Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions. What is the volume of the solid whose base is the region in the first quadrant bounded by y=$\sqrt { x }$, y=2-x, and the x-axis, and whose cross sections perpendicular to the base and parallel to the y-axis are semicircles?

Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions. What is the volume of the solid whose base is the region in the first quadrant bounded by y=$\sqrt { x }$, y=2-x, and the y-axis, and whose cross sections perpendicular to the base and parallel to the x-axis are square?

Let $\left(1-x^{2}\right) y^{\prime \prime}+2 x y^{\prime}-2 y=0 \quad(-1<x<1) ; y_{1}(x)=x$. So, a differential equation and one solution $y_1$ are given. Use the method of reduction of order to find a second linearly independent solution $y_2$.

Graph each function using the techniques of shifting, compressing or stretching, and reflections. Start with the graph of the basic function and show all stages. $h(x)=-2(x+1)^{3}+3$

Use digits to write forty-seven million, fourteen.

Find the simple interest and the total amount earned. $860 at 6$ for 6 months

Choose the general slicing method, the disk/washer method, or the shell method to answer the following questions. What is the volume of the solid whose base is the region in the first quadrant bounded by y$= \sqrt { x }$, y=2-x, and the x-axis, and whose cross sections perpendicular to the base and parallel to the y-axis are squares?

Supervisor: "There are 3 teams of 18 employees working today. Company policy says that we need to have 1 supervisor for every 8 employees on the floor. There are a few supervisors who are out sick so I hope we have enough." Supervisor: "We need __________ supervisors working tonight so we should be OK."

Company $B$ needs to hire $30$ new employees. Ten percent ($10\%$) of applicants do not meet the basic business requirements for the job. $12\%$ of the remaining applicants do not pass the pre-screening assessment, $23\%$ of those remaining applicants do not show up for the interview, and $5\%$ of those applicants fail the background investigation.

How many applicants need to apply in order to meet the hiring target?

A) $30$; B) $45$; C) $50$; D) $52$; E) $60$.

Consider a solid whose base is the region in the first quadrant bounded by the curve $y=\sqrt{3-x}$ and the line $x=2$ and whose cross sections through the solid perpendicular to the x-axis are squares.
a. Find an expression for the area $A(x)$ of a cross section of the solid at a point $x$ in $[0,2]$ .

b. Write an integral for the volume of the solid.

A projectile is fired upward, and its velocity (in m/s) is given by $v(t)=\frac { 200 } { \sqrt { t + 1 } }$, for $t \geq 0$.

Graph the velocity function for $t \geq 0$.

A customer ordered a product online for $\$299$ and was charged an additional $\$10$ for shipping and handling. The customer received a rebate of $\$99$ and a $\$25$ credit for turning in an old cell phone. After a tax of $4\%$ was applied, how much did the customer pay for the product?

For a given function f, explain the steps used to solve the initial value problem F'(t)=f(t), F(0)=10.

Calculate the work required to stretch the following springs 1.25 m from their equilibrium positions. Assume Hooke's law is obeyed. A spring that requires a force of $250 \mathrm{~N}$ to be stretched $0.5 \mathrm{~m}$ from its equilibrium position.