, f(x)) is a local minimum. a) always b) sometimes c)…

A: Please note that following the guidelines only one question is to solved.

Q: S dx x² √√9-x² 2

A:

Q: Evaluate: AT -dx B. 이집 는 d 를

A: Evaluate the integral ∫0πxsinx1+cos2xdx

Q: 7. Which of the following statements is true? The volume of the solid formed by rotating the region…

A: Volume

Q: Evaluate xdx A√²+x+1-³x+2+ √(x + 2)² +²1+C B. √² + x + 1 - ² 1 x + ³ + √(x + 2)² + ² 1 + C…

A:

Q: Given f(x) = 3x³ +22x² - Part: 0 / 2 Part 1 of 2 -21x-40, answer the following. Factor f(x), given…

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0,4)…

A:

Q: Find the curvature K of the curve, where s is the arc length parameter. r(s) = (1 + s)i + j K = (No…

A: The given problem is solved below in detail.

Q: The volume of the solid obtained by rotating the region enclosed by 1 x² y = with limits of…

A: We have to find the volume of the solid.

Q: QUESTION 1 Let I = fxe³x. To solve I, we need to apply O Integration by substitution O Integration…

A: The answer is given below.

Q: P 3. Evaluate the integral fx cos(3x²) dx as an infinite series. (You do not need to find the radius…

A:

Q: Find the derivative of the function g(x)=√t-sin (t) dt . Iv

A:

Q: Use the divergence of the vector field to compute F(x, y) = (tan-1 (2²)) i + (xy-2 +82²) j 4 fo…

A:

Q: Given the vector field F(x,y,z)= , find the divergence and the curl of F.

A:

Q: Find the lower sum for f(x) = x + 2 on the interval [0, 5] using 5 rectangles. 10 Submit your answer…

A: I appended the formula used in the solution part of the question

Q: 3 여 x 3

A: Given: 121-111231X=0-21

Q: 12. For an object whose velocity in ft/sec is given by v(t) = cos(t), what is its distance, in feet,…

A: Topic = Integration

Q: Find the limit, if it exists. If the limit does not exist, explain why. limx→∞((√x^2+2x) −x) You…

A: Given :limx→∞x2+2x-x

Q: 3. 3 1 S (2x - 4y)dydx 1 -1

A:

Q: Find the following for the given equation. r(t) = e−t, 8t2, 3 tan(t)   (c)  Find r'(t) · r''(t).

A: Find the following for the given equation. r(t) =&lt; e−t, 8t2, 3 tan(t) &gt;   (c)  Find r'(t) ·…

Q: Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 5.4%…

A:

Q: Find the derivative. G(t) = sinh(ln(t))

A: Topic = Derivative

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given: y'+ye3x+7=-2y2