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Irina-Kira [14]

3 years ago

5

324 = a2I need it for homework

2 answers:

Ad libitum [116K]3 years ago

8 0

You didn't specify the topic so I will solve it in 3 topics
solving for a, you take roots of both sides and solve a=18,-18
using the quadratic formula, solve the equation for aa by finding aa, bb, and ccof the quadratic then applying the quadratic formula.

a=±√321a=±321

a≈17.91647286,−17.91647286

for factoring, Factor and set each factor equal to zero.

a=√321,−√321a=321,-⁢321

a≈17.91647286,−17.91647286

PSYCHO15rus [73]3 years ago

5 0

342 = a²

switch sides:

for x² = f(a) the solutions are x = √ f(a) and - √ f(a)

therefore:

√ 342 = 18

-√ 342 = - 18

a = 18 and a = - 18

hope this helps!

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<u>ANSWER</u>

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

<u>EXPLANATION</u>

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We substitute

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$y = r \sin( \theta)$

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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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