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.

a basketball coach was criticized in a newspaper for not trying out every combination of players. if the team roster has 14 players and every player can play every position how many 5-player combinations are possible?

Consider Cardano's problem of finding two numbers whose sum is 10 and whose product is 40.

a) Cardano knew beforehand that no such (real) numbers existed. How did he know? Can you prove it?

b) Solve the system of equations x+y=10 and xy=40 to find Cardano's complex solution.

c) Check that this solution does work-that is, thatb the sum of your complex numbers is 10 and that their product is 40.

189. An altitude of a triangle is a segment that joins one of the three vertices to a point on the line that contains the opposite side, the intersection being perpendicular. For example, consider the triangle whose vertices are A = (0, 0), B = (8, 0), and C = (4, 12). (a) Find the length of the altitude from C to side AB. What is the area of ABC? (b) Find an equation for the line that contains the altitude from A to side BC. (c) Find an equation for the line BC. (d) Find coordinates for the point F where the altitude from A meets side BC. It is customary to call F the foot of the altitude from A. (e) Find the length of the altitude from A to side BC. (f) As a check on your work, calculate BC and multiply it by your answer to part (e). You should be able to predict the result. (g) It is possible to deduce the length of the altitude from B to side AC from what you have already calculated. Show how.

Suppose that in an assortment of 30 calculators there are 5 with defective switches. Draw with and without replacement. (Enter the probabilities as fractions.)

(a) If one machine is selected at random, what is the probability it has a defective switch?

with replacement

without replacement

(b) If two machines are selected at random, what is the probability that both have defective switches?

with replacement

without replacement

(c) If three machines are selected at random, what is the probability that all three have defective switches?

with replacement

without replacement