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4 years ago

Please help due today!

Mathematics

1 answer:

iVinArrow [24]4 years ago

4 0

Answer:

20.6

Step-by-step explanation:

Coordinates given:

D(-3,2)
E(4,2)
F(4,-3)

Plotted, these points give a right triangle with hypotenuse DF

Distance DE = 4 - (-3) = 7
Distance EF = 2 - (-3) = 5
Distance DF = √(7²+5²) = √84 = 8.6

Perimeter

P = 7 + 5 + 8.6 = 20.6

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Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

The average rate of change of a function over the interval $[a,b]$ is equal to $\frac{f(b)-f(a)}{b-a}$ , hence:

$\frac{f(b)-f(a)}{b-a}\\\\\frac{f(9)-f(5)}{9-5}\\\\\frac{14-(-4)}{9-5}\\ \\\frac{14+4}{4}\\ \\\frac{18}{4}\\ \\\frac{9}{2}$

Therefore, the average rate of change of $f(x)$ over the interval $[5,9]$ is $\frac{9}{2}$ .

Part B

Do the same thing as in Part A:

$\frac{f(b)-f(a)}{b-a}\\ \\\frac{f(1)-f(0.25)}{1-0.25}\\ \\\frac{2-5}{0.75}\\ \\\frac{-3}{0.75}\\ \\-4$

Therefore, the average rate of change of $g(x)$ over the interval $[0.25,1]$ is $-4$ .

Part C

To interpret our answer from Part B in terms of the real world it represents, we say that between 0.25 seconds and 1 second, the ball falls at a rate of 4 feet per second (since our average rate of change is negative).

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