*In a scene from "The Martian" Matt Damon shoots a flare straight up into the sky. The

height (in feet) of the flare after t seconds is

given by

s(t) = -3t? + 100t +3

What is the velocity of the flare when it is

moving toward the ground and its position is

equal to 131 feet?

(

The velocity is 4.094ft/s

Step-by-step explanation:

Given

Required

Find the velocity at 131ft

First, calculate the time taken to reach 131 ft

This gives:

Rewrite as:

Expand

Factorize

Factor out t - 32

Split

Solve for t

Since 32 > 4/3, then the flare is going up at 4/3s and coming down at 32s

The velocity is calculated as:

So, we have:

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2