Find a set of parametric equations to represent the graph of the given rectangular equation using the parameters (a) t = x and (b) t = 2 - x. $y=x^{3}-x^{2}$

Let

$$\mathbf { u } = \langle 3 , - 2 \rangle \text { and } \mathbf { v } = \langle - 2,5 \rangle.$$

Find the component form of the vector.

$$- 2 \mathbf { u } + 5 \mathbf { v }$$

Two and three hundredths is how much less than three and two tenths? Write the answer in words.

For each function, evaluate (a) g(0, 0, 0); (b) g(1, 0, 0); (c) g(0, 1, 0); (d) g(z, x, y); (e) g(x+h, y+k, z+l), provided such a value exists. $g(x, y, z)=\ln (x+y+z)$

-3p + 2(5p - 12) = -73

Use Gaussian elimination to find the complete solution to each system, or show that none exists.

$$\left\{\begin{aligned} 2 x - 3 y + z & = 1 \\ x - 2 y + 3 z & = 2 \\ 3 x - 4 y - z & = 1 \end{aligned} \right.$$

A vertex of a feasible region does not always have whole-number coordinates. Sometimes you may need to round coordinates to find the solution. Using the objective function and the constraints at the right, find the whole-number values of x and y that minimize C Then find C for those values of x and y.

$$\begin{array}{l}{C=6 x+9 y} \\ {\left\{\begin{array}{l}{x+2 y \geq 50} \\ {2 x+y \geq 60} \\ {x \geq 0, y \geq 0}\end{array}\right.}\end{array}$$

use a graphing utility to graph the function and approximate the limit. Write an approximation that is accurate to four decimal places. Then create a table of values for the function and use the result to verify your approximation numerically. lim x→0 e^2x-1/x

This exercise is based on the following Excel sheet, which shows the projected 2020 and 2030 U.S. male and female population in various age groups, as well as per capita incomes.

$$\begin{matrix} & \text{} & \text{2020 Population} & \text{} & \text{2030 population}\\ \text{Age} & \text{Mean Income (\$1000)} & \text{Female (Millions)} & \text{Male (Millions)} & \text{Female (Millions)} & \text{Male (Millions)}\\ \text{15 to 24} & \text{14} & \text{23} & \text{24} & \text{25} & \text{26}\\ \text{25 to 44} & \text{42} & \text{43} & \text{43} & \text{45} & \text{46}\\ \text{45 to 64} & \text{48} & \text{43} & \text{41} & \text{42} & \text{41}\\ \text{65 to 84} & \text{29} & \text{31} & \text{20} & \text{40} & \text{31}\\ \end{matrix}$$

Use matrix algebra to estimate the total income for females in 2020. (Round the answer to two significant digits.)

Use summation notation to write each arithmetic series for the specified number of terms. $5+6+7+\ldots ; n=7$

The symbol P represents an amount of money at a time designated as present. The following symbols also represent a present amount of money and require similar calculations. Explain what each symbol stands for: PW, PV, NPV, DCF, and CC.

Prove u x (v x w) = (u · w)v - (u · v)w.

Compare each pair of graphs and find any points of intersection. $y=\frac{1}{x} \text { and } y=\frac{1}{x^{2}}$

Solve each quadratic equation using any method. $4 x^{2}-25=0$