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3 years ago

14 25/100 answer please as a decimal number

Mathematics

2 answers:

timofeeve [1]3 years ago

5 0

The answer as a decimal would be 57/4 but simplified would be 14 1/4

shusha [124]3 years ago

3 0

Answer:

14.25

Step-by-step explanation:

14 is the hole number and for the decimal part all you have to do is 25÷100

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###

To compute the last integral, you can integrate by parts:

$u=r\implies\mathrm du=\mathrm dr$

$\mathrm dv=r\sqrt{1+r^2}\,\mathrm dr\implies v=\dfrac13(1+r^2)^{3/2}$

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For this integral, consider a substitution of

$r=\sinh s\implies\mathrm dr=\cosh s\,\mathrm ds$

$\displaystyle\int_0^4(1+r^2)^{3/2}\,\mathrm dr=\int_0^{\sinh^{-1}4}(1+\sinh^2s)^{3/2}\cosh s\,\mathrm ds$

$\displaystyle=\int_0^{\sinh^{-1}4}\cosh^4s\,\mathrm ds$

$=\displaystyle\frac18\int_0^{\sinh^{-1}4}(3+4\cosh2s+\cosh4s)\,\mathrm ds$

and the result above follows.

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Step-by-step explanation:

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2 years ago

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