Answer each of the following questions involving direct, inverse, joint, and combined variations. Choose your answer from the given choices. For items number 10-15, attach a copy of your solutions in this form. 1. What type of variation involves 3 or more quantities that may vary directly? * *Direct Variation*Inverse Variation*Joint Variation*Combined Variation 2. This type of variation states that the two quantities increase at the same time or decrease at the same time. * *Direct Variation*Inverse Variation*Joint Variation*Combined Variation 3. Translate "the cost c varies directly as the number of n pencils" into equation. * *c = kn*k = cn*n = k/c*c = k/n4. The speed r of a moving object is inversely proportional to the time t travelled is written as * *r = kt*r = k/t*t = kr*t = r/k5. Which of the following types of variation states that the decrease of one quantity results to the increase of the other quantity? * *Direct Variation*Inverse Variation*Joint Variation*Combined Variation 6. If y varies directly as x and y = 24, when x = 3, then what is the value of k? * *4*6*8*12 7. Which of the following phrases illustrate an inverse variation? * *The area of the wall to the amount of paint used to cover it*The amount of money raised in a concert to the number of tickets sold*The time a teacher spends in checking papers to the number of students*The age of a used car to its resale value 8. If s varies directly as t and inversely as v, then which of the following equations describes the relation among the three variables s, t, and v? * *s = k / tv*s = kv / t*1/s = kt/ v*s = kt / v 9. This is a variation where one quantity varies directly to other quantity and inversely to the other quantity. * *Direct Variation*Inverse Variation*Joint Variation*Combined Variation10-12. Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. * (Show solution) *-140*140*-4* 4 13-15. The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour? *(Show solution) *308.05 ft*295.75 ft*296.09 ft*253.5 ft

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Description: Answer each of the following questions involving direct, inverse, joint, and combined variations. Choose your answer from the given choices. For items number 10-15, attach a copy of your solutions in this form. 1. What type of variation involves 3 or

(10-12) Given :- Suppose y varies jointly as x and z . If y =-180 when z =15 and x =-3, To…

Answered: 10-12. Suppose y varies jointly as x &…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Answer each of the following questions involving direct, inverse, joint, and combined variations. Choose your answer from the given choices. For items number 10-15, attach a copy of your solutions in this form.

1. What type of variation involves 3 or more quantities that may vary directly? *

*Direct Variation

*Inverse Variation

*Joint Variation

*Combined Variation

2. This type of variation states that the two quantities increase at the same time or decrease at the same time. *

*Direct Variation

*Inverse Variation

*Joint Variation

*Combined Variation

3. Translate "the cost c varies directly as the number of n pencils" into equation. *

*c = kn

*k = cn

*n = k/c

*c = k/n

4. The speed r of a moving object is inversely proportional to the time t travelled is written as *

*r = kt

*r = k/t

*t = kr

*t = r/k

5. Which of the following types of variation states that the decrease of one quantity results to the increase of the other quantity? *

*Direct Variation

*Inverse Variation

*Joint Variation

*Combined Variation

6. If y varies directly as x and y = 24, when x = 3, then what is the value of k? *

*12

7. Which of the following phrases illustrate an inverse variation? *

*The area of the wall to the amount of paint used to cover it

*The amount of money raised in a concert to the number of tickets sold

*The time a teacher spends in checking papers to the number of students

*The age of a used car to its resale value

8. If s varies directly as t and inversely as v, then which of the following equations describes the relation among the three variables s, t, and v? *

*s = k / tv

*s = kv / t

*1/s = kt/ v

*s = kt / v

9. This is a variation where one quantity varies directly to other quantity and inversely to the other quantity. *

*Direct Variation

*Inverse Variation

*Joint Variation

*Combined Variation

10-12. Suppose y varies jointly as x & z. If y = -180 when z = 15and x = -3,then find y when x = 7 and z = -5. * (Show solution)

*-140

*140

*-4

* 4

13-15. The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour? *

(Show solution)

*308.05 ft

*295.75 ft

*296.09 ft

*253.5 ft

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