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2 years ago

6

I need help with this math problem!

1 answer:

kherson [118]2 years ago

4 0

Answer: (50, 70)

The answer is (50, 70).

Step-by-step explanation:

Hope this helps =)

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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

How old is the 7th person that walked in?

mario62 [17]

7th person that walked in would be 66 years old

7 0

3 years ago

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Laura is training to run a race. She keeps track of the number of miles she runs. She has been training for 5 weeks, and she has

V125BC [204]

Answer:

8 miles per week!

Step-by-step explanation:

40 miles / 5 weeks = 8!

so it would be 8 miles per week.

i hope this helps!!

4 0

2 years ago

Point a is at (-7,-7) and m is at (-6,-1) what are the coordinates of point b

AlekseyPX

Answer:

The coordinates of point b are (-5,5).

Step-by-step explanation:

Given:

Point a is at (-7,-7) and m is at (-6,-1).

So, to find the coordinates of point b.

Let a (-7,-7) be $(x_{1},y_{1})$ , m (-6,-1) and b $(x_{2} ,y_{2})$ .

Now, putting the formula to get the coordinates:

$m=\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2}$

⇒ $(-6,-1)=\frac{-7+x_{2}}{2} , \frac{-7+y_{2}}{2}$

So, here we will make two equations to find the value of $x_{2} andy_{2}$ :

$-6=\frac{-7+x_{2}}{2}$

multiplying both sides by 2

⇒ $-12=-7+x_{2}$

⇒ $-5=x_{2}$

And, now same method for getting the value of $y_{2}$ .

$-1=\frac{-7+y_{2}}{2}$

multiplying both sides by 2

⇒ $-2=-7+y_{2}$

⇒ $5=y_{2}$ .

The value of $(x_{2} ,y_{2})$ = $(-5,5)$ .

Therefore, the coordinates of point b are (-5,5).

4 0

3 years ago

How much would $500 invested at 8% interest compounded continuously be worth after 3 years? round your answer to the nearest cen

erik [133]

To solve this, you'll need the interest formula: <span> P(1 + rt).

Then, plug in the numbers:
$500(1.08*3) = $1,620. That's your answer.</span>

4 0

3 years ago

Read 2 more answers