Find the values of the six trigonometric functions of an angle $\theta$ in standard position with point $P(-3,4)$ on the terminal side of the angle.

Length of a shadow A straight road makes an angle of $15^{\circ}$ with the horizontal. When the angle of elevation of the sun is $57^{\circ}$, a vertical pole at the side of the road casts a shadow $75$ feet long directly down the road, as shown in the figure. Approximate the length of the pole.

If the cost of producing x items is given by the function C(x), and the total revenue when x items are sold is R(x), then the profit function is P(x)=R(x)-C(x). Show that the instantaneous rate of change in profit is 0 when the marginal revenue equals the marginal cost.

Cost, revenue, and profit The total cost and total revenue for a certain product are given by

$$\begin{aligned} &C(x)=38.80 x+4500 \\ &R(x)=61.30 x \end{aligned}$$

(a) Find the marginal cost.

(b) Find the marginal revenue.

( c ) Find the marginal profit.

(d) Find the number of units required to break even.

a force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find θ when F = 5000 pounds and W = 15000 pounds.

find the binomial coefficient. 20C20

Find the indicated nth partial sum of the arithmetic sequence. $0.5,1.3,2.1,2.9, \ldots, n=10$

The floor function $f(x)=\lfloor x\rfloor$ gives the greatest integer smaller than or equal to $x$. This function is not continuous on the interval $[1,3]$. Show that $f$ is integrable on $[1,3]$ and that $\int_1^3\lfloor x\rfloor d x=3$.

Determine another point on a line given two points on the line.

$$(2,-4),(4,-2)$$

Use double integration to find the volume of each solid. The solid bounded by the cylinder x²+y²=9 and the planes z=0 and z=3-x.

write the first five terms of the geometric sequence. a1 = 8, r = 2

In this exercise , find the standard form of the equation of the ellipse with center at the origin.

Foci: $(\pm 5,0)$; Major axis of length 12

Find an equation of the ellipse with center at the origin.

Foci: $(\pm 5,0)$; Major axis of length $12$

In this exercise, evaluate using Pascal's Triangle.

$$\left(\begin{array}{l}8 \\ 7\end{array}\right)$$