MAT 286 Study Guide - Midterm Guide: Multiple Integral, Canada Goose, Ellipse

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turquoisegnu128

9 Jan 2019

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I problem number i possible points i score. [5 points for each problem. ] (a) j(4x 3 + 6x - 5) dx (b) j4e- 3 (c) j-x---=-2-+-5- dx x (d) jxsinx dx. 4: for (a) and (b), find the values of the definite integrals. For (c) and (d), each of the improper integrals, determine if it converges or diverges, and find the value of each that converges. [5 points for each problem. ] r 2 (a) i, (x 3)dx. 6: find the average value of each function on the given interval. (a) f(x) = vx+t; 7: the average length and width of the eggs of canadian geese are 10. 0 em and. Assuming that the eggs are of the shape of an ellipsoid. Find the average volume of the eggs of canadian geese, by the method of solid of revolution. [the equation for an ellipse is :2 + ~2 = 1. ]

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Mr and Mrs Spin operate a Ferris Wheel at various shows and carnivals. A passenger sits in a capsule and enjoys the ride and views. Below is a diagram showing their magnificent wheel:
Passengers embark and disembark the capsule from the platform (a maximum of 6 passengers are allowed at any given time). The time for a passenger to enter the capsule and return to the platform is 6x minutes. The process repeats until the final passenger(s) embark at no later than 10 pm each evening. The Ferris Wheel runs in an anti-clockwise direction. The height h, in metres, from the ground to a capsule, is measured from the ground to the ball on top of any capsule. It is modelled by 𝒉(𝒕) = 𝒂 − 𝐛cos (𝝅/ 𝟑) A passenger pays 3y dollars for a ride on the wheel. The variables a, b, x and y are as follows:  a is equal to 14 (i.e. a=14)  b is equal to the last digit of your student id plus 2 (e.g. if your id is 4567891 then b=3).  x is equal to the third digit of your id plus 3 (e.g. if your id is 4567891 when x=9).  y is equal to the month that you are born plus 6 (e.g. if you are born in July then y=13). Mr and Mrs Spin would like you to do the following mathematical analysis and present the results in a report for their consumption.
Task 1:
What are the minimum and maximum height of a capsule on the Ferris Wheel?
Task 2:
Determine the heights of each of the capsules on the Ferris Wheel while passengers either embark or disembark a capsule. Present these heights in table form, with appropriate labelling.
Task 3:
Determine the time when the final passenger(s) will disembark the capsule and the Ferris Wheel cease for the evening (remember that the final passengers will embark no later than 10 pm). Note, it is possible that the final passenger(s) may embark the capsule prior to 10 pm, so the answer to this task may not be 10 pm + 6x.

Task 4:
Evaluate the number of capsules that will have a passenger(s) embark for any day, given the Ferris Wheel will commence at 4 pm and the time for passenger(s) to embark and disembark is considered negligible.
Task 5:
On average, 4.8 passengers, on any given day, will embark on a capsule each time. Given the answer to Task 4, find the total number of passengers, on average, that will take a ride on the Ferris Wheel in a day.
Task 6:
Given the answers to Tasks 4 and 5, determine the total ticket sales made on a given day.
Task 7:
Create a set of equations to determine:
1. The number of capsules on a given day could be filled with passengers.
2. The total number of passengers on any given day, for an average.
3. The total ticket sales for any given day, based on the number of capsules per day and an average number of passengers per capsule.
Task 8:
Create a schedule (in table form) for total ticket sales for a day, given average passengers between 4 and 6 inclusive and in increments of 0.2 (i.e. 4, 4.2, 4.4, 4.6, etc.) per capsule.
Task 9:
Report these results in a document for Mr and Mrs Spin. An appendix should show all working out for each of the tasks. This document is electronic in format and no handwriting is acceptable.

ochredinosaur493

1. Evaluate the expression 2x - 2 for the value of x = -3

2. Factor: xsquare + 4x - 32 (x-4)(x+8) (x-4)(x-8) (x-4)(x-8) (x-16)

3. Factor: xsquare - 25 (x-5) (x+5)2 (x+5)(x-5) (x-5)(x-5)

4. Evaluate -u2v3 when u=4 and v=-2 128 64 32 -128

5. Using an online calculator, determine whether the value of x=7 is a solution of the equation. x Yes No

6. Explain why x=7 IS or IS NOT a solution of the equation. 7 + 1/x+2=8

7. Solve the equation and check your solution: -2 - 4x = 30

8. Solve the equation and check your solution: 67x - 24 = 3x + 8(8x - 3) 67 -3 -67 All real numbers

9. Solve the equation and check your solution. 5x/2 - x/6 = 14 10 6 7 9

10. Solve the quadratic equation by factoring: xsquare - 6x + 5 = 0 -1, 5 -1,-5 1,-5 1,5

11. The imaginary number i represents:

12. Find real numbers a and b such that the equation is true: a+ bi = 14 + 2i a=16, b=4 a=18, b=6 a=14, b=2 a=15, b=14

13. Find all solutions to the following equation. /4x - 8 = /4x + 9 x = -17/4 x=9 No solution x=-17

14. In a given amount of time, James drove twice as far as Rachel. Altogether they drove 120 miles. Write an equation to help find the number of miles driven by each. Use R as the variable to represent miles driven by Rachel and J for Jamesâ miles.

15. Karen works for $10 an hour. A total of 25% of her salary is deducted for taxes and insurance. She is trying to save $450 for a new set of tires. Write an equation to help determine how many hours she must work to take home $450 if she saves all of her earnings. Be sure to save the equation you write, as you will use it to answer the next question in this quiz. 10h - .25=450 10h + .25(10h)=450 h -.25 (10h)=450 10h - .25(10h)=450

16. Using the equation you wrote in the previous problem, find the actual amount of hours Karen must work to take home $450 if she saves all of her earnings. Show your work. 17. The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width. Hint: Perimeter = width + length + width + length

18. Twice a number is added to the number and the answer is 80. Write an equation to solve this problem. 2n + n=80 2n = 80 2n + 80=n 80 + n=2n

19. If 4 is subtracted from twice a number, the result is 10 less than the number. Write an equation to solve this problem. Use n as the variable to represent the number.

20. Multiply the following binomials: (x + 5)(x - 5)

MAT 286 Study Guide - Midterm Guide: Multiple Integral, Canada Goose, Ellipse

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