You are working in a laboratory that studies the effects of currents in various crystals. One of the experiments involves a requirement for a steady current of I = 0.500 A in a wire that delivers the current to the crystal. Both the wire and the crystal are in a chamber whose interior temperature T will vary from $-40.0^{\circ} \mathrm{C}$ to $150^{\circ} \mathrm{C}$. The wire is made of tungsten and is of length L = 25.0 cm and radius r = 1.00 mm A test run is being made before the crystal is added to the circuit. Your supervisor asks you to determine the range of voltages that must be supplied to the wire in the test run to maintain its current at 0.500 A.

Use the General Power Rule to find the derivative of the function. $s(t)=\sqrt{2 t^{2}+5 t+2}$

A student of mass 60.0 kg, starting at rest, slides down a slide 20.0 m long, tilted at an angle of $30.0^{\circ}$ with respect to the horizontal. If the coefficient of kinetic friction between the student and the slide is 0.120, find the force of kinetic friction.

The compressibility $\kappa$ of a substance is defined as the fractional change in volume of that substance for a given change in pressure:

$$\kappa=-\frac{1}{V} \frac{d V}{d P}$$

(a) Explain why the negative sign in this expression ensures $\kappa$ is always positive. (b) Show that if an ideal gas is compressed isothermally, its compressibility is given by $\kappa_{1}=1 / P$. (c) Show that if an ideal gas is compressed adiabatically, its compressibility is given by $\kappa_{2}=1 /(\gamma P) .$ Determine values for (d) $\kappa_{1}$ and (e) $\kappa_{2}$ for a monatomic ideal gas at a pressure of 2.00 atm.

Three moles of an argon gas are at a temperature of 275 K. Calculate the root-mean-square (rms) speed of an atom in the gas.

Let x=-4 and y=2. Evaluate each expression. $|-3 x+4 y|$

Work each problem. Find a value of c so that $y=x^2-10x+c$ has exactly one x-intercept.

Discuss the validity of each statement. If the statement is always true, explain why. If not, give a counterexample. If f is a polynomial, then, as x approaches 0, the right-hand limit exists and is equal to the left-hand limit.

Write the augmented matrix for each system and give its dimension. Do not solve.

$$\begin{aligned} &4 x-2 y+3 z-4=0\\ &3 x+5 y+z-7=0\\ &5 x-y+4 z-7=0 \end{aligned}$$

Perform each operation. Write answers in standard form. $(4-3 i)^{2}$

In a study designed to investigate the effects of a strong magnetic field on the early development of mice, ten cages, each containing three 30-day-old albino female mice, were subjected for a period of 12 days to a magnetic field having an average strength of 80 Oe/cm. Thirty other mice, housed in ten similar cages, were not put in the magnetic field and served as controls. Listed in the table are the weight gains, in grams, for each of the twenty sets of mice.

$$\scriptstyle \begin{array}{c} \hline \text { In Magnetic Field } & \text { Not in Magnetic Field } \\ \hline\end{array}$$

$$\scriptstyle\begin{array}{cccc} \text { Cage } & \text { Weight Gain (g) } & \text { Cage } & \text { Weight Gain (g) } \\ \hline 1 & 22.8 & 11 & 23.5 \\ 2 & 10.2 & 12 & 31.0 \\ 3 & 20.8 & 13 & 19.5 \\ 4 & 27.0 & 14 & 26.2 \\ 5 & 19.2 & 15 & 26.5 \\ 6 & 9.0 & 16 & 25.2 \\ 7 & 14.2 & 17 & 24.5 \\ 8 & 19.8 & 18 & 23.8 \\ 9 & 14.5 & 19 & 27.8 \\ 10 & 14.8 & 20 & 22.0 \\ \hline \end{array}$$

Test whether the variances of the two sets of weight gains are significantly different. Let $\alpha=0.05 .$ For the mice in the magnetic field, $s_{X}=5.67 ;$ for the other mice, $s_{Y}=3.18$.

Particle accelerators, such a s the Large Hadron Collider, use magnetic fields to steer charged particles a round a ring. Consider a proton ring with 36 identical bending mag nets connected by straight segments. The protons move along a 1.0-m-long circular arc as they pass through each magnet. What magnetic field strength is needed i n each magnet to steer protons around the ring with a speed of $2.5 \times 10^{7} \mathrm{m} / \mathrm{s}$? Assume that the field is uniform inside the magnet, zero outside.

Find the relative rate of change of f(x) at the indicated value of x. Round to three decimal places. f(x)=420-5 x; x=25

Monochromatic light at 577 nm illuminates a diffraction grating with 325 lines/mm. Determine the highest order that can be observed with this grating at the given wavelength.