Question

Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for...

Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for the points is given by T(x,y,z)=x^2y(1−z), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t=3.

(Use decimal notation. Give your answer to two decimal places.)

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for...
Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉. If the temperature for the points is given by T(x,y,z)=x^2y(8−z), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t=1. (Use decimal notation. Give your answer to two decimal places.)
Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉r1=〈sin⁡(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉.r2=〈cos⁡(t),1−t,t^3〉. If the temperature for...
Two spacecraft are following paths in space given by r1=〈sin(t),t,t^2〉r1=〈sin⁡(t),t,t^2〉 and r2=〈cos(t),1−t,t^3〉.r2=〈cos⁡(t),1−t,t^3〉. If the temperature for the points is given by T(x,y,z)=x^2y(5−z),T(x,y,z)=x^2y(5−z), use the Chain Rule to determine the rate of change of the difference D in the temperatures the two spacecraft experience at time t=2. (Use decimal notation. Give your answer to two decimal places.)
Consider the parametric equations below. x = t sin(t),    y = t cos(t),    0 ≤ t ≤ π/3...
Consider the parametric equations below. x = t sin(t),    y = t cos(t),    0 ≤ t ≤ π/3 Set up an integral that represents the area of the surface obtained by rotating the given curve about the x-axis. Use your calculator to find the surface area correct to four decimal places
- Given cos(x)=-1/12 with 180°<x<270°. Find cos(x/2) - Given sin(x)= (squareroot 5)/3 where x is an...
- Given cos(x)=-1/12 with 180°<x<270°. Find cos(x/2) - Given sin(x)= (squareroot 5)/3 where x is an acute angle. Find sin(x/2)
1. Graph the curve given in parametric form by x = e t sin(t) and y...
1. Graph the curve given in parametric form by x = e t sin(t) and y = e t cos(t) on the interval 0 ≤ t ≤ π2. 2. Find the length of the curve in the previous problem. 3. In the polar curve defined by r = 1 − sin(θ) find the points where the tangent line is vertical.
7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3...
7. For the parametric curve x(t) = 2 − 5 cos(t), y(t) = 1 + 3 sin(t), t ∈ [0, 2π) Part a: (2 points) Give an equation relating x and y that represents the curve. Part b: (4 points) Find the slope of the tangent line to the curve when t = π 6 . Part c: (4 points) State the points (x, y) where the tangent line is horizontal
3.2) If a(t)=<-1/(t+1)^2, sec^3 t+ tan^2 t sec t,-t sin t+ 2 cos t- 2> represents...
3.2) If a(t)=<-1/(t+1)^2, sec^3 t+ tan^2 t sec t,-t sin t+ 2 cos t- 2> represents the acceleration of a particle at time t with v(0)=〈2,-1, 0〉 and r(0)=〈0, 2, 0〉 then find the distance from the the particle to the plane 2x- 3y+z= 10 at t= 1 (ie Find the Distance from the particle to the Plane)
Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty =...
Solve the following differential equations 1. cos(t)y' - sin(t)y = t^2 2. y' - 2ty = t Solve the ODE 3. ty' - y = t^3 e^(3t), for t > 0 Compare the number of solutions of the following three initial value problems for the previous ODE 4. (i) y(1) = 1 (ii) y(0) = 1 (iii) y(0) = 0 Solve the IVP, and find the interval of validity of the solution 5. y' + (cot x)y = 5e^(cos x),...
Assume you are given two resistors with resistances R1=4.0 kΩ and R2=6.0 kΩ and two capacitors...
Assume you are given two resistors with resistances R1=4.0 kΩ and R2=6.0 kΩ and two capacitors with capacitances C1=4.0 µF and C2=6.0 µF. a) Calculate the equivalent resistances Req and the equivalent capacitance Ceq if the resistors are connected in series and the capacitors are connected in parallel. b) Now, use the Req and Ceq that you calculate in part (a) to construct an RC circuit. If an emf of 27 V is suddenly applied across Req and Ceq, calculate...
A standing wave on a string fixed at both ends is described by y(x,t)=2 sin((π/3)x)cos((π/3)t), where...
A standing wave on a string fixed at both ends is described by y(x,t)=2 sin((π/3)x)cos((π/3)t), where x and y are given in cm and time t is given in s. Answer the following questions a) Find the two simplest travelling waves which form the above standing wave b) Find the amplitude, wave number, frequency, period and speed of each wave(Include unit in the answer) c) When the length of the string is 12 cm, calculate the distance between the nodes...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT