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2 years ago

Write the equation of the line (in point-slope form) that passes through the point (-3, 4) and has a slope of 6.

Mathematics

1 answer:

Roman55 [17]2 years ago

8 0

Answer:

y = 6x + 22

Step-by-step explanation:

y-intercept = 4 - (6)(-3)

= 4 + 18 = 22

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150 is 200% of what number?

ale4655 [162]

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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:

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

7 0

3 years ago

Can someone solve this question

pogonyaev

(g/f)(x)= g(x)/f(x) =

= (x² - 6) /(3x +1)

3x+1≠0

3x≠-1

x≠ - 1/3

(g/f)(x)= (x² - 6) /(3x +1), when x≠ - 1/3

Answer: A.

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3 years ago

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Answer:

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Step-by-step explanation:

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