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Alik [6]
3 years ago
14

A rectangle has a width of 2.5. When the length of this rectangle is decreased by 5 inches, the new area of the rectangle is 17.

5.
Part A: Write an equation to represent this situation, where x represents the original length of the rectangle.
Part B: Find the original length of the rectangle.
Mathematics
1 answer:
kati45 [8]3 years ago
7 0
<h3><u>Part A: An equation to represent this situation, where x represents the original length of the rectangle is:</u></h3>

17.5 = (x-5) \times 2.5

<h3><u>Part B: Original length of the rectangle is 12 inches</u></h3>

<em><u>Solution:</u></em>

Given that,

A rectangle has a width of 2.5

Therefore,

width = 2.5 inches

Let "x" be the original length of the rectangle

When the length of this rectangle is decreased by 5 inches

Therefore,

New length = x - 5

The new area of the rectangle is 17.5 square inches

Therefore,

<em><u>The area of rectangle is given as:</u></em>

Area = length \times width

17.5 = (x-5) \times 2.5\\\\17.5 = 2.5x - 12.5\\\\2.5x = 17.5 + 12.5\\\\2.5x = 30\\\\x = 12

Thus original length of the rectangle is 12 inches

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The value of an investment A (in dollars) after t years is given by the function A(t) = A0ekt. If it takes 10 years for an inves
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We know that \text{ln}(e)=1, so

\text{ln}(3)=10k\cdot 1

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Dividing both sides by 1000, we will get:

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Take natural log of both sides:

\text{ln}(9)=\text{ln}(e^{\frac{\text{ln}(3)}{10}*t)

\text{ln}(9)=\frac{\text{ln}(3)}{10}*t\cdot\text{ln}(e)

\text{ln}(9)=\frac{\text{ln}(3)}{10}*t\cdot1

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Divide both sides by \text{ln}(3):

\frac{20\text{ln}(3)}{\text{ln}(3)}=\frac{\text{ln}(3)*t}{\text{ln}(3)}

20=t

Therefore, it will take 20 years for the investment to be $9,000.

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