91Ó°ÊÓ

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region about the indicated axis or line.

Find the value of the expression accurate to four decimal places. a. \(\sinh 2\) b. \(\cosh 4\) c. \(\operatorname{sech} 3\)

Find the center of mass of the system comprising masses \(m_{k}\) located at the points \(x_{k}\) on a coordinate line. Assume that mass is measured in kilograms and distance is measured in meters. $$ \begin{array}{l} m_{1}=2, \quad m_{2}=4, \quad m_{3}=6 ; \quad x_{1}=-3, \quad x_{2}=-1, \\ x_{3}=4 \end{array} $$

Find the work done in lifting a 50 -lb sack of potatoes to a height of \(4 \mathrm{ft}\) above the ground.

A rectangular swimming pool is \(40 \mathrm{ft}\) long, \(15 \mathrm{ft}\) wide, and \(9 \mathrm{ft}\) deep. If the pool is filled with water to a depth of \(8 \mathrm{ft}\), find the force exerted by the water (a) on the bottom of the pool and (b) on one end of the pool.

Find the center of mass of the system comprising masses \(m_{k}\) located at the points \(x_{k}\) on a coordinate line. Assume that mass is measured in kilograms and distance is measured in meters. $$ \begin{array}{l} m_{1}=3, \quad m_{2}=1, \quad m_{3}=5, \quad m_{4}=6 ; \quad x_{1}=-4, \\ x_{2}=-1, \quad x_{3}=1, \quad x_{4}=3 \end{array} $$

How much work is done in lifting a \(4-\mathrm{kg}\) bag of rice to a height of \(1.5 \mathrm{~m}\) above the ground?

Find the value of the expression accurate to four decimal places. a. \(\operatorname{csch} 3\) b. \(\tanh (-2)\) c. \(\operatorname{coth} 5\)

Use the method of cylindrical shells to find the volume of the solid generated by revolving the region about the indicated axis or line.

Find the value of the expression accurate to four decimal places. a. \(\cosh 0\) b. \(\operatorname{sech}(-1)\) c. \(\operatorname{csch}(\ln 2)\)