Plot the following parabolic functions in Excel and then answer the discussion question below . Use at least 8 points for each plot: Each graph is worth 15 points and must include 8 points. 1) y=x2-6x+8 2) y=x2+4 3) y=(-1/2)(x2) 4) What is the maximum number and the minimum number of x-intercepts for a parabola? Why? (15 points) In order to obtain full credit, you will need to plot the functions in Excel or using the Open Office feature and attach the results to your response.

Four people are using a voting weight system to make decisions. They have the weights of 7,5,4,and 2. They use a quota of 13. Compute the Banzhaf power index for the voter of weight 5.

1) Determine the two angles

sin(2θ)=0.9179.

2)Determine the solution sets

12cos^2θ=3

I have no idea of what is happening when the professor explains how they got the angles or soln sets, they automatically know what quadrant it is in and what angle it should be, and what the next angle(s), sets are. I cant imagine it. I don't know how they see that on the unit circle.

Suppose you have a piece of cardboard with length 32 inches and width 20 inches and you want to use it to create a box. You would need to cut a square out of each corner of the cardboard so that you can fold the edges up. But what size square should you cut? Cutting a small square will make a shorter box. Cutting a large square will make a taller box.

Since we haven’t determined the size of the square to cut from each corner, let the side length of the square be represented by the variable x. Write a simplified polynomial expression in x and note the degree of the polynomial for each of the following geometric concepts:

The length of the base of the box once the corners are cut out, the width of the base of the box once the corners are cut out, the height of the box, the perimeter of the base of the box, the area of the base of the box, the volume of the box.

a. Suppose the earth were wrapped tightly in a 25,000 mile belt. Now suppose someone adds 1 mile to the belt. If the belt is raised uniformly above the earth’s surface, how high above the surface will it be? Give your answer in feet. (Guess first, before you calculate this.)

b. This time, suppose someone adds 1 foot to the belt. Again, raise the belt uniformly above the earth’s surface—how high will the belt be? Give you answer in inches.

c. Finally, suppose a regulation NBA basketball is wrapped tightly in a 29.5 inch belt. Now suppose someone adds 1 foot to the belt. If the belt is raised uniformly above the ball’s surface, how high will it be? Give your answer in inches. Are you surprised by this result?

Why do  perpendicular bisectors of the three sides of a triangle all meet at a single point? and also why do  angle bisectors of the three sides of a triangle all meet at a single point ?

1) Find the intervals of increasing and decreasing for f(x) = 2x3 – 4x2.
2) Find the local minimum and maximum points, if any, of                         f(x) = 2x3 – 15x2 + 36x – 14. 3) Find the inflection points, if any, of f(x) = 2x3 – 15x2 + 36x – 14. Give the intervals of concavity upward and downward for f(x). 4) Find the absolute maximum and minimum of f(x)= 2x3 – 15x2 + 36x – 14 on the interval [0,5]. 5) Sketch the graph of y = 2x3 – 15x2 + 36x – 14 using the information from #2-4 along with the intercepts. 6) Given C = .02x3 + 55x2 + 1250, find the number of units x that produces the minimum average cost per unit, ?. ̅ 7) Find the maximum, minimum, and inflection points of f(x) = x4 – 18x2 + 5.

Give a method for solving Fermat's Problem when a triangle has an agle greater than 120°.

Show that in any triangle the angle bisectors are concurrent. The point where they meet is called the incenter of the triangle, and is the center of the incircle, whose radius is the distance from the incenter to any of the sides of the triangle.

4).

(a) Calculate the five-number summary of the land areas of the states in the U.S. Midwest. (If necessary, round your answer to the nearest whole number.)

(b) Explain what the five-number summary in part (a) tells us about the land areas of the states in the midwest

(c) Calculate the five-number summary of the land areas of the states in the U.S. Northeast. (If necessary, round your answer to the nearest whole number.)

(d) Explain what the five-number summary in part (c) tells us about the land areas of the states in the Northeast

(d) Contrast the results from parts (b) and (d).
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5).Find the five-number summary for the data on highway mileage shown below.

Earth’s orbit around the Sun is an ellipse that is almost a circle. The Sun is at one focus, the major axis is 299,190,000 km in length, and the minor axis is 299,148,000 km in length. What are the minimum and maximum distances from Earth to the Sun?

The vertices of a triangle determine a circle, called the circumcircle of the triangle. Show that if P is any point on the circumcircle of a triangle, and X, Y, and Z are the feet of the perpendiculars from P to the sides of the triangle, then X, Y and Z are collinear.

How do I prove (step by step) Thales' Theorem?

Find the oblique asymptote for the rational function f(x)= 3x³ - 27x² + 60x / 2x² + 2x - 40

Find the composite function g o f when f(x)= 3x-5 / x-1 and g(x)= x+6 / 4x-9 (I got 9x-11 / 3x-11)

Modeling with Functions

In this course you have learned the characteristics of different types of functions and have practiced solving application problems involving modeling with these functions. For each scenario below, decide what type of function would best model the situation. Explain why you chose that type of function. Show your work in writing the function to model the situation. Be sure to state what the independent variable represents. Then use your model to answer the questions for that scenario.

1. Susan decides to take a job as a transcriptionist so that she can work part-time from home. To get started, she has to buy a computer, headphones, and some special software. The equipment and software together cost her $1000. The company pays her $0.004 per word, and Susan can type 90 words per minute.

   1. What type of function would be best to model this scenario? Choose one of the following: linear, quadratic, polynomial of degree 3 or higher, rational, exponential, or logarithmic. Explain why you chose this answer.

   2. Write a formula for the function you chose to model this scenario. What does the independent variable in your function represent?

   3. How many hours must Susan work to break even, that is, to make enough to cover her $1000 start-up cost? Show how you found the answer.

   4. If Susan works 4 hours a day, 3 days a week, how much will she earn in a month? Show how you found the answer.