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.

Velocity is 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

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

2) Acceleration of the particle will be

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

velocity of the particle at t=

 V() = (0)i + (8)j + 8k = =

acceleration at t=

A() = (8)i + (0)j +0k = = 8

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.

true !

step-by-step explanation: