*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:

step-by-step explanation:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

step-by-step explanation:

given that megan owns a clothing boutique.

the profits of 2010, 11, are recorded and shown as follows:

years since     2010 0     1     2     3       4       5

profits made in 1000's   39       84     111     120   111     84

we find that profit gradually increases form 2010 to 2013 upto 120,   then starts decreasing.

the profits for 2012 and 2014 are the same while that of 2011 and 2015 are also the same.

this shows that there is symmetry about the line profit = 120000

hence answer is:

a.   since the profit made in 2012 is equal to the profit made in 2014, the profit is           symmetric about the line y = 120,000.

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