To enclose a yard, a fence is built against a large building, so that fencing material is used only on three sides. Material for the ends costs $15 per ft; material for the side opposite the building costs$25 per ft. Find the dimensions of the yard of maximum area that can be enclosed for $2400.

Compound A has the molecular formula $\mathrm{C}_{14} \mathrm{H}_{25} \mathrm{Br}$ and was obtained by reaction of sodium acetylide with 1, 12-dibromododecane. On treatment of compound A with sodium amide, it was converted to compound B ($\mathrm{C}_{14} \mathrm{H}_{24}$). Ozonolysis of compound B gave the diacid $\mathrm{HO}_{2} \mathrm{C}\left(\mathrm{CH}_{2}\right)_{12} \mathrm{CO}_{2} \mathrm{H}$. Catalytic hydrogenation of compound B over Lindlar palladium gave compound C ($\mathrm{C}_{14} \mathrm{H}_{26}$), and hydrogenation over platinum gave compound D ($\mathrm{C}_{14} \mathrm{H}_{28}$). C yielded $\mathrm{O} \square \mathrm{CH}\left(\mathrm{CH}_{2}\right)_{12} \mathrm{CH} \square \mathrm{O}$ on ozonolysis. Assign structures to compounds A through D so as to be consistent with the observed transformations.

A rectangular field is bounded on one side by a river and on the other three sides by a fence. Find the dimensions of the field that will maximize the enclosed area if the fence has a total length of 320 ft.

A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30 degree. At what rate is the distance from the plane to the radar station increasing a minute later?

If a ball is thrown vertically upward with a velocity of 80 ft/s, then its height after t seconds is s = 80t - 16t^2. What is the maximum height reached by the ball?

Find the following. $\int\left(6 t^{2}-8 t+7\right) d t$

Determine concavity and the x-values where points of inflection occur. Do not sketch the graphs. $y=\frac{1}{10} x^{5}-3 x^{3}+17 x+43$

Show that the function $f(x)=\frac{x}{x+1}$ is increasing on any interval not containing x=-1.

In a discussion of an inferior good, Persky$^{4}$ solves an equation of the form $u_{0}=A \ln \left(x_{1}\right)+\frac{x_{2}^{2}}{2}$ for $x_{1},$ where $x_{1}$ and $x_{2}$ are quantities of two products, $u_{0}$ is a measure of utility, and A is a positive constant. Determine $x_{1}.$

Solve the systems algebraically.

$$\left\{\begin{array}{l} {\frac{1}{2} z-\frac{1}{4} w=\frac{1}{6}} \\ {\frac{1}{2} z+\frac{1}{4} w=\frac{1}{6}} \end{array}\right.$$

Based on the E1 mechanism for the conversion of a tertiary alkyl chloride to an alkene as summarized in arrows 3 and 4, which arrow(s) correspond(s) to exothermic processes? A. Arrow 3 B. Arrow 4 C. Both 3 and 4 D. Neither 3 nor 4

Find the volume of the cone. Round your answer to the nearest tenth. Radius = 2 ft, Height = 6 ft

Express the area under the curve $y=x^{4}+5 x^{2}+x$ from 2 to 7 as a limit.

A small-appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a week and$12,000 to produce 1500 toaster ovens a week. Express the cost as a function of the number of toaster