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3 years ago

The positions of two divers from the water’s surface after a dive are shown:

Mathematics

1 answer:

Travka [436]3 years ago

8 0

Answer:

Step-by-step explanation:

the 4 one

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Step-by-step explanation:

9 lawns is 3 times as much as 3 lawns

it will take 3 times as long

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What is 29/12 as a decimal

ivolga24 [154]

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Step-by-step explanation:

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So to celebrate my actual return and to start drama (kinda)<br><br>What is 3+3x3-3x3+3+3+3x3-17

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3 years ago

What is the average rate of change of f(x) = -x2 + 3x + 6 over the interval –3

Rufina [12.5K]

Answer:

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Step-by-step explanation:

To find the average rate of change of a function over a given interval, basically you need to find the slope. The mathematical definition of the slope is very similar to the one we use every day. In mathematics, the slope is the relationship between the vertical and horizontal changes between two points on a surface or a line. In this sense, the slope can be found using the following expression:

$Average\hspace{3}rate\hspace{3}of\hspace{3}change=Slope=\frac{y_2-y_1}{x_2-x_1} =\frac{f(x_2)-f(x_1)}{x_2-x_1}$

So, the average rate of change of:

$f(x)=-x^2+3x+6$

Over the interval $-3$

Is:

$f(x_2)=f(3)=-(3)^2+3(3)+6=-9+9+6=6\\\\f(x_1)=f(-3)=-(-3)^2+3(-3)+6=-9-9+6=-12$

$\frac{\Delta y}{\Delta x} =\frac{f(x_2)-f(x_1)}{x_2-x_1} =\frac{6-(-12)}{3-(-3)} =\frac{18}{6}= 3$

Therefore, the average rate of change of this function over that interval is 3.

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3 years ago