help | Mathematics | Page 1

vocal owl Oct 1, 2024, 11:09 AM

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help me with this plz

wintry kelpBOT Oct 1, 2024, 11:09 AM

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vocal owl help me with this plz

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frail spoke Oct 1, 2024, 11:14 AM

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try finding the angle

vocal owl Oct 1, 2024, 11:29 AM

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frail spoke try finding the angle

i dont have any lead

hollow sun Oct 1, 2024, 11:30 AM

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OK, try starting with the formula for the area of a sector and the forumla for an arc length.

vocal owl Oct 1, 2024, 11:30 AM

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theata/360 * pi r(square)

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is for area

hollow sun Oct 1, 2024, 11:31 AM

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Yes!

vocal owl Oct 1, 2024, 11:31 AM

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and theata/360 * 2 * pi * r

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for arc length

hollow sun Oct 1, 2024, 11:31 AM

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Yes. OK, what infomation do we have that we can put in these?

vocal owl Oct 1, 2024, 11:31 AM

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we have area

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but no angle

hollow sun Oct 1, 2024, 11:32 AM

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Yes. We don't need the angle in this case. Quick question, do we have the arc length?

vocal owl Oct 1, 2024, 11:32 AM

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yea

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its the same as radius

hollow sun Oct 1, 2024, 11:33 AM

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Yes! OK, set the sector area equal to the area, and the arc length equal to the radius (as it is equal to the radius in this case)

vocal owl Oct 1, 2024, 11:34 AM

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ok

hollow sun Oct 1, 2024, 11:34 AM

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Try writing it down on paper, it can make it a lot easier.

vocal owl Oct 1, 2024, 11:35 AM

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is the angle 2 pi?

hollow sun Oct 1, 2024, 11:36 AM

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How did you get that? I don't know to be honest. What have you written down so far?

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The angle gets removed eventually.

vocal owl Oct 1, 2024, 11:37 AM

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i wrote theata/360 * 2 * pi * r=r (cos the radius = arc length)

hollow sun Oct 1, 2024, 11:38 AM

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Yes, that is right. theata/360 * 2 * pi * r = r. What about the area?

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We need two equations

vocal owl Oct 1, 2024, 11:38 AM

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hmm

hollow sun Oct 1, 2024, 11:39 AM

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vocal owl theata/360 * pi r(square)

You mentioned the formula for the area of a sector up here.

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And we know the area of the sector already.

vocal owl Oct 1, 2024, 11:39 AM

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yea

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but the angle is missing

hollow sun Oct 1, 2024, 11:40 AM

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We don't need it. For problems like this, just work with the information you have.

vocal owl Oct 1, 2024, 11:40 AM

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so what should i substitute it as?

hollow sun Oct 1, 2024, 11:41 AM

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We'll get to that in a bit. Have you got a equation for the area of the sector?

vocal owl Oct 1, 2024, 11:41 AM

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still working on it

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i got it to theata * r = 68.12

hollow sun Oct 1, 2024, 11:43 AM

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Is that 68.12 rounded?

vocal owl Oct 1, 2024, 11:43 AM

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yea

hollow sun Oct 1, 2024, 11:44 AM

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Ok. In this case, we need to keep things as precise as possible. For example, don't multiply or divide by pi and then round. In this case, try just making the formula for the area of a sector equal to the area of the sector. What do you get when you do that?

vocal owl Oct 1, 2024, 11:47 AM

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θr = 14580/pi

spring zephyr Oct 1, 2024, 11:47 AM

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uh, sorry to butt in, but isn’t the arc length equal to r?

vocal owl Oct 1, 2024, 11:47 AM

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how?

spring zephyr Oct 1, 2024, 11:47 AM

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according to the picture it is

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even the question says it

vocal owl Oct 1, 2024, 11:48 AM

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oh yea

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sry

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i missread it and thought u said arc length = pi

hollow sun Oct 1, 2024, 11:50 AM

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Ok, we should have an equation like this: theta/360 * pi*r^2 = 40.5

vocal owl Oct 1, 2024, 11:50 AM

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yea

hollow sun Oct 1, 2024, 11:50 AM

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You need to rearrange for theta in both this equation and the one for the arc length we got earlier, theta/360 * 2pir = r

spring zephyr Oct 1, 2024, 11:52 AM

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But can’t we calculate theta really easily?

hollow sun Oct 1, 2024, 11:54 AM

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spring zephyr But can’t we calculate theta really easily?

We don't know r. We're trying to get two equations that we can solve simultaneously.

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We could use theta/360 2pi*r = r and divide both sides by r to get theta, yes. But we need to find r, not theta.

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In fact, if we do that, we get theta/360 * 2 * pi = 1.

vocal owl Oct 1, 2024, 11:57 AM

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hollow sun We could use theta/360 *2*pi*r = r and divide both sides by r to get theta, yes....

but by finding θ cant we use it to solve the area equation?

hollow sun Oct 1, 2024, 11:57 AM

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Yes, we can. Let's try that.

vocal owl Oct 1, 2024, 11:57 AM

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oh ok

hollow sun Oct 1, 2024, 11:58 AM

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Remember to keep theta in it's exact form!

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So, in this case, theta = 360/(2*pi) = 180/pi

vocal owl Oct 1, 2024, 11:59 AM

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yea

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so θ = 57.30 (2 d.p)

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is it correct?

hollow sun Oct 1, 2024, 12:01 PM

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We have two simultaneous equations, theta = 180/pi and (when you rearrange the area formula for pi) theta = 14580/(pi*r^2).

hollow sun Oct 1, 2024, 12:01 PM

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vocal owl is it correct?

Yes

vocal owl Oct 1, 2024, 12:01 PM

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oh ok

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nice

hollow sun Oct 1, 2024, 12:01 PM

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But it's not in exact form.

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We need to keep pi in the equation. Try setting those two equations for theta equal to each other and solve for r.

vocal owl Oct 1, 2024, 12:03 PM

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hollow sun We need to keep pi in the equation. Try setting those two equations for theta eq...

equal to what?

hollow sun Oct 1, 2024, 12:06 PM

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We have two equations for theta. theta = 14580/(pir^2) and theta = 180/pi. Because both are equal to theta, it means that 14580/(pir^2) = 180/pi

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We now have an equation where the only varible is r, so we can solve for it.

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I told you theta goes away 😄

vocal owl Oct 1, 2024, 12:08 PM

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ohhhhhhhhhh

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thank you very much

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+close

#help