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3 years ago

Lucie drank 3/4 of a pint of bottled water. One serving of the water is 7/8 of a pint. How much of a serving did she drink.

2 answers:

8 0

7/8
3/4
I'm order for them to have the same denominator you need to multiply so:
¾×2=6/8
So she drank 6/8 pints of water

Xelga [282]3 years ago

8 0

First, let's make it so that they share a common denominator.

3/4 x 2/2 = 6/8

So Lucie drank 6/8 of a pint, or 75% of it. 7/8 - 6/8 = 1/8. So there is 1/8 of water left, or 12.5%.

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Find the value of tan(sin^-1(1/2))

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If you know that $\sin\dfrac\pi3=\dfrac12$ , then you know right away

$\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3$

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Otherwise, you can derive the same result. Let $\theta=\sin^{-1}\dfrac12$ , so that $\sin\theta=\dfrac12$ . $\sin^{-1}$ is bounded, so we know $-\dfrac\pi2\le\theta\le\dfrac\pi2$ . For these values of $\theta$ , we always have $\cos\theta\ge0$ .

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$\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2$

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as expected.

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See picture for solution to your problem.

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Answer:

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