Ryan boards a ferris wheel at the 3-o'clock position and rides the ferris wheel for multiple revolutions. the ferris wheel rotates at a constant angular speed of 6.5 radians per minute and has a radius of 30 feet. the center of the ferris wheel is 36 feet above the ground. let t represent the number of minutes since the ferris wheel started rotating.

a. write an expression (in terms of t) to represent the varying number of radians 0 cody has swept out since the ride started.

b. write an expression (in terms of t) to represent cody's height (in feet) above the center of the ferris wheel.

c. write an expression (in terms of t) to represent cody's height (in feet) above the ground.

a)

r(t) = 6.5t radians

b)

C(t) = 30cos(6.5*t) feet

c)

H(t) = 36 - C(t)

Step-by-step explanation:

The situation is depicted in the picture attached considering the center of the wheel as the center of the coordinates system

a. Write an expression (in terms of t) to represent the varying number of radians 0 Cody has swept out since the ride started.

Since the angular speed is constant, to find an expression for the angle r(t) in radians we just cross-multiply:

6.5 radians __________ 1 minute

r(t) radians ____________  t minutes

and obviously,

r(t) = 6.5t radians

b. Write an expression (in terms of t) to represent Cody's height (in feet) above the center of the Ferris wheel.

The height C(t) above the center after t minutes is given by

C(t) = 30cos(r(t)) ===>  C(t) = 30cos(6.5*t) feet

When C(t) < 0 means that Cody is below the center of the wheel.

c. Write an expression (in terms of t) to represent Cody's height (in feet) above the ground.

Since the center of the Ferris wheel is 36 feet above the ground, the height H(t) above the ground after t minutes is given by

H(t) = 36 - C(t)

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)