Problem #$4$: By making an appropriate substitution, which of the following integrals is equal to

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{dx}{x^4(x^2-9{)}^{\frac{3}{2}}}?$

$($A$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^6()}{3^{7}si{n}^2()}d$

$($B$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^4()}{3^{7}si{n}^2()}d$

$($C$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^6()}{3^{6}si{n}^2()}d$

$($D$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^6()}{3^{6}si{n}^3()}d$

$($E$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^4()}{3^{6}si{n}^3()}d$

$($F$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^5()}{3^{6}si{n}^2()}d$

$($G$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{co{s}^7()}{3^{6}si{n}^3()}d$

$($H$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{to{s}^5()}{3^{7}si{n}^3()}d$

E AND D ARE WRONG

A ring $($hollow cylinder$)$ of mass $2\mathrm{.}07$ kg $,$ inner radius $5\mathrm{.}10$ cm $,$ and outer radius $6\mathrm{.}15$ cm rolls $($without slipping$)$ up an inclined plane that makes an angle of $=38\mathrm{.}2,$ as shown in the figure below. At the moment the ring is at position $x=1\mathrm{.}86m$ up the plane, its speed is $2\mathrm{.}80\frac{m}{s}.$ The ring continues up the plane for some additional distance and then rolls back down. It does not roll off the top end. How much further up the plane does it go $?1\mathrm{.}97$ m

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The minute hand of Big Ben, the famous Parliment Building tower clock in London, is $4\mathrm{.}10$ m long and has a mass of $127\mathrm{.}8$ kg $.$ Calculate the angular momentum of the minute hand. $715\mathrm{.}4k{g}^{***}{m}^2$

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The hour hand has a length of $2\mathrm{.}39$ m and a mass of $75\mathrm{.}6$ kg $.$ Calculate the angular momentum of the hour hand. $0\mathrm{.}42k{g}^{**}\frac{m^2}{s}$

$$ Submission not graded. Use more significant figures. Tries $\frac{0}{10}$ Previous Tries