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3 years ago

The measure of arc LK is?

Mathematics

1 answer:

Oksi-84 [34.3K]3 years ago

5 0

Answer:

Step-by-step explanation:

Because MK is a diameter, then angle L is a right angle. We already know that the measure of angle K is 50, so the measure of angle M has to be 40 because of the triangle angle-sum theorem. The rule for inscribed angles and the arcs they cut off is that the angle is half the measure of its intercepted arc or, likewise, the arc is twice the measure of the angle that cuts it off. Since arc LK is across from angle M and is cut off by angle M, then arc LK is twice the measure of angle M, and is 80. That's the same reason why angle L is 90; arc MK is a semi-circle, with a degree measure of 180, and angle L is half of that.

Arc LK = 80

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Answer:

$128,500

Step-by-step explanation:

Find out how much he will earn from his 1st year to 24th.

1st year = 48000

2nd year = 48000 + 3500 = 51500

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4th year = 55000 + 3500 = 58500

5th year = 58500 + 3500 = 62000

6th year = 62000 + 3500 = 65500

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9th year = 72500 + 3500 = 76000

10th year = 76000 + 3500 = 79500

11th year = 79500 + 3500 = 83000

12th year = 83000 + 3500 = 86500

13th year = 86500 + 3500 = 90000

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15th year = 93500 + 3500 = 97000

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18th year = 104000 + 3500 = 107500

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20th year = 111000 + 3500 = 114500

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22nd year = 118000 + 3500 = 121500

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3 years ago

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4 years ago

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$\sec^2\theta=1+\tan^2\theta\implies \sec\theta=\pm\sqrt{1+\tan^2\theta}$

Since $\cos\theta>0$ for $0$ , we have $\sec\theta>0$ , so we take the positive root. Now,

$\sec\theta=\sqrt{1+\left(\dfrac{12}5\right)^2}=\dfrac{13}5$

- - -

$\tan\theta=\dfrac{\sin\theta}{\cos\theta}$
$\cos^2\theta=1-\sin^2\theta$

In the first quadrant, cosine is positive, so

$\cos\theta=\sqrt{1-\sin^2\theta}$

and in turn,

$\sin\theta=\dfrac35\implies\cos\theta=\sqrt{1-\left(\dfrac35\right)^2}=\dfrac45$
$\implies\tan\theta=\dfrac{\frac35}{\frac45}=\dfrac34$

- - -

In the previous problem, we had $\cos\theta=\dfrac45$ , so we must have $\tan\theta=\dfrac34$ , which means

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