Consider the production of gold during the California gold rush (1848–1888). The production of gold can be modeled by $G(t)=\frac{(25 t)}{\left(t^{2}+16\right)},$ where t is the number of years since the rush began $(0 \leq t \leq 40)$ and G is ounces of gold produced (in millions). Find when the maximum (local and global) gold production occurred, and the amount of gold produced during that maximum.

Find the local and/or absolute maxima for the function over the specified domain.

$$f(x)=x^{2}+3 \text { over }[-1,4]$$

Compare the Lilliputians with the Brobdingnagians. Then write a sentence stating the major difference between the two societies.

Find the length of the curve. $r(t)=\lang{t,\ 3cost, 3sint \rang},\ -5\leq t \leq 5$

Solve. Locate 5 points on the first graph so that it shows a function. Then change one number in one of the ordered pairs. Locate the new set of points on the second graph to show a relation that is not a function. Explain your strategy.

Determine whether the function y = x²e^x - 5x² is a solution of the differential equation xy’ - 2y = x³e^x.

Solve. $10=26-2 \sqrt{5 x-1}$

Sketch a graph of $y=x^{3}.$

Find the expected value of the probability distribution

$$\begin{array}{ccccc}{x} & {15} & {18} & {21} & {24} \\ {p} & {0.20} & {0.25} & {0.30} & {0.25}\end{array}$$

Let $X$ be the random variable whose value is $n$ if the first success occurs on the $n$th trial when independent Bernoulli trials are performed, each with probability of success $p$. a) Find a closed formula for the probability generating function $G_x$. b- Find the expected value and the variance of $X$ using the closed form for the probability generating function found in part (a).

How many moles of H+ ions are present in the following aqueous solutions?

1.4 mL of 0.75 M hydrobromic acid,

Verify that the following functions are solutions to the given differential equation. $y = 2 e ^ { - x } + x - 1 \text { solves } y ^ { \prime } = x – y$

The output voltage of an AC generator is given by $\Delta v = \left( 1.20 \times 10 ^ { 2 } \mathrm { V } \right) \sin ( 30 \pi t )$. The generator is connected across a 0.500-H inductor. Find the rms voltage across the inductor.

In Ben's state, the weekly unemployment compensation is 55% of the 26-week average for the two highest-salaried quarters. A quarter is three consecutive months. For July, August, and September, Ben earned a total of $22,400. In October, November, and December, he earned a total of$22,800. Determine Ben's weekly unemployment compensation.