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erma4kov [3.2K]
3 years ago
14

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation 2 l plus 2 w equals 48 can

be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?
9 feet
18 feet
30 feet
33 feet
Mathematics
1 answer:
Lelu [443]3 years ago
7 0

Answer:

2l + 2w = 48

if garden is 15' long

2(15) + 2w = 48 \\ 30 + 2w = 48 \\ 30 - 30 + 2w = 48 - 30 \\ 2w = 18 \\  \frac{2w}{2}  =  \frac{18}{2}  \\ w = 9 \: feet \: wide

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cos is defined as: cos(x)=\frac{adjacent}{hypotenuse}

We can also define tan as: tan(x)=\frac{sin(x)}{cos(x)}

because plugging in the definitions of sin and cos in we get: tan(x)=\frac{(\frac{opposite}{hypotenuse})}{(\frac{adjacent}{hypotenuse})}\\\\tan(x)=\frac{opposite}{hypotenuse}*\frac{hypotenuse}{adjacent}\\\\tan(x)=\frac{opposite}{adjacent}

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So using this definition of tan(x) we can use the givens sin(x) and cos(x) to find tan(x)

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plugging in sin(x) and cos(x) we get:

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We usually don't like square roots in the denominator, and from here we want to rationalize the denominator which we do by removing the square root from the denominator.

We can do this by multiplying the fraction by: \frac{\sqrt{89}}{\sqrt{89}} which doesn't change the value of the fraction since it simplifies to 1, but it gets rid of the square root in the denominator

tan(x)=\frac{44}{\sqrt{89}}*\frac{\sqrt{89}}{\sqrt{89}}\\\\tan(x)=\frac{44\sqrt{89}}{89}

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1 year ago
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