Find the position vector for a particle with acceleration, initial velocity, and initial position given below. ä(t) = 3ti + 6 sin(t)j + cos(6t)k v(0) = 2i + 5j + 3k F(0) = 21 – 53 – 5k F(t) i+ Question Help: D Video Add Work

Q: dx Ух — 12

A:

Q: sider the function f(x) 3x on the interval |- 2, 2]. Find the average or mean slope of the ction on…

A: Topic:-  derivatives

Q: II. Use the first fundamental theorem of calculus to find F'(x) .Write your final answer on the box.…

A:

Q: f(x) 7xe-x, y = 0, 0 <x < 1 ketch the region bounded by the graphs of the equations. 3- 2- y 3

A:

Q: Evaluate the improper iterated integral. 9. x2 dy dx 1 + y?

A:

Q: Use the formula K(t) = r(t) × r"(t)|| ||r(t)||* to find k(t). r(t) = 11 cos(t)i+11 sin(t)j + 6tk…

A:

Q: f(x) = (-3x³ + 4) 7, which of the following is f'(x)? f' (x) = 63x² (-3x° + 4)-8 - f' (x) = 63x(-3x…

A: Topic:- derivatives    Using  Derivatives of x^n = nx^(n-1)

Q: d²y of the following equation then simplify whenever possible. 3) Find and dx dx- x = 3em y = 4e-m

A:

Q: se Hooke's Law to determine the work done by the variable force in the spring problem. A force of 9…

A: Given is the question of hooks law.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. p 2…

A: Given problem:-

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

A:

Q: Evaluate Sae 2a (a2 + 9) d. 3c

A:

Q: dz and ду dz Find z = a° In (1+ cy) az dz ду ||

A:

Q: Solve by Gauss-Jordan elimination

A: answer is in next step

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A:

Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

A:

Q: Test the convergence of cach of the following two scrics. n" 2n +3 (1) 2 n! (ii) Зп + 2 n=1 n=1

A:

Q: Sketch the graph of the function f(x) = x³ – 2x² – 5x + 6 using calculus – based analysis. -

A: Given problem:- Sketch the graph of the function f(x) = x3 – 2x2 − 5x + - 6 using calculus - based…

Q: What is the differential equation whose solution represents the family y = Ae3x + Be4x+Cxe4x? O…

A: Given problem:- Find the differential equation whose solution represents the family y=Ae3x +Be-4x…

Q: (y – Jx² + y² )dx -xdy = 0, when x = v3 and y = 1

A:

Q: ne graph of f(x) = (2x + 1)- %3|

A:

Q: 1 Find the length of the curve y (x2 + 2)3/2 from x = 0 to x =9. 3

A:

Q: 2. Show that if x and y are two vectors, then

A: Replace x→ by u→ &amp; y→ by v→     Graphing software do not accept label x, y To show: u - v ≤u±v≤u…

Q: Use logarithmic differentiation to find

A: answer is in next step

Q: Find the area between the loops of the limacon r= 7(1+2 cos 0). Area =

A:

Q: the tunchon: a certain check point is given by 30) 13 VE Find the, çar pesihon, St), af Assame that…

A: In this velocity function is given, so to find the position function we need to integrate the…

Q: sheet of paper for a poster is to be 18 ft2 in area. The margins at the top and bottom are to be 9…

A: Ler the the dimensions of the sheet is  x and y in order to maximize the print area

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A: Given:        ∮C7xydx+4xydy  Where C is the rectangle bounded by x=-1, x=2,y=1 and y=5  The formula…

Q: The marginal cost of producing the xth box of CDs is 90 + x + The total cost to produce 100 boxes is…

A:

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

A:

Q: For the function y=JHx +1 + Find: a) The equation of the tang ent liné at X = 2 b) The equation of…

A: Given,            y=4x+1+2xTo find : a The equation of the tangent line at x=2.                b The…

Q: Evaluate the derivative of the function: x2 f(x) = ( x²+1 8x (æ²+1)° O 8a(a² –1) (2²+1) O 1 4x…

A: Use the chain rule for finding the derivative

Q: Evaluate the line integral / (4x + 8y)d.x + (4x – 9y)dy along the curve C : x = 10 cos t, y = 20…

A:

Q: 1. Suppose you are in charge of payouts for a competitive 10K race. You decide that the top 12…

A: (A) Solution:  In both options total amount is same i.e. $546,000 but option B situation will be…

Q: 1) Find and of the following equation then simplify whenever possible. dx x = 2u* – u3 + u – 11 , y…

A:

Q: Evaluate the integral (8x + 12y)dx + (9x – y)dy along the parabolic (8x +12y)dx + (9x – y)dy along…

A:

Q: Find curl(4= i+ 5x j+ 6y k). curl(4: i+ 5x j + 6y k) = ( i )i + ( i )j +( i

A: We have to find curl

Q: Let a be a real number and f(x, y) = 3ax?y + 6xy3. Let v = 3i – j and let V f(r, y) denote the…

A:

Q: 6) Find the linear approximation to R(t) = VE at t=32 Use the linear approximation to approximate…

A:

Q: Find V. (V x F), if F(x, y, z) = 6e"²i+ 2xe³j – 3ek. - V·(V × F) =

A:

Q: Suppose that the number of employees in a new company is expected to grow, with the number of…

A:

Q: Find the vector v with the given magnitude and the same direction as u. Magnitude Direction ||v|| =…

A:

Q: d d Calculate ri(t) · r2(t)] and r:(t) x r2(t)] first by differentiating dt dt the product directly…

A:

Q: The motion of a point on the circumference of a rolling wheel of radius 3 feet is described by the…

A: Given: r→t = 310t-sin10ti→+31-costj→ We know the following rt  =…

Q: Find the volume oF the solid that results when the region enclosed by the give N curves y=e ソ=o, ×=…

A:

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Here,  a→(t)=3t i^+6 sin(t)j^+cos(2t)k^⇒v→(t)=∫3t i^+6 sin(t)j^+cos(2t)k^dt⇒v→(t)=3t22 i^+6…

Q: Find y': y = /5+ 2x – x² - 1-x O y = V5+2x-a2 1 O y = 2/5+2x-a2 7-2x O y = 2/5+2x-a²2 O y = /2 – 2x

A:

Q: 3 if x 2 the one-sided derivatives of f at x = 2 whether f' (2) exists. If it exists, specify its…

A:

Q: If f(x) = u(x)t(x)w(x), then f'(x)= a) u'(x)t'(x)w'(x) b) u'(x) + t'(x) + w'(x) c) u(x)t'(x)w'(x) +…

A: Solution ) f (x) = u(x) t(x) w(x) To differentiate use product rule  [ Formula d/dx ( f (x) . g(x) )…

Q: Find the extrema for F(x) = x*/x+1 on the interval [-l]

A: