Problem 1
A force of 6 pounds is required to keep a spring stretched \(\frac{1}{2}\) foot beyond its normal length. Find the value of the spring constant and the work done in stretching the spring \(\frac{1}{2}\) foot beyond its natural length.
Problem 1
Find the length of the indicated curve. \(y=4 x^{3 / 2}\) between \(x=1 / 3\) and \(x=5\)
Problem 1
FInd the volume of the solid generated when the region \(R\) bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps. (a) Sketch the region \(R\). (b) Show a typical rectangular slice properly labeled. (c) Write a formula for the approximate volume of the shell generated by this slice. (d) Set up the corresponding integral. (e) Evaluate this integral. y=\frac{1}{x}, x=1, x=4, y=0 ; \text { about the } y \text { -axis }
Problem 1
A discrete probability distribution for a random variable \(X\) is given. Use the given distribution to find \((a)\) \(P(X \geq 2)\) and \((b) E(X)\). $$ \begin{array}{l|llll} x_{i} & 0 & 1 & 2 & 3 \\ \hline p_{i} & 0.80 & 0.10 & 0.05 & 0.05 \end{array} $$
Problem 1
Particles of mass \(m_{1}=5, m_{2}=7\), and \(m_{3}=9\) are located at \(x_{1}=2, x_{2}=-2\), and \(x_{3}=1\) along a line. Where is the center of mass?
Problem 2
Find the length of the indicated curve. \(y=\frac{2}{3}\left(x^{2}+1\right)^{3 / 2}\) between \(x=1\) and \(x=2\)
Problem 2
FInd the volume of the solid generated when the region \(R\) bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps. (a) Sketch the region \(R\). (b) Show a typical rectangular slice properly labeled. (c) Write a formula for the approximate volume of the shell generated by this slice. (d) Set up the corresponding integral. (e) Evaluate this integral. y=x^{2}, x=1, y=0 ; \text { about the } y \text { -axis }
Problem 2
John and Mary, weighing 180 and 110 pounds, respectively, sit at opposite ends of a 12 -foot teeter board with the fulcrum in the middle. Where should their 80 -pound son Tom sit in order for the board to balance?
Problem 2
A discrete probability distribution for a random variable \(X\) is given. Use the given distribution to find \((a)\) \(P(X \geq 2)\) and \((b) E(X)\). $$ \begin{array}{l|lllll} x_{i} & 0 & 1 & 2 & 3 & 4 \\ \hline p_{i} & 0.70 & 0.15 & 0.05 & 0.05 & 0.05 \end{array} $$
Problem 3
FInd the volume of the solid generated when the region \(R\) bounded by the given curves is revolved about the indicated axis. Do this by performing the following steps. (a) Sketch the region \(R\). (b) Show a typical rectangular slice properly labeled. (c) Write a formula for the approximate volume of the shell generated by this slice. (d) Set up the corresponding integral. (e) Evaluate this integral. \(y=\sqrt{x}, x=3, y=0 ;\) about the \(y\) -axis
