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Kobotan [32]
2 years ago
13

The length of a rectangle is 2 centimeters more than five times the width. The perimeter is 114 inches. Find the width and the l

ength.
Mathematics
1 answer:
gogolik [260]2 years ago
7 0
1. Let L=length and W=width
2. L=5w+2
3. The perimeter can be solved as follows:
(5w+2) + (5w+2) + w + w = 114 in
12w + 4 = 114 in
12w = 110
w = 110/12
w = 9.17
L = 47.83
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Part A:

The average rate of change refers to a function's slope. Thus, we are going to need to use the slope formula, which is:

m = \dfrac{y_2 - y_1}{x_2 - x_1}

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You can see that we are given the x-values for our interval, but we are not given the y-values, which means that we will need to find them ourselves. Remember that the y-values of functions refers to the outputs of the function, so to find the y-values simply use your given x-value in the function and observe the result:

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h(1) = 3(5)^1 = 3 \cdot 5 = 15

h(2) = 3(5)^2 = 3 \cdot 25 = 75

h(3) = 3(5)^3 = 3 \cdot 125 = 375


Now, let's find the slopes for each of the sections of the function:

<u>Section A</u>

m = \dfrac{15 - 3}{1 - 0} = \boxed{12}

<u>Section B</u>

m = \dfrac{375 - 75}{3 - 2} = \boxed{300}


Part B:

In this case, we can find how many times greater the rate of change in Section B is by dividing the slopes together.

\dfrac{m_B}{m_A} = \dfrac{300}{12} = 25


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Answer:

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