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2 years ago

Which of the following coordinates is located in Quadrant I?

Mathematics

1 answer:

oee [108]2 years ago

5 0

Answer:

(4,6)

Step-by-step explanation:

quadrant 1 always has positive coordinates so the only one with all positive coordinates is (4,6)

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Unit rates... please help

harina [27]

When rates are expressed as a quantity of 1 such as 2 feet per second or 5 miles per hour, that is the definition of unit rates.

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3 years ago

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denis23 [38]

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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]

<u>ANSWER</u>

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

<u>EXPLANATION</u>

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

Put each number with the equation it goes with.

jenyasd209 [6]

Answer:

For the first box, the answer is 3.

For the second box, the answer is -1.

For the third box, the answer is 0.

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