Week 7 Question 1 A particle starts moving at time t = 0 and follows the path defined by x = sin(1-t), y = cos(1-t), with x and y in metres. What is the total distance in %3D metres that the particle has moved after Tseconds? а. Т b. There is not enough information to solve the problem. С. 1/T d. 1-T e. (1 - T)2

Q: Question 4 Calculate the length of the curve y = (z + 2)3/2 on the interval (-2, 1]: A) The arc…

A:

Q: Question 6 4 pts For which x-value(s) is the tangent line to the curve y=tan x parallel to the line…

A:

Q: 4. Find the arc length of function y = x2+ x- 2, -2 SXS1

A: Given: y=f(x)=x2+x-2  and -2≤x≤1 We have to find the arc length of the functionf(x).

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: A 1.5 diameter bicycle wheel moving at a constant rate takes 3 seconds to make one revolution.…

A:

Q: Find the length of the curve 7(t) = (4 cos(3t), 4 sin(3t), 4t) for – 4 <t < 2 Give your answer to…

A:

Q: 2:(b) Find the exact arc length of the curve x=e"(sint+ cost), y=e" (sint – cost) over the interval…

A: Given

Q: The curve to the left (red) is approximated with little segments. Each segment makes a triangle [1].…

A: The given function is: y=3x32-1 To find the arc length of the curve.

Q: Let C be the graph of the equation In(3y – 2e") = sinh“(Tx) – tan(y – 1). | dy (a) Find dr (b) Find…

A:

Q: 2. A bead is sliding down the curve given by the equation 2xy? . 1/y = 1. When the bead reaches the…

A: In this question, concept of derivative is used. Derivative The derivative expresses the rate of…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: 15. Suppose you start at the point (0, 0, 3) and move 5 units along the curve x = 3 sin t, y = 4t, z…

A:

Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

A:

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: Suppose the velocity of a particle at time t is given by 3/19 (t+1) + VI+1 7(1) tan(t) %3D 1+ t2

A:

Q: Example 3 Find k (t) for the circular helix K x = a cost, y = a sint, z = ct where a > 0.

A: Curvature k(t) of the vector

Q: An equation of the kangent and hormat. X+sinx líne to khe curve Y =xê

A:

Q: |3| 7/7 2) Find the arc length of y = ln (sec x) from x = 0 to r 11

A:

Q: Question 2 Find an equation for the line tangent to the curve at the point defined by the given…

A:

Q: For problems 3 & 4 find the arc length function for the given vector function. 3. i (t) = (t² , 2r°,…

A:

Q: Starting from the point (0, 4, -2) reparametrize the curve r (t) = (0 – 2t) i + (4 – 2t) j + (-2 +…

A:

Q: 3/ 10. Find the arc length of the curve y = x/2 +4 from x = 4to x = 9.

A:

Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),…

A: We have to find dsdtt0=π4

Q: а. A particle moves along a straight line with an acceleration of a = 4 sin m/s². If the…

A: As you haven't mentioned so I'm doing only part (a).  a) i. The acceleration of the particle after 2…

Q: 4. The position of a particle at time t is given by x(t) = 5+4 sin(t) y(t) = 2 − 4 cos(t) 0<t</ (a)…

A: This is a problem of parametric curve and Integration.

Q: QUESTION 3 3 The arc length of the portion of the curve y=x? with 0SxS4 is о попе OS10.1938 s9.0734…

A:

Q: ( + The oscillation of a spring-mass system is determined by u" + 2u = 0.Which of the following…

A:

Q: At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by M(t) = 3.85(10 – t)² In(t…

A:

Q: QUESTION 3 Suppose you walk along a circle centered at the origin in the >y-plane. Let dx/dt and…

A: The sign of x and y in the first quadrant is + and + respectively. The sign of x and y in the second…

Q: 5. R = (sin 2t , cos 2t , 2t3/2), 0 <t<1.

A:

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

A:

Q: Suppose that a particle moves along a straight line with velocity v(t) = 5 – 4t, where 0<t< 2 (in…

A:

Q: 1 + for 1 < y < 2 17. x = 4 8y2"

A:

Q: 12. Given the acceleration, Initial velocity, and initlal position of a body moving on a coordinate…

A:

Q: Question 5 A planning engineer for a new flour mill must present some estimates to his company…

A:

Q: Table Q3: Interest rate offered by a private bank of over 6 years time 2017 6.50 2019 4.85 2020 Year…

A:

Q: Suppose now that the person begins walking away from the light pole at a constant rate of 0.6 meters…

A: Note: We will only answer up to three sub-parts as the exact one is not specified. Please resubmit…

Q: dx dy = Cos 20. do Given that r= cos 0 ; = - sin 20 and d0 The slope of the tangent line to the…

A: Slopes of tangent is dy/dx . Finding dy/dx at theta = 0.

Q: The arc length of the curve defined by the equations x(t) 10 cos(11t) and y(t) = 3t for 1 <t< 5 is…

A:

Q: dx L% = 1+ dy dy

A: Given equation of curve; y  = (x/2)3/2 , x = 0 to x = 2

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Problem 9. For an external force, F(t) = 28 cos(3t), find the function y(t) that describes the…

A: The auxiliary equation is:  2m2+32=0m2=-16m=±4i

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: The objective of the problem is to find the distance traveled by the particle whose position is…

Q: dR Q5:-The velocity of a particle moving in space is particle position as a function of t, if R= 2i…

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Assume the motion of a mass-spring system with damping is governed by d²x dx +b 1 +16x = 0; x(0)=;,…

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Find the distance traveled by a particle with position (x, y) as t varies in the given time…