Consider a $15-\mathrm{cm} \times 20-\mathrm{cm}$ printed circuit board $\mathrm{(PCB)}$ that has electronic components on one side. The board is placed in a room at $20^{\circ} \mathrm{C}$. The heat loss from the back surface of the board is negligible. If the circuit board is dissipating $8 \mathrm{~W}$ of power in steady operation, Find the average temperature of the hot surface of the board, assuming the board is $(a)$ vertical; $(b)$ horizontal with hot surface facing up; and $(c)$ horizontal with hot surface facing down. Take the emissivity of the surface of the board to be $0.8$ and assume the surrounding surfaces to be at the same temperature as the air in the room.

Use Stokes’ Theorem to evaluate

$$\mathbf{F}(x,y,z)=(x+y^2-2)\mathbf{i}+2xy\mathbf{j}+(x^2+yz^2)\mathbf{k};$$

S is the part of the paraboloid z = 4 - x squared - y squared above the xy-plane with an outward normal

Use a graphing utility to approximate (rounded to two decimal places) the local maximum value and local minimum value of $f(x)=x^{3}-2 x^{2}-4 x+5,$ for -3 < x < 3.

At what value of x does the quadratic function $f(x)=a x^{2}+b x+c, a \neq 0,$ have a stationary point? Under what conditions is the stationary point a local maximum or a local minimum?

Bird Migration Power P is the rate at which energy E is consumed per unit time. Ornithologists have found that the power consumed by a certain pigeon flying at velocity $v \mathrm{~m} / \mathrm{s}$ is described well by the function $P(v)=17 v^{-1}+10^{-3} v^3 \mathrm{~J} / \mathrm{s}$. Assume that the pigeon can store $5 \times 10^4 \mathrm{~J}$ of usable energy as body fat. (a) Find the velocity $v_{\text {pmin }}$ that minimizes power consumption.

What is the product of two squared and two to the sixth power? express using exponents.

You have a 1-m-wide, 2-m-long 14-kg wooden board. If you place a 5.0-kg pot of soup in one corner of the board, where is the center of mass of the board-pot system?

What is the chance that the next person I meet will be different from me? The diversity index, from 0 (no diversity) to 100, measures the chance that two randomly selected people are of a different race or ethnicity. The diversity index in the United States varies widely from region to region, from as high as 81 in Hawaii to as low as 11 in Vermont. The bar graph at the top of the next column shows the national diversity index for the United States for four years the period from 1980 through 2010.

The data in the graph can be modeled by the formula

$$D=0.7 x+34 \text {, }$$

where $D$ is the national diversity index for the United States $x$ years after 1980.

How well does the formula model the national diversity index for 2010?

Which end of the muscle typically moves?

Provide structures for the semicarbazone and the $2,4$-dinitrophenylhydrazone of citral.

Complete the square for this expression. Write the resulting expression as a binomial squared.

$$x^2-x+ \square$$

Consider a 15-cm × 20-cm printed circuit board (PCB) that has electronic components on one side. The board is placed in a room at $20^\circ C.$ The heat loss from the back surface of the board is negligible. If the circuit board is dissipating 8 W of power in steady operation, determine the average temperature of the hot surface of the board, assuming the board is (a) vertical, (b) horizontal with hot surface facing up, and (c) horizontal with hot surface facing down. Take the emissivity of the surface of the board to be 0.8 and assume the surrounding surfaces to be at the same temperature as the air in the room. Evaluate air properties at a film temperature of $32.5^\circ C$ and 1 atm pressure. Is this a good assumption?

How do negative signs on residuals affect the sum of squared residuals?

Identify and describe two muscle tissues.