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3 years ago

In triangle ABC, c is the hypotenuse, 0=25°, and b =3, Find the length of c ?

Mathematics

1 answer:

Charra [1.4K]3 years ago

8 0

Answer:

$\large\boxed{c\approx3.31}$

Step-by-step explanation:

Use cosine:

$cosine=\dfrac{adjacent}{hypotenuse}$

$\cos\theta=\dfrac{b}{c}$

We have:

$\theta=25^o\to\cos25^o\approx0.9063\\\\b=3$

Substitute:

$\dfrac{3}{c}=0.9063$

$\dfrac{3}{c}=\dfrac{9063}{10000}$ cross multiply

$9063c=30000$ divide both sides by 9063

$c\approx3.31$

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The clearance between a pin and the collar around it is important for the proper performance of a disc drive for small computers

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(a) The distribution of (Y - X) is N (0.001, 0.0005).

(b) The probability that the pin will not fit inside the collar is 0.023.

Step-by-step explanation:

The random variable X is defined as the diameter of the pin and the random variable Y is defined as the diameter of the collar.

The distribution of X and Y is:

$X\sim N(0.525, 0.0003)\\Y\sim N(0.526, 0.0004)$

The random variables X and Y are independent of each other.

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Compute the expected value of (Y - X) as follows:

$E(Y-X)=E(Y)-E(X)=0.526-0.525=0.001$

The mean of (Y - X) is 0.001.

Compute the variance of (Y - X) as follows:

$V(Y-X)=V(Y)+V(X)-2Cov(X,Y)\\=V(Y)+V(X);\ X\ and\ Y\ are\ independent\\=0.0003^{2}+0.0004^{2}\\=0.00000025$

$SD(Y-X)=\sqrt{0.00000025}=0.0005$

The standard deviation of (Y - X) is 0.0005.

Thus, the distribution of (Y - X) is N (0.001, 0.0005).

(b)

Compute the probability of [(Y - X) ≤ 0] as follows:

$P(Y-X\leq 0)=P(\frac{(Y-X)-\mu_{Y-X}}{\sigma_{Y-X}}\leq \frac{0-0.001}{0.0005})=P(Z$

*Use a z-table for the probability value.

Thus, the probability that the pin will not fit inside the collar is 0.023.

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