The acceleration of an object (in m/s2) is given by the function a(t) = 5 sin(t). The initial velocity of the object is v(0) = 4 m/s. Round your answers to four decimal places. a) Find an equation v(t) for the object velocity. v(t) = b) Find the object's displacement (in meters) from time 0 to time 3. meters c) Find the total distance traveled by the object from time 0 to time 3. > Next Question meters

Q: A tank half-filled with water is in the form of a rectangular parallel piped 5ft deep, 15 ft wide…

A: Answer is c

Q: Find the general antiderivative of f(x) = = + C -28²³-03-2/3 + √²

A:

Q: S dx 3 cos x-2 sinx+3

A:

Q: d. y = ار نے

A:

Q: 60° IIPII=23 Q Find the EXACT components of the vector above using the angle shown. P Check Answer…

A:

Q: When completing the square, a quadratic trinomial is turned into which one of the following? A…

A: Given.

Q: Find a vector with initial point (-4,-2, 1) and terminal point (-12, 5, -8). Then find a unit vector…

A: Given problem:- Find a vector v→with initial point -4,-2,1 and terminal point -12,5,-8.Then find a…

Q: Find the partial sum S, of the geometric sequence that satisfies the given conditions. 2 a=²₁r = ₁ n…

A: Please see the below picture for detailed solution.

Q: An investor has $10000 to invest in either a bond that matures in 5 years or a business that will…

A:

Q: Evaluate the following indefinite integral. 1 √2 + 3x² Note: Don't forget your C! And be sure to use…

A:

Q: Find the cross product u x 7 where u = 51 -3j+k and = (-1, -3,2). uxv=

A: To find the cross product u→×v→ where u→=5i-3j+k and v→=-1, -3, 2.

Q: Find the domain and range for the function f(x) = LO T 5 3x 1- e

A: Find the domain and range of the function fx=51-e3x

Q: Consider the function f(t) = 10 sec² (t) - 3t³. Let F(t) be the antiderivative of f(t) with F(0)…

A:

Q: Find 2 -1 (3x³ + 7x¹) dx

A: Here we have to solve definite integral

Q: 4. If ricost cosh t+j sint sinh t, where i and j are constant orthogonal vectors prove that (a)…

A: Given r = i cost cosht + j sint sinht

Q: Q3. Find the distance between the points AB and BC where A is (2,1,0), B is (-1,3,1) and C is (-1,…

A: The points A2,1,0, B-1,3,1 and C-1,0,1 we have to find the distance between the points AB and BC…

Q: Find foda + C

A:

Q: 3) Graph and evaluate and evaluate 5 dx -2 7 6 و اس ام اس اب 5 4 3 2 101 -7-6-5-4-3 -2 -1 0 1 2 3 4…

A: Topic = Functions

Q: e cos(x) = 1 + sin(xy) 2 2

A:

Q: Q2. Find the second order partial derivative of x² - y² + 2xz - xy + yz.

A:

Q: Find the area of the sector of a circle with diameter 32 feet and an angle of 45 Round your answer…

A:

Q: For the given function find an equation for the inverse function f-1(x).  f(x)=3x-1

A: To find out the inverse of the function given.

Q: 2. Let f(x, y) = |x − 1| · yś. (a) Compute, if they exist, the partial derivatives få and fy at the…

A:

Q: Find the arc length (s) of the curve (t) 8 = r(t) = (5e³t, 4e³t, 2e³t) for 0 ≤ t ≤ ln(4)

A: The arc length s of a curve r→t = xt, yt, zt for a≤t≤b is given by s = ∫abx't2+y't2+z't2 dt

Q: Evaluate [(e²/² - x)(e²/² + x) dx. Show your work.

A:

Q: Find -(62). Type In(x) for the natural logarithm function. da

A: Topic = Derivative

Q: y (2x + y 2) dx O a. y (2x + y) = Ce - 2(x + y) dy = 0

A: y2x+y-2dx-2(x+y)dy=0 Lets check for exactness.…

Q: Find fxy(x,y) if f(x,y) = (x² + y²) 7. fxy(x,y) = ...

A:

Q: An 8 by 8 checkerboard has alternating black and white squares. How many distinct squares, with…

A: Given: an square box in which 64 square box (black and white)

Q: Let E be the solid below z = 50- x² - y² and above the square [-5, 5] × [-5, 5] Given the solid has…

A: Let's find moment of inertia of E about z axis.

Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

A: We have to find the area between the curves.

Q: Q-3: a) b). Using logarithmic differentiation, find the derivative of -3x√2x-5 (6-5x)4 - 34x = 0.…

A:

Q: 5) Show that to order O(h²), the central difference formula for the partial derivative მ3u(x,t) əx3…

A:

Q: Let f(x) = x^2 - 4x + 1. What is the equation of the tangent line to f(x) at x = 2? Use the limit…

A: Please see the below picture for detailed solution.

Q: 3. Water is leaking from a trough at the rate of 0.8 L/s. The trough has a trapezoidal cross…

A:

Q: Determine the real number a such that u x v and i are orthogonal, where u = 5i + j - 9k and v = 6i -…

A:

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7.

A:

Q: Answer the following True or False. 1 COS T dz = ln(cos z) +C

A: Our Aim is to answer whether the value of integral obtained is true or false.Given integral…

Q: Find a plane through the points (6,-8,5), (5,6,5), (-6,-7,3) Check Answer

A:

Q: Write a limit using summations that would equal 0 tan (2x) dx.

A:

Q: Differentiate the following function. You do not need to simplify the derivative. ƒ'(x) = 5 f(x) =…

A: Derivative of function f(x)=lnx5

Q: Problem 1. You are fencing in an area next to your house so your cats can lounge outside. The cat…

A: We have given the length of material that is avialble for fencing is 27 feet.

Q: A supermarket sells two brands of granola: brand A at $p per pound and brand B at $q per pound. The…

A: We have to find partial derivatives and new values of x and y .

Q: 16

A:

Q: Let à = (-5, 4, Find the projection proja b =< 4) and b = (-4, 0, -1). of b onto a. -

A:

Q: How do I find tangential and normal components of the acceleration, from question 5b

A: Let's find tangential and normal components of acceleration.

Q: The function f is shown below. What is the value of answer in simplest form. -10-9-8 -7 -6 -5 -4 -3…

A: This question is related to definite integration, we will solve it using given information.

Q: Find the future value at 5.25% interest, compounded continuously for 5 years, of the continuous…

A:

Q: Pls answer fast 2+2

A:

Q: A company produces two types of solar panels per year: x thousand of type A and y thousand of type…

A: