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3 years ago

The length of a rectangle is twice it’s with the perimeter of a rectangle is 126 feet.

Mathematics

1 answer:

madreJ [45]3 years ago

3 0

Answer:

Length = 42 feet

Width = 21 feet

Step-by-step explanation:

Let the length and width be represented by L and W

L = 2W

Perimeter (P) = 126 feet

2(L + W) = 126

L + W = 126/2 = 63

2W + W = 63

3W = 63

W = 63/3 = 21 feet

L = 2W = 2 × 21 feet = 42 feet

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Answer:

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3 years ago

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AVprozaik [17]

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Step-by-step explanation:

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3 years ago

Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

ANSWER

${r}^{2} = 4 \cos2\theta$

EXPLANATION

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

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3 years ago