1. Divide. (Simplify your answer completely.)

÷

2. Solve. (Enter your answers as a comma-separated list.)

+

=

3. Solve by using the quadratic formula. (Enter your answers as a comma-separated list.)

w² + 9w − 5 = 0

w =

4.

Find the coordinates of the x-intercepts of the parabola given by the equation. (If an answer does not exist, enter DNE.)

y = x² − x − 12

Approximate the net signed area under the graph of y=x-1 curve on [0,2], using rectangles with n=4 and n=8 when taking the right end points as your sampling points (sampling points are the points where you are measuring the heights of the rectangles).

Have a picture of the graph and all the specific values. For example, for n=4 , you interval of [0,2] of f(x) will have f(1/2)times delta x +f(1)*delta x+ f(3/2)*delta x+f(2)*delta x=the area of A1+A2+A3+A4=?? Delta x is, of course, the width of our rectangles. It is equal to the distance between the two sampling points! Then you will divide into n=8 subintervals....You will need deltax= (2-0)/8=1/4 , and you will need f(1/4)*deltax+f(2/4)*deltax+... =you will have 8 rectangles. Area= ( approximately) A1+A2+A3+A4+A5+A6+A7+A8

The only solution to the equation x^2 − xy + y^2 = 0 is the origin. Prove that statement is
true by converting to polar coordinates. To be clear, you need to show two things:
a. The origin is a solution to the equation (easy).
b. There is no other point which is a solution to the equation (not easy).

If a non•homogeneous system of equations has one dependent row or equation, then (select all that apply): i) the RREF of the augmented matrix will have a row of zeros ii) there will be infinitely many solutions iii) the complementary homogeneous solution will have many solutions iv) the coefficient matrix will not have an inverse v) none of the above

The product of (7x³ + 5x - 8)(2 - 3x) is _______

Is (x + 2) a factor of P(x) = 4x³ - 6x² + 2x - 12?  Explain.

1.) Using synthetic substitution and the Remainder Theorem, I know that the remainder is ________

2.) Based upon this answer in #1, and in applying the Factor Theorem, I know that (x + 2)_____    is/isn't a factor of P(x) because ______

SHOW how you can completely factor the polynomial expression x³ + x² - 16x + 20

Find the total value TV of the given income stream and also find its present value PV (at the beginning of the given interval) using the given interest rate. (Round your answers to the nearest cent.) R(t) = 14,000e^0.06t, 0 ≤ t ≤ 3, at 8%

Find the total value TV of the given income stream and also find its present value PV (at the beginning of the given interval) using the given interest rate. (Round your answers to the nearest cent.) R(t) = 54,000, 0 ≤ t ≤ 12, at 4%

TV = $

PV = $

Compute the distance from the point x = (-5,5,2) to the subspace W of R³ consisting of all vectors orthogonal to the vector (1, 3, -2).

The surface z = 3x^(2) + (1/6)x^(3) - (1/8)x^(4) - 4y^(2) is intersected by the plane 2x - y = 1. The resulting intersection is a curve on the surface. Find a set of parametric equations for the line tangent to this curve at the point (1,1,-23/24).

The radius of a circular oil slick expands at a rate of 6 m/min.

(a) How fast is the area of the oil slick increasing when the radius is 24 m?

????=
?2/???

(b) If the radius is 0 at time ?=0, how fast is the area increasing after 3 mins?

????=
?2/???

ASK YOUR TEACHER

Recall from Example 1 that whenever Suzan sees a bag of marbles, she grabs a handful at random. She has seen a bag containing three red marbles, four green ones, three white ones, and three purple ones. She grabs eight of them. Find the probability of the following event, expressing it as a fraction in lowest terms. HINT [See Example 1.]

She does not have all the green ones.

Can somebody please do an explanation of each aspect of Stokes' Theorem, including explaining the whole theorem, definitions that are used in the theorem, and the Calculus content that came from those definitions. Every piece should be dissected and explained. When possible, it would great if you explained in your own words instead of a strict definition. I appreciate the help :)

You start a t-shirt manufacturing plant. You spend $8 on each shirt you produce,

and then sell them to a clothing store for $10 each. Each month, your building lease costs you $12000.

(a) Compute a cost function C(x) for the business.
(b) Compute a revenue function R(x) for the business.
(c) Compute a profit function P (x) for the business.

(d) Finally, compute the marginal cost function C(x).

A financial advisor has up to 50,000$ to invest, with the stipulation that at least $15000 is used to purchase Treasury bonds and at most $25,000 in corporate bonds. a) Construct a set of inequalities that describes the relationship between buying corporate vs Treasury bonds, where the total amount invested must be less than or equal to $30,000. ( Let C be the amount of money invested in corporate bonds, and T the amount invested in Treasury bonds) b) construct a feasible region of investment; that is, shade in the area on a graph that satisfies the spending constraints on both corporate and treasury bonds.

Use Simpson's Rule with n = 10 to approximate the area of the surface obtained by rotating the curve about the x-axis. Compare your answer with the value of the integral produced by your calculator. (Round your answer to six decimal places.)

y = x + sqrt x, 2 ≤ x ≤ 5