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

Each Year the Leadership Class holds a dance to raise money. The dance is rarely well attended because the sponsor belongs to an older generation that is unfamilier with today's taste in music. The profit, P, made on the dance can be modeled by the function written below. The ticket price, t, is in dollars.

P(t) = -16t² +800t - 4000 P(t) = -16(t-25)² + 6000 P(t) = -16(t² -50t +250)

1. The break even point (where profit is zero) = ?

2. The loss if the dance gets cancelled and no tickets are sold = ?

3. The number of tickets sold to maximize profit = ?

4. The maximum profit = ?

5. The number of tickets sold to make a profit of $2400 = ?

find a 3x3 solution using substitution

5x-2y+3z=20

2x-4y-3z=-9

x+6y-8z=21

A plane flying horizontally at an altitude of 2 mi and a speed of 510 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 3mi away from the station. (Round your answer to the nearest whole number.)

A medical study has shown that the first 20 days of radiation therapy, a particular type of malignant tumor decreases at a rate according to the function M'(t)=−0.015t^2+0.01t where MM represents the mass (in grams) of the tumor and tt is the time (in days) since the beginning of the radiation treatment. If a tumor of this particular type has a mass of 150 grams just prior to the start of radiation treatment,

a. Rounded to the nearest tenth, at what rate will the tumor be changing in 5 days?  grams per day

b. in 20 days?  grams per day

c.c. Rounded to the nearest tenth, what will the mass of the tumor be in 5 days?  grams

d.d. in 20 days?  grams

Find the rank and the nullity of the linear transformation:

T : P2 → P1, T(? + ?? + ??^2) = (? + ?) + (? − ?)x

Transformation: Given the function f(x) = 4x³ - 2x + 7, find each of the following. Then discuss how each expression differs from the other.

a) f(x) + 2

b) f (x + 2)

c) f(x) + f (2)

Unit 6 DQ Follow-up #1: Variation

Unit 6 DQ Follow-up # 1 question: If y varies directly as , explain why doubling x would not cause y to be doubled as well.

Unit 6 DQ Follow-up #2: Variation

Unit 6 DQ1 Follow-up #2 Question: If y varies directly as x and x varies inversely as z, how does y vary with regard to z? Why?

Use a system of equations to find the parabola of the form

y=ax^2+bx+c

that goes through the three given points.

(2,-12)(-4,-60)(-3,-37)

The weight of an object on a planet is directly proportional to the weight of the object on Earth. A 12 pound object on Earth weighs 54 pounds on this planet. Express the weight of an object on this planet, y, as a function of the weight of the object on Earth, x . Round the k value to 3 decimal places.

Find the work (in ft-lb) required to pump all the water out of a cylinder that has a circular base of radius 6 ft and height 200 ft. Use the fact that the weight-density of water is 62.4 lb/ft3.

Find the work (in ft-lb) required to pump all the water out of the cylinder if the cylinder is only half full.

5. The concentration of hydronium ions C in a solution with a pH of x is C = 10−x , with C measured in moles per liter. How quickly is the pH changing when the pH is 9 and the concentration is increasing by 2 · 10−10 (moles per liter) per minute?

6. A spherical balloon is being deflated while keeping its shape. How quickly is its surface area changing when the radius is 3 cm and the volume is decreasing by 1 cubic centimeter per second? (Hint: first find out how quickly the radius is changing.)

5. Wyatt is designing a hollow cylindrical metal can with volume 1000 cm3. The material used to make the circular top and bottom of the can costs twice as much as the material used to make the side of the can. What dimensions should Wyatt choose in order to minimize the cost of the can?

   Show all your work, round off the numerical part of your final answer to four (4) decimal places, and express your final answer in the form of a complete sentence, using the correct units.

1-) Set up (but DO NOT COMPUTE) an integral for the volume of the solid obtained by rotating the region bounded by the graphs of y = 0, y = √ x − 2, and x = 4 around the y-axis.

2-) Find the area enclosed by one petal of the four-leaved rose curve r(θ) = sin(2θ).

Find a pair of vectors, a → and b → that satisfy all of the following conditions:

• a → + b → = 〈 9 , 5 , 5 〉
• a → is parallel to 〈 5 , 1 , 2 〉
• b → is orthogonal (perpendicular) to {5,1,2}