The Notes: Write a general formula to describe the variation: the square of T varies directly with the cube of a and inversely with the square of d; ...

Thursday, August 11, 2011

Write a general formula to describe the variation: the square of T varies directly with the cube of a and inversely with the square of d; ...

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Because $\displaystyle{{T}}^{{2}}$ is directly proportional to $\displaystyle{{a}}^{{3}},$ then $\displaystyle{{a}}^{{3}}$ must be at the numerator. $\displaystyle{{T}}^{{2}}$ is inversely proportional to $\displaystyle{{d}}^{{2}}$ means $\displaystyle{{d}}^{{2}}$ is at the denominator. Also it may be multiplied by any constant $\displaystyle{C}.$

So the general formula for $\displaystyle{{T}}^{{2}}$ is $\displaystyle{{T}}^{{2}}={C}\cdot\frac{{{a}}^{{3}}}{{{d}}^{{2}}}.$ It is given that for $\displaystyle{a}={3}$ and $\displaystyle{d}={2}$ must be $\displaystyle{T}={5}.$ We can find $\displaystyle{C}$ from this:

$\displaystyle{{5}}^{{2}}={C}\cdot\frac{{{3}}^{{3}}}{{{2}}^{{2}}},$ so $\displaystyle{C}=\frac{{{25}\cdot{4}}}{{27}}=\frac{{100}}{{27}}$ and $\displaystyle{{T}}^{{2}}=\frac{{100}}{{27}}\cdot\frac{{{a}}^{{3}}}{{{d}}^{{2}}}.$

And if we want a formula for $\displaystyle{T},$ not $\displaystyle{{T}}^{{2}},$ it is

$\displaystyle{T}=\pm\sqrt{{{C}}}\cdot\frac{{{a}}^{{\frac{{3}}{{2}}}}}{{d}}=\pm\frac{{10}}{{{3}\sqrt{{{3}}}}}\cdot\frac{{{a}}^{{\frac{{3}}{{2}}}}}{{d}}=\pm\frac{{{10}\sqrt{{{3}}}}}{{{9}}}\cdot\frac{{{a}}^{{\frac{{3}}{{2}}}}}{{d}}.$

The Notes

Thursday, August 11, 2011

Write a general formula to describe the variation: the square of T varies directly with the cube of a and inversely with the square of d; ...

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What are hearing tests?

Thursday, August 11, 2011

Write a general formula to describe the variation: the square of T varies directly with the cube of a and inversely with the square of​ d; ...

No comments:

Post a Comment

What are hearing tests?

Write a general formula to describe the variation: the square of T varies directly with the cube of a and inversely with the square of d; ...