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3 years ago

Calculate the average rate of change for the given function, from x = −3 to x = 7.

Mathematics

1 answer:

emmainna [20.7K]3 years ago

6 0

Answer:

The average rate of change for the given function, from x = −3 to x = 7 will be:

Average rate = -5

Step-by-step explanation:

Given the table

x f(x)

-3 50

3 10

7 0

As the interval is from x = -3 to x = 7.

at x₁ = -3, f(x₁) = 50

at x₂ = 7, f(x₂) = 0

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]

= [0 - 50] / [7-(-3)]

= [-50] / [7+3]

= -50 / 10

= -5

Therefore, the average rate of change for the given function, from x = −3 to x = 7 will be:

Average rate = -5

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1) Resultant fraction: $\frac{65}{63}$

2) Total soil: $1\frac{7}{8}$ pounds

3) Result of the product: $\frac{35}{2}$

Step-by-step explanation:

In this problem, we want to find the product between the two fractions

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In order to find this product, we have to multiply the numerators of each fraction and the denominators of each fraction. We get:

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Now we simplify, dividing both numerator and denominator by 2:

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Here we have:

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$s=\frac{3}{8}$ (amount of soil (in pounds) that each pot can contain)

In order to find the amount of soil that Andy needs to fill all the pots, we have to multiply the number of pots (n) by the amount of soil that each pot can contain (s).

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In order to do so, we first have to rewrite each fraction as an improper fraction.

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For the 2nd fraction:

$3\frac{3}{4}=\frac{3\cdot 4+3}{4}=\frac{12+3}{4}=\frac{15}{4}$

Now we can finally find the product of the two fractions:

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Where in the last step, we divide both the numerator and the denominator by 6.

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