Consider two rectangular surfaces perpendicular to each other with a common edge which is $1.6 \mathrm{~m}$ long. The horizontal surface is $0.8 \mathrm{~m}$ wide and the vertical surface is $1.2 \mathrm{~m}$ high. The horizontal surface has an emissivity of $0.75$ and is maintained at $400 \mathrm{~K}$. The vertical surface is black and is maintained at $550 \mathrm{~K}$. The back sides of the surfaces are insulated. The surrounding surfaces are at $290 \mathrm{~K}$, and can be considered to have an emissivity of $0.85$. Find the net rate of radiation heat transfers between the two surfaces, and between the horizontal surface and the surroundings.

Use inductive reasoning to predict the next equation in the pattern.

$$\begin{aligned} &5=\frac{5(2)}{2}\\ &5+10=\frac{10(3)}{2} \\ &5+10+15=\frac{15(4)}{2} \\ &5+10+15+20=\frac{20(5)}{2} \end{aligned}$$

Consider the surface represented by the vector-valued function r(u, v) = 3 cos v cos ui + 3 cos v sin uj + sin vk. Use a computer algebra system to do the following. (a) Graph the surface for 0 ≤ u ≤ 2π and -π/2 ≤ v ≤ π/2. (b) Graph the surface for 0 ≤ u ≤ 2π and π/4 ≤ v ≤ π/2. (c) Graph the surface for 0 ≤ u ≤ π/4 and 0 ≤ v ≤ π/2. (d) Graph and identify the space curve for 0 ≤ u ≤ 2π and v = π/4. (e) Approximate the area of the surface graphed in part (b). (f ) Approximate the area of the surface graphed in part (c).

Find a parametric representation for the surface.

Write an expression using powers. Then answer the questions using numbers in standard form. A photo album has 6 sections. Each section contains 6 pages and each page holds 6 photos. How many photos can be placed in the album?

Find the equation of the ellipse that will just fit inside a box that is 8 units wide and 4 units high.

Electric current is measured using the unit of____

A series LRC-circuit has resistor of 8 ohms, an inductor of 1 henry and capacitor of 0.04 farads. The initial charge on the capacitor is 1 coloumb, and there is initially no current in the circuit. Assume $V(t)=0$ for $t>0$. (a) Formulate the IVP for the charge across the capacitor. (b) Determine the charge across the capacitor for $t>0$. (c) Find the current in the circuit for $t>0$. (d) What are the long-term values of charge and current in the circuit?

Find the surface area of the prism.

A bank advertises an account that pays a monthly interest rate of 0.3% compounded continuously. What value do you use for r in the continuously compounded interest formula? Explain.

Describe and sketch the surface.

$$z=3$$

Mary purchases a 12-year bond for $60,000.00. At the end of 12 years, she will redeem the bond for approximately$95,600.00. If the interest is compounded quarterly, what was the interest rate on the bond?

The decimal digits 0 through 5 are encoded as 3-bit binary numbers. They are transmitted in disjoint windows of length 3 least significant bit first and are input to a Mealy model circuit. The circuit generates an output of 1 (0) when the third bit is received if the 3 bits have even (odd) parity; the circuit output is a don’t-care for the first 2 bits. Construct an incompletely specified table for the circuit.

A hydrogen atom at rest in the laboratory emits the Lyman $\alpha$ radiation. (a) Compute the recoil kinetic energy of the atom. $(b)$ What fraction of the excitation energy of the $n=2$ state is carried by the recoiling atom?