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earnstyle [38]
3 years ago
5

If cosh x = 13 5 and x > 0, find the values of the other hyperbolic functions at x.

Mathematics
1 answer:
givi [52]3 years ago
7 0
Recall that

\cosh^2x-\sinh^2x=1\implies \cosh x=\pm\sqrt{1+\sinh^2x}

You're given that \cosh x=\dfrac{13}5>0, so omit the negative root. Then

\dfrac{13}5=\sqrt{1+\sinh^2x}\implies\sinh^2x=\dfrac{144}{25}\implies\sinh x=\pm\dfrac{12}5

Because x>0, you have \sinh x>0 too, so omit the negative root again. Then \sinh x=\dfrac{12}5.

Now,

\mbox{sech }x=\dfrac1{\cosh x}=\dfrac5{13}
\mbox{csch }x=\dfrac1{\sinh x}=\dfrac5{12}
\tanh x=\dfrac{\sinh x}{\cosh x}=\dfrac{\frac{12}5}{\frac{13}5}=\dfrac{12}{13}
\coth x=\dfrac1{\tanh x}=\dfrac{13}{12}
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Answer:

Option C is the correct answer.

C.  5•(-20)

Step-by-step explanation:

We are told that the insurance payment for the car follows a certain pattern that can be represented through an expression. The payment is decreasing by $20 every year. As we don't know the total payment amount per period, so we cannot calculate how much is paid per period/year for insurance but we can calculate the rate at which this payment is decreasing.

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Here, A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093).

i.e. A person can be 90% confident that  the true proportion of teenagers who drive their own car to school lies in (0.5907, 0.9093).

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