A manufacturing plant is designed to be in the shape of a regular pentagon with 92.5 ft on each side. A security fence surrounds the building to form a circle, and each corner of the building is to be 25.0 ft from the closest point on the fence. How much fencing is required?

Solve for the specified variable. $\triangle s$ = s_2 - s_1 for s_1

A rectangular piece of sheet metal is 2 in. longer than it is wide. A square piece 3 in. on a side is cut from each comer. The sides are then turned up to form an uncovered box of volume $765 \mathrm{in} .^{3}$. Find the dimensions of the original piece of metal.

Let $\mathbf{x}=\mathbf{x}_{0}+t \mathbf{v}$ be a line in $R^{n}$, and let $T : R^{n} \rightarrow R^{n}$ be a linear operator on $R^{n}$. What kind of geometric object is the image of this line under the operator T? Explain your reasoning.

A stairway 1.0 m wide goes from the bottom of a cylindrical storage tank to the top at a point halfway around the tank. The handrail on the outside of the stairway makes an angle of 31.8 degrees with the horizontal, and the radius of the tank is 11.8 m. Find the length of the handrail.

A friend says that only mirrors and other shiny surfaces reflect light. Explain what is wrong with this reasoning.

Solve the linear system by Gauss-Jordan elimination.

$$\begin{aligned} 2 x_{1}+2 x_{2}+2 x_{3} &=0 \\-2 x_{1}+5 x_{2}+2 x_{3} &=1 \\ 8 x_{1}+x_{2}+4 x_{3} &=-1 \end{aligned}$$

Find the interval of convergence for the power series.

$$\sum_{k=1}^{\infty} \frac{(-1)^{k} x^{k}}{9 k^{2}-1}$$

Part of the Tower Bridge in London is a drawbridge. This part of the bridge is 76.0 m long. When each half is raised, the distance between them is 8.0 m. What angle does each half make with the horizontal?

Briefly explain whether investors should expect a higher return from holding portfolio A versus portfolio B under capital asset pricing theory (CAPM). Assume that both portfolios are fully diversified.

$$\begin{matrix} \text{ } & \text{Portfolio A} & \text{Portfolio B}\\ \text{Systematic risk (beta)} & \text{1.0} & \text{1.0}\\ \text{Specific risk for each individual security} & \text{High} & \text{Low}\\ \end{matrix}$$

Polaris is always directly over (a) the North Pole. (b) any location north of the equator. (c) the equator. (d) the South Pole.

Explain two criticisms of the DSM.

A bar magnet whose mass is 0.02 kg and whose magnetic dipole moment is $\langle 6,0,0\rangle\ \mathrm{A} \cdot \mathrm{m}^{2}$ is suspended on a low-friction pivot in a region where external coils apply a magnetic field of $\langle 1.5,0,0\rangle\ \mathrm{T}.$ You rotate the bar magnet slightly in the horizontal plane and release it. What is the angular frequency of the oscillating magnet?

Consider the following portfolio. You write a put option with exercise price $90 and buy a put with the same expiration date with exercise price$95. a. Plot the value of the portfolio at the expiration date of the options. b. Now, plot the profit of the portfolio. Hint: Which option must cost more?