Week 1
40. What does it mean if two quantities vary directly?
If two quantities vary directly, it means that they change in the same direction.
41. In your own words, explain how to solve a variation problem.
To solve a variation problem, I would need to be able to solve one-step equations, linear equations, and possibly literal equations.
42. What does it mean if two quantities vary inversely?
It means that the values of the two variable change in the opposite direction.
43. Explain what is meant by combined variation. Give an example with your explanation.
Combined variation is where a variable depends on two or more other variables and varies directly with some and varies inversely with others.
If y varies directly as x and inversely as z, and y = 24 when x = 48 and z = 4, find x when y = 44 and z = 6.
Step One: y = kx z
Step Two:
24= k(48) 4
24= 12k
2=k
Step Three:
y= 2x z
Step Four:
44= 2x z
44= x 3
132= x
44. Explain what is meant by joint variation. Give an example with your explanation.
Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.
y = 7xz, here y varies jointly as x and z.
47. We have seen that the daily number of phone calls between two cities varies jointly as their populations and inversely as the square of the distance between them.This model, used by telecommunication companies to estimate the line capacities needed among various cities, is called the gravity model.
Compare the model to Newton’s formula for gravitation on page 400 and describe why the name gravity model is appropriate. The gravity model equation is similar to Newton’s formula for gravitation.
Newton’s formula:
F = Gm1m2/r2
Gravity Model: g = GM/r2
References iCoach Math. (2013). Retrieved from http://www.icoachmath.com/
If two quantities vary directly, it means that they change in the same direction.
41. In your own words, explain how to solve a variation problem.
To solve a variation problem, I would need to be able to solve one-step equations, linear equations, and possibly literal equations.
42. What does it mean if two quantities vary inversely?
It means that the values of the two variable change in the opposite direction.
43. Explain what is meant by combined variation. Give an example with your explanation.
Combined variation is where a variable depends on two or more other variables and varies directly with some and varies inversely with others.
If y varies directly as x and inversely as z, and y = 24 when x = 48 and z = 4, find x when y = 44 and z = 6.
Step One: y = kx z
Step Two:
24= k(48) 4
24= 12k
2=k
Step Three:
y= 2x z
Step Four:
44= 2x z
44= x 3
132= x
44. Explain what is meant by joint variation. Give an example with your explanation.
Joint variation is a variation where a quantity varies directly as the product of two or more other quantities.
y = 7xz, here y varies jointly as x and z.
47. We have seen that the daily number of phone calls between two cities varies jointly as their populations and inversely as the square of the distance between them.This model, used by telecommunication companies to estimate the line capacities needed among various cities, is called the gravity model.
Compare the model to Newton’s formula for gravitation on page 400 and describe why the name gravity model is appropriate. The gravity model equation is similar to Newton’s formula for gravitation.
Newton’s formula:
F = Gm1m2/r2
Gravity Model: g = GM/r2
References iCoach Math. (2013). Retrieved from http://www.icoachmath.com/
References: iCoach Math. (2013). Retrieved from http://www.icoachmath.com/