For the following exercise,

The volume $V$ of a sphere with respect to its radius $r$ is given by $V=\frac{4}{3} \pi r^3$.

Find the instantaneous rate of change of V when r = 3 cm.

Draw all the stereoisomers for each of the following: a. 1-chloro-3-methylpentane e. 1,2-dichlorocyclobutane b. 1-bromo-2-methylpropane f. 1,3-dichlorocyclohexane c. 3-chloro-3-methylpentane g. 1,4-dichlorocyclohexane d. 3,4-dichlorohexane h. 1-bromo-2-chlorocyclobutane

Find the inverse by Gauss-Jordan or state that it does not exist.

Check by using

$$\mathbf{A} \mathbf{A}^{-1}=\mathbf{A}^{-1} \mathbf{A}=\mathbf{I}$$

$$\left[\begin{array}{lll}0 & 8 & 0 \\ 0 & 0 & 4 \\ 2 & 0 & 0\end{array}\right]$$

a) Write an equation for the formation of NH₃(g) from its elements in their standard states. Express your answer as a chemical equation. Identify all of the phases in your answer.

b) Find ΔH°_f for NH₃(g) from Appendix IIB in the textbook. Express your answer using three significant figures.

c) Write an equation for the formation of CO₂(g) from its elements in their standard states. Express your answer as a chemical equation. Identify all of the phases in your answer.

d) Find ΔH°_f for CO₂(g) from Appendix IIB in the textbook. Express your answer using four significant figures.

A manufacturer of projection TVs must ship a total of at least 1000 TVs to its two central warehouses. Each warehouse can hold a maximum of $750 \mathrm{TVs}$. The first warehouse already has $150 \mathrm{TVs}$ on hand, whereas the second has $50 \mathrm{TVs}$ on hand. It costs $\$ 8$ to ship a TV to the first warehouse, and it costs $\$ 16$ to ship a TV to the second warehouse. How many TVs should be shipped to each warehouse to minimize the cost? What is the minimum cost?

A car travels at an average speed of $30 \mathrm{~mph}$ for $1 \mathrm{~mi}$. Is it possible for the car to increase its speed during the next mile so that its average speed for the $2 \mathrm{~mi}$ is $60 \mathrm{~mph}$?

Sketch all the possible stereoisomers of (a) [Rh(bipy) $\left.(o-\text { phen })_2\right]^{3+}$, (b) $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3(\text { bipy }) \mathrm{Br}\right]^{2+}$, (c) square-planar $\left[\mathrm{Pd}(e n)(\mathrm{CN})_2\right]$

Use the boundedness theorem to show that the real zeros of $P(x)$ satisfy the given conditions.

$P(x)=2 x^5-x^4+2 x^3-2 x^2+4 x-4$; no real zero greater than $1$

Use Descartes's rule of signs to determine the possible number of positive real zeros and the possible number of negative real zeros for each function. $f(x)=x^{5}+3 x^{4}-x^{3}+2 x+3$

What is the instantaneous rate of change at x=-2 of the function $f(x)=\frac{x-1}{x^{2}+2}$? (A) $-\frac{1}{6}$, (B) $\frac{1}{9}$, (C) $\frac{1}{2}$, (D) -1.

Name the following compounds. a. $\mathrm{Na}_2 \mathrm{SO}_4$ b. $\mathrm{Na}_3 \mathrm{~N} \quad c. \mathrm{CuCl}$ d. $\mathrm{Cr}_2 \mathrm{O}_3$

In the equation $P=B \times R, P=$ part, $B=$ base, or whole, and $R=$ rate, or percent. Use the following forms of the equation to solve this application problem.

$$P=B \times R \quad B=\frac{P}{R} \quad R=\frac{P}{B}$$

You will first need to read the problem carefully to determine whether base, part, or rate is unknown. Round rates to the nearest tenth of a percent.

College students are offered a $6\%$ discount on a dictionary that sells for $\$ 18.50$. Find the reduced price.

Write the expression in simplest form. Assume all variables are positive.

$$√75x^5y^6/36xz^5$$

The line segments A̅B̅C̅ and P̅Q̅R̅ are divided proportionally by B and Q. AB < BC and PQ < QR. Find AB and BC when AC = 21, PQ = 14, and QR = 35.