A room has volume 100m³, and initially contains normal air. Every minute, 2m³ of gas is pumped in, which is 1.9m³ air, and 0.1m³ xenon. Every minute, 2m³ of well-mixed gas is pumped out. What volume of xenon will be in the room after 1 hour?

Factor the polynomial as a product of linear factors: x⁴-5x³+12x²-2x-20

Separation of Variables:

The rate at which fuel is being used by a Wartsila-Sulzer RTA96-C Turbocharged Diesel Engine is proportional to the amount of fuel already consumed at time t. If there are 2 gallons consumed when t 0 and 3 gallons consumed when t 5, how many gallons will be used when t = 9?

A group of retailers will buy 116 televisions from a wholesaler if the price is $300 and 156 if the price is $250. The wholesaler is willing to supply 104 if the price is $220 and 184 if the price is $310. Assuming that the resulting supply and demand functions are linear, find the equilibrium point for the market. (q, p) =

(a) Show that B {[2, 3, 0,1],[1, 1, 1,1]} is a maximal linearly independent subset of S {[1, 4, 1,2],[1, 1, 1,1],[3, 2,1, 0],[2, 3, 0,1]}.

(b) Calculate dim(span(S)).

(c) Does span(S) R4? Why or why not?

An elastic band is hung on a hook and a mass is hung on the lower end of the band. When the mass is pulled downward and then released, it vibrates vertically. The equation of motion is ? = 2 /3 cos(8?)− 1 /6 sin(8?), ? ≥ 0, where ? is measured in centimeters and ? in seconds. (Take the positive direction to be downward.)

g. How far from its equilibrium position does the mass travel?

h. Find the total distance traveled by the mass during the first 4? seconds.

i. When is the mass speeding up when heading downward?

1. Tickets for the school play cost $5 for students and $8 for adults. On opening night, all 360 seats were filled, and the box office revenues were $2610. How many student and how many adult tickets were sold?

2. A $76,000 trust is to be invested in bonds paying 8%, CDs paying 7%, and mortgages paying 10%. The bond and CD investment must equal the mortgage investment. To earn a $6670 annual income from the investments, how much should the bank invest in bonds?

3. Suppose that Janine desires 46 grams of protein and 38 grams of dietary fiber daily. One serving of kidney beans has 8 grams of protein and 6 grams of dietary fiber. One serving of refried pinto beans has 6 grams of protein and 6 grams of dietary fiber. If a serving of kidney beans costs $0.45 and a serving of refried pinto beans costs $0.35, then how many servings of each should Janine eat to minimize cost and still meet her requirements?

Suppose you want to buy a new car and trying to choose between two models:

Model A: costs $17,000 and its gas mileage is 20 miles per gallon and its insurance is $200 per year.

Model B: costs $25,000 and its gas mileage is 35 miles per gallon and its insurance is $400 per year.

If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:

Find a formula for the total cost of owning Model A where the number of years is the independent variable.

Find a formula for the total cost of owning Model B where the number of years is the independent variable.

Find the total cost for each model for the first five years.

If you plan to keep the car for four years, which model is more economical? How about if you plan to keep it for six years?

Find the number of years in which the total cost to keep the two cars will be the same.

Identify the number of months where neither car holds a cost of ownership advantage.

What effect would the cost of gas doubling have on cost of ownership? Graph or show hand calculations.

If you can sell neither car for 40% of its value at any time, how does the analysis change? Graph or show hand calculations.

Find a point within a triangle such that the sum of the square of its distances from the three angular points is a minimum.

1.The domain of r(t)=〈sin(t),cos(t),ln(t+1)〉 is

Select one:

a. (−∞,−1]
b. (π,2π)

c. (−∞,−2]
d. (−π,2π)
e. ℝ

f. (−1,∞)

2. The limt→πr(t) where r(t)=〈t2,et,cos(t)〉 is

Select one:

a. 〈π2,eπ,−1〉

b. undefined

c. 〈π2,eπ,1〉
d. π2+eπ
e. 〈π2,eπ,0〉

3.Let v(t)=〈2t,4t,t2〉. Then the length of v′(t) is

Select one:

a. 20‾‾‾√+2t

b. 20+4t2

c. 20+2t‾‾‾‾‾‾‾√

d. 20+4t2‾‾‾‾‾‾‾‾√

e. 6+2t‾‾‾‾‾‾√
f. 1

4. The curvature of a circle centred at the origin with radius 1/3 is

Select one:

a. 1

b. 1/3

c. undefined

d. 3

e. 10

Evaluate the following integral using the Midpoint Rule​ M(n), the Trapezoidal Rule​ T(n), and​ Simpson's Rule​ S(n) using nequals4. Integral from 2 to 6 StartFraction dx Over x cubed plus x plus 1 EndFraction Using the Midpoint​ Rule, ​M(4)equals

plot each point and form the triangle ABC. Verify that the triangle ABC is a right triangle. Find its area. A= (-5, 10) B (2,7) C (-1,0)

"If A and B are similar then A and B are orthogonally similar. " Prove or disprove this statement.

Find the vertex, focus, directrix, and focal width of the parabola.

(y + 2)^{2 = -8(x - 1)}