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$\frac{20b}{{\left(4b^3\right)}^3}$

1. A body falls from rest against resistance proportional to the square root of the speed at any instant. If the body attains speed V1 and V2 feet per second, after 1 and 2 seconds in motion, respectively, find an expression for the limiting velocity.

Noting that the magnetic field lines of a bar magnet resemble the electric field lines of a pair of equal and opposite charges, do you expect the magnetic field to rapidly decrease in strength with distance from the magnet? Is this consistent with your experience with magnets?

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A simple pendulum has length 20cm.it was displaced at an angle ${15}^{\circ <!--\; \circ \; -->}$ and then released to execute simple harmonic motion. How much time is required for the pendulum to reach maximum speed?

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I know how to use this algorithm when I am integrating rational functions, but my textbook has omitted the actual proof for why it works. If someone could please help me with this question:
Prove that given a and b, there are constants $c_1$ and $c_2$ so that
$\frac{ax+b}{(x-<!--\; -\; -->1{)}^2}=\frac{c_1}{x-<!--\; -\; -->1}+\frac{c_2}{(x-<!--\; -\; -->1{)}^2}$

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1.Find $({\log }_2<!--\; \; -->x{)}^2$ if ${\log }_2<!--\; \; -->({\log }_8<!--\; \; -->x)={\log }_8<!--\; \; -->({\log }_2)x$.
2.If $x,y>0,{\log }_y<!--\; \; -->x+{\log }_x<!--\; \; -->y=\frac{10}{3}$ and xy=144, then find $\frac{x+y}{2}$

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What is the antiderivative of ${\displaystyle \tan \left(x\right)}$ ?

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Factor each polynomial.
${\displaystyle 16q^2-25}$

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Find the mean and median wage.
A supervisor at $\mathrm{\$}1,200$ a week, an inventory manager at $\mathrm{\$}700$ a week, six stock boys at $\mathrm{\$}400$ a week and four drivers at $\mathrm{\$}500$ are employed by a small warehouse.
Mean:
The sum of all the entries divided by the total number of entries is known mean.

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The numbers on the doors of four adjacent offices are consecutive odd integers. If their sum is 976 find the four office numbers.

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