Calcular el volumen del sólido de revolución que se forma al girar alrededor del eje " \( y \) " la función \( f(x)=-x^{2}+10 \)

Use a calculator to evaluate the expression. \( \frac{\ln 9+\ln 3}{\log 9+\log 3} \) \( \frac{\ln 9+\ln 3}{\log 9+\log 3} \approx \square \)

\( \int _{}^{}\cot (x)^{3}\csc (x)^{2} d \)

Differentiate. \( f(x)=\sqrt{11 x-x^{3}} \) 1

Find an equation for the line tangent to the graph of the given function at the indicated point. \( f(x)=\frac{x^{3}}{2} \) at \( (-8,-256) \)

A business estimates that the salvage value V of a piece of machinery after t years is given by, \( \mathrm{V}(\mathrm{t})=\$ 34,000 e^{-0.4 \mathrm{t}} \). After what amount of time will the salvage value be \( \$ 1986 \) ?