A cylindrical tank with radius $5m$ is being filled with water at a rate of $3m^{3}/\min$. How fast is the height of the water increasing. The radius $r=5m$ The rate of water is $\dfrac{dV}{dt}=3m^{3}/\min$ The height of the water in the cylinder is $h$ The volume of a cylinder is given by the...
The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of 3 cm/s . When the length is 20 cm and the width is 10 cm, how fast is the area of the rectangle increasing? To set up the equation, I have $A=lw$. Differentiate both sides of the equation, I have...
Suppose $Fin$ is a class of all finite groups. Define, $\Sigma$ as the set of all functions $f$ from $Fin$ to $\mathbb{Z}$, such that $f(E) = 1$, where $E$ is the trivial group. Now, if $f, g \in \Sigma$, define $f \ast g = \Sigma_{H \triangleleft G} f(H)g(\frac{G}{H})$. It is not hard to see, t...
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