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alexandr402 [8]
3 years ago
7

An experiment finds that runners with the longest legs complete a mile run in less time. Identify the relation between leg lengt

h and time of a mile run.
Mathematics
1 answer:
N76 [4]3 years ago
3 0

Answer:

The relation between the leg length and the time of a mile run is an inverse relation.

Step-by-step explanation:

Inverse relation is one between two variables in which as the value of one of the variables increases, then the value of the other decreases.

From the given question the longer the leg of a runner, the lesser the time to complete a mile run. This implies that as the length of the leg of a runner increases, the time to cover a mile decreases. Therefore, the relation between the leg length and time is an inverse relation.

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We will use the sine and cosine of the sum of two angles, the sine and consine of \frac{\pi}{2}, and the relation of the tangent with the sine and cosine:

\sin (\alpha+\beta)=\sin \alpha\cdot\cos\beta + \cos\alpha\cdot\sin\beta

\cos(\alpha+\beta)=\cos\alpha\cdot\cos\beta-\sin\alpha\cdot\sin\beta

\sin\dfrac{\pi}{2}=1,\ \cos\dfrac{\pi}{2}=0

\tan\alpha = \dfrac{\sin\alpha}{\cos\alpha}

If you use those identities, for \alpha=x,\ \beta=\dfrac{\pi}{2}, you get:

\sin\left(x+\dfrac{\pi}{2}\right) = \sin x\cdot\cos\dfrac{\pi}{2} + \cos x\cdot\sin\dfrac{\pi}{2} = \sin x\cdot0 + \cos x \cdot 1 = \cos x

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\tan \left(x+\dfrac{\pi}{2}\right) = \dfrac{\sin\left(x+\dfrac{\pi}{2}\right)}{\cos\left(x+\dfrac{\pi}{2}\right)} = \dfrac{\cos x}{-\sin x} = -\cot x
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Step-by-step explanation:

When given two points and asked to find the slope, you can find the answer using slope formula which is:

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