Describe in words how to take a partial derivative.

Determine the polynomial function whose graph passes through the point.

$$(0.072,0.203),(0.120,0.238),(0.148,0.284)$$

(a) Derive an equation for converting Fahrenheit temperatures directly to absolute temperatures in kelvins. (b) Which is the lower temperature, $300^{\circ} \mathrm{F}$ or 300 K?

Can you increase the rotational kinetic energy of a wheel without changing its translational kinetic energy? Explain.

Use a software program or a graphing utility to solve the system of linear equations.

$$\begin{align*} 3x+3y+12z &= 6\\ x+y+4z &= 2 \\ 2x+5y +20z &= 10 \\ -x +2y+8z &= 4 \end{align*}$$

Solve the system of linear equations.

$$\begin{align*} x_1 - 2x_2 &= 0 \\ 6x_1+2x_2 &= 0 \\ \end{align*}$$

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. $\lim _{x \rightarrow 0} \frac{x}{e^{x}}=1$

The Michaelis-Menten equation models the rate v of an enzymatic reaction as a function of the concentration [S] of a substrate S. In the case of the enzyme chymotrypsin the equation is $v=\frac{0.14[\mathrm{S}]}{0.015+[\mathrm{S}]}$ Use a graphing calculator or computer to graph v as a function of [S].

Solve the system of linear equations.

$$\begin{align*} 0.05x_1 - 0.03x_2 &= 0.21 \\ 0.07x_1+0.02x_2 &= 0.17 \\ \end{align*}$$

Isoprene has sometimes been used as a starting material in the laboratory synthesis of terpenes. In one such synthesis, the first step is the electrophilic addition of 2 mol of hydrogen bromide to isoprene to give 1,3 dibromo-3-methylbutane. Write a series of equations describing the mechanism of this reaction.

Sketch the image of the unit square [a square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1)] under the specified transformation. T is the shear represented by T(x, y) = (x + 2y, y).

Use the bond dissociation enthalpy data in the table to calculate $\Delta H^{\circ}$ for (a) the monofluorination and (b) the monoiodination of methane. What is the main reason the values are so different?

Solve the quadratic equation. a. $-5 x^{2}-19=144$ b. $3 x^{2}+17=209$

There are four distinctly different K mesons. Why do we not assign to them the isospin quantum number T = 3/2 so that they would constitute an isospin quartet?