Find the values of the 5 remaining trigonometric functions given the value and constraints.

csc = 3/2 where cos < 0

Chelsea took out three loans for a total of ?$78000 to start an organic orchard. Her? business-equipment loan was at an interest rate of? 11%, the? small-business loan was at an interest rate of 5?%, and her? home-equity loan was at an interest rate of 4.5?%. The total simple interest due on the loans in one year was ?$4605. The annual simple interest on the? home-equity loan was ?$105 more than the interest on the? business-equipment loan. How much did she borrow from each? source?

A Population Model The population of the world in 2013
was 7.13 billion people and was growing at a rate of 1.1% per
year. Assuming that this growth rate continues, the model
P(t) = 7.1311.0112^(t-2013) represents the population P (in
billions of people) in year t.
(a) According to this model, when will the population of the
world be 10 billion people?
(b) According to this model, when will the population of the
world be 12.2 billion people?

A saleswoman sells a? dried-fruit mixture for

?$5.90

per pound and nuts for

?$14.55

per pound. She wants to blend the two to get a

10?-lb

mixture that she will sell for

?$9.36

per pound. How much of each should she? use? Solve using matrices.

Solve for x

x^4 + 2x^3 + 2x^2 + 3x + 1 = 0

Let x ∈ R³ be nonzero and let A be the matrix whose columns are x, 2x, 3x in this order. Show that x is an eigenvector of A and find a basis for the null space of A.

Orca J-43 is sighted in Pudget Sound at the following depths (in feet) at certain times t (in minutes) measured from sea level. D(t) =    59 0 ≤ t < 5 t 2 − 22t + 144 5 ≤ t < 10 24 10 ≤ t < 18 8(t − 15) 18 ≤ t ≤ 22 (a) What is the range of the function D? Strategy then final result, no algebra steps (b) Another orca, K-97, also shows her presence in Pudget sound. If her depths (measured at the same time as above) is given by g(t) = 2t + 1, at which times are both whales at the same depth? Strategy then final result, no algebra steps

P(x) = x6 − 7x3 − 8

(a) Find all zeros of P, real and complex.

(b) Factor P completely.

In many cities and towns across the United States, the numbering system of the roads is based on a grid, similar to the latitude and longitude lines on a globe. Suppose the green lines in the following graph represent two east-west and two north-south running roads in a Midwestern town.

Write equations for the two horizontal and two vertical lines that represent roads in the town.






2. The Willis Tower (formerly known as the Sears Tower) in Chicago, Illinois, is the tallest building in the United States. Measuring 1,450 feet, the tower contains 110 stories filled with a combination of office and retail space. The base of the tower is made up of nine 75’ × 75’ squares. Suppose the square graphed on the coordinate plane below represents the base of the Willis Tower.

Write equations for the two horizontal and two vertical lines that pass through the square.



3. Think of another real-world situation that might involve horizontal and vertical lines. Write a description of the situation and draw the graph of a coordinate plane with two horizontal and two vertical lines to represent your situation. Draw the lines so that two of them pass through positive values and the other two pass through negative values on the coordinate plane. Then write equations for all four of the lines on your graph.

Did you drive to work or school today? When you are driving at a constant speed, the amount of gas left in the tank can typically be modeled by a linear equation. The equation y = -2x + 15 would represent a car that has a full 15-gallon tank and burns 2 gallons of gas an hour when x is the number of hours driven and y is the amount of gas in the tank. Find a linear relationship (equation) that you would use or rely on in your field when you receive your degree, and explain what it is and how it is used. Identify the initial condition, such as the full tank of gas above, and the rate of change. For a linear equation, the rate of change (slope) needs to be constant. If you can’t find one in your field, broaden your research to include any real-world application.

What color is the sky? What color are the clouds?

Under certain water​ conditions, the free chlorine​ (hypochlorous acid,​ HOCl) in a swimming pool decomposes according to the law of uninhibited decay. After shocking a​ pool, the pool​ boy, Geoff, tested the water and found the amount of free chlorine to be 2.4 parts per million​ (ppm). ​ Twenty-four hours​ later, Geoff tested the water again and found the amount of free chlorine to be 2.1 ppm. What will be the reading after 2 days​ (that is, 48 ​hours)? When the chlorine level reaches 1.0​ ppm, Geoff must shock the pool again. How long can Geoff go before he must shock the pool​ again?

Discussion 3 Solve and write an essay.

1111 réponses non lues.1111 réponses.

Essay: 2 [ x - (4 + 2x) + 3 ] - 2x - 2 = 4 [2x - (3 - x) + 5] + 6x + 28

Students, you have to do an essay for this discussion. The essay is consist of a introduction, a body, and a conclusion. You have write this essay like you are teaching your children, co-worker, or a stranger how to work this problem. The introduction is where you will define all of the terms of the problem and list all the rules. In which, you tell me what type of problem it is, if it's an equation and linear, if it has parenthesis and bracket, which have to be defined and what you would to solve the problem. The body is where you will work the problem, write out in sentence structure how you work the problem. Make sure you put the problem in your essay and everything that you did to work the problem. Lastly, the conclusion is where you will explain what the person should get for working the way that you worked it, and what they should learn

Maximize objective function P=3x+4y

subject to: x + y ≤ 7 x ≥ 0

x+4y ≤ 16 y ≥ 0

A recipe calls for 1 1/5 cups of flour for every 1/2 teaspoon of salt. Suppose you put 4 cups of flour in a mixing bowl. How much salt should you add?