Solve for l
l=\frac{49\times \left(\frac{T}{\pi }\right)^{2}}{8}
T\geq 0
Solve for T
T=\frac{2\pi \sqrt{2l}}{7}
l\geq 0
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T=4\pi \sqrt{\frac{l}{98}}
Multiply 2 and 2 to get 4.
4\pi \sqrt{\frac{l}{98}}=T
Swap sides so that all variable terms are on the left hand side.
\frac{4\pi \sqrt{\frac{1}{98}l}}{4\pi }=\frac{T}{4\pi }
Divide both sides by 4\pi .
\sqrt{\frac{1}{98}l}=\frac{T}{4\pi }
Dividing by 4\pi undoes the multiplication by 4\pi .
\frac{1}{98}l=\frac{T^{2}}{16\pi ^{2}}
Square both sides of the equation.
\frac{\frac{1}{98}l}{\frac{1}{98}}=\frac{T^{2}}{\frac{1}{98}\times 16\pi ^{2}}
Multiply both sides by 98.
l=\frac{T^{2}}{\frac{1}{98}\times 16\pi ^{2}}
Dividing by \frac{1}{98} undoes the multiplication by \frac{1}{98}.
l=\frac{49T^{2}}{8\pi ^{2}}
Divide \frac{T^{2}}{16\pi ^{2}} by \frac{1}{98} by multiplying \frac{T^{2}}{16\pi ^{2}} by the reciprocal of \frac{1}{98}.
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