Mathematics: The equation r(t)=(8 sin t) i+(8 cos t) j+(8t) k is the position of a particle in space at time t. Find the particle s velocity and acceleration vectors. Then write the particle s velocity at t= 3π 2 as a product of its speed and direction.

The equation r(t)=(8 sin t) i+(8 cos t) j+(8t) k

Ответ:

brandy2115

07.02.2022

Mathematics

Velocity is $8\sqrt{2}$ and Acceleration is 8

Step-by-step explanation:

Equation of position of the particle

r(t) = (8sint)i + (8cost)j + (8t)k

1) Velocity of the particle is $\frac{dr}{dt}$

V(t) = dr/dt = (8cost)i + (-8sint)j + 8k

2) Acceleration of the particle will be $\frac{dv}{dt}$

A(t) = dv/dt = (-8sint)i + (-8cost)j + 0k

velocity of the particle at t= $\frac{3pi}{2}$

V( $\frac{3pi}{2}$ ) = (0)i + (8)j + 8k = $\sqrt{8^2+8^2}$ = $8\sqrt{2}$

acceleration at t= $\frac{3pi}{2}$

A( $\frac{3pi}{2}$ ) = (8)i + (0)j +0k = $\sqrt{8^2}$ = 8

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Ответ:

audrey435

02.06.2022

Mathematics

Step-by-step explanation:

Set this up as a proportion. The idea is that if we can find out the number of "no" votes based on the ratio of 5:7, then we can add the "no" votes to the number of "yes" votes to get the total number of votes.

$\frac{yes}{no}:\frac{5}{7}=\frac{3710}{x}$

Cross multiply to get

5x = 25790 so

x = 5194 "no" votes.

5194 + 3710 = 8904 total votes

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The equation r(t)=(8 sin t) i+(8 cos t) j+(8t) k is the position of a particle in space at time t. Find the particle's velocity and acceleration vectors. Then write the particle's velocity at t= 3π 2 as a product of its speed and direction.

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