For each demand equation, express the total revenue R as a function of the price p per item, sketch the graph of the resulting function, and determine the price p that maximizes total revenue in each case. q=−5p+1,200

Find the 32 nd term of each sequence. $213,201,189,177, \dots$

Evaluate the following integrals using the method of your choice. A sketch is helpful. $\iint _ { R } \frac { d A } { 4 + \sqrt { x ^ { 2 } + y ^ { 2 } } } ; R = \{ ( r , \theta ) : 0 \leq r \leq 2 \pi / 2 \leq \theta \leq 3 \pi / 2 \}$

The price p (in dollars) and the quantity x sold of a certain product obey the demand equation $p=-\frac{1}{3} x+100$ (a) Find a model that expresses the revenue R as a function of x. (b) What is the domain of R? (c) What is the revenue if 100 units are sold? (d) What quantity x maximizes revenue? What is the maximum revenue? (e) What price should the company charge to maximize revenue?

Evaluate the expression. 32. 5(2)² - 6

Solve the inequality by using tables or graphs.

$$x ^ { 2 } + 2 x - 4 \geq – 1$$

Find the associated exponential decay or growth model. Q=1,000 when t=0; half-life=1

$f(x)=\sin x,-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}, g(x)=\cos x, 0 \leq x \leq \pi,$ and $h(x)=\tan x,-\frac{\pi}{2}<x<\frac{\pi}{2}$. Find the exact value of each composite function. $g^{-1}\left(f\left(-\frac{5 \pi}{6}\right)\right)$

Write an exponential growth or decay function to model each situation. Then find the value of the function after the given amount of time. An antique car is worth $32,000, and its value grows by 7% per year; 5 years.

Find the associated exponential decay or growth model. Q=2,000 when t=0; half-life=5

Perform the multiplication or division and simplify. $\frac{5}{x-1} \cdot \frac{x-1}{25(x-2)}$

Find the steady-state temperature u(x, y) in the infinite plate defined by $-\infty<x<\infty, y>0$ if the boundary condition at y = 0 is

$$u(x, 0)=\left\{\begin{array}{ll}{u_{0},} & {|x|<1} \\ {0,} & {|x|>1}\end{array}\right.$$

.

Complete the table. What can you conclude?

$$\begin{matrix} \text{x} & \text{0} & \text{1} & \text{2} & \text{3} & \text{4} & \text{5} & \text{6}\\ \ {\frac{x-3}{x^{2}-x-6}}\\ \ {\frac{1}{x+2}}\\ \end{matrix}$$

Find the values of x and y that satisfy the equation. -10x + 12i = 20 + 3y