Draw a cube in one-point perspective so that the vanishing point is to the right of the cube.

Graph the function. y = 1/2 |x|

Complete the table using domain of {-2, -1, 0, 1, 2} for each function shown. Graph each. $f(x)=4(0.5)^{x}$

$$\begin{matrix} \text{x} & \text{-2} & \text{-1} & \text{0} & \text{1} & \text{2}\\ \text{f(x)}\\ \end{matrix}$$

Graph the function. y = x + 3; domain: 0, 1, 2, 3, 4, and 5

(a) Show that the given differential equation has a regular singular point atx=0.(b) Determine the indicial equation, the recurrence relation, and the roots of the indicial equation.(c) Find the series solution(x>0)corresponding to the larger root.(d) If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also. 2x2y''+3xy'+(2x2−1)y=0

(a) Show that the given differential equation has a regular singular point at x=0.(b) Determine the indicial equation, the recurrence relation, and the roots of the indicial equation.(c) Find the series solution(x>0)corresponding to the larger root.(d) If the roots are unequal and do not differ by an integer, find the series solution corresponding to the smaller root also. 3x2y''+2xy'+x2y=0

Jason has two part-time jobs. He earns $15 an hour working at the help desk at a local library. He also mows lawns earning$25 per lawn. How much does he earn in a week if he works at the help desk for 2 hours each on Monday and Wednesday and for 4 hours on Friday and he mows 4 lawns on the weekend?

Suppose that people are equally likely to have been born on any day of the week. You meet a new friend, and ask her on what day of the week she was born. List the simple events in the sample space. What is the probability that she was born on a weekend (Saturday or Sunday)?

Convert the given coordinates to the indicated ordered pair.

$$( 2 , - 2 \sqrt { 3 } ) \text { to } ( r , \theta )$$

Compute and plot the convolution y[n]=x[n]*h[n], where x[n]=(1/3)^-n u[-n-1] and h[n]=u[n-1].

(a) Find the solution of the given initial value problem.

(b) Draw a graph of the solution.

$$y''+3y'+2y=δ(t−5)+u_{10}(t); \ y(0)=0, \ y'(0)=1/2$$

use the Laplace transform to solve the given initial value problem.y(4)−4y”'+6y'−4y'+y=0;y(0)=0,y'(0)=1,y"(0)=0,y"'(0)=1

Furnco manufactures desks and chairs. Each desk uses 4 units of wood, and each chair uses 3. A desk contributes $40 to profit, and a chair contributes$25. Marketing restrictions require that the number of chairs produced be at least twice the number of desks produced. If 20 units of wood are available, formulate an LP to maximize Furnco’s profit. Then graphically solve the LP.

Furnco manufactures tables and chairs. A table requires 40 board ft of wood, and a chair requires 30 board ft of wood. Wood may be purchased at a cost of $1 per board ft, and 40,000 board ft of wood are available for purchase. It takes 2 hours of skilled labor to manufacture an unfinished table or an unfinished chair. Three more hours of skilled labor will turn an unfinished table into a finished table, and 2 more hours of skilled labor will turn an unfinished chair into a finished chair. A total of 6,000 hours of skilled labor are available (and have already been paid for). All furniture produced can be sold at the following unit prices: unfinished table,$70; finished tabic, $140; unfinished chair,$60; finished chair, $110. Formulate an LP that will maximize the contribution to profit from manufacturing tables and chairs.