Question

Solve the variations:
1. If (a) varies inversely as (b), and a=9 when b=4, find a when b=12.
2. What is the value of the constant in the variation in problem 31?
3. x varies directly as y and inversely as z. If x=1 when y=2 and z=6, then what is the value of y when x=12 and z=1and 1/2?
4. What is the value of the constant in the variation in problem 33?

How in the world do i do these? Please help.

Answer 1

# 1

If a varies inversely as b, then


a = k/b for some constant k


We know that when a = 9, b = 4, so plug these in to get


9 = k/4


From here, solve for k


9 = k/4

9*4 = k

36 = k

k = 36


So the equation is a = 36/b


Now onto finding the value of a when b = 12. So just plug in b = 12 and simplify


a = 36/b

a = 36/12

a = 3


So when b = 12, a = 3

Answer 2

# 2

I don't see problem #31, so I can't answer it

Answer 3

Number 31? huh?

Answer 4

# 3

"x varies directly as y and inversely as z" means that


x = ky/z


We're given x=1, y=2 and z=6, so


1 = k*2/6

1 = 2k/6

1 = k/3

1*3 = k

k = 3


Giving the equation


x = 3y/z


if x=12 and z = 1 1/2, then


x = 3y/z

12 = 3y/(3/2) .... Note: 1 and 1/2 = 3/2

12*(3/2) = 3y

36/2 = 3y

18 = 3y

18/3 = y

6 = y

y = 6


So when x = 12 and z = 1 1/2, y = 6

Answer 5

In #2, it says

"2. What is the value of the constant in the variation in problem 31?"

but I don't see #31

Answer 6

sorry. typo. its talking about number 1

Answer 7

& number 4 at the end is suppose to say number 3.

Answer 8

oh that makes a ton more sense now

Answer 9

Ha. sorry.

Answer 10

# 2

the constant of variation is k = 36

Answer 11

# 4

the constant of variation is k = 3

Answer 12

Thank you so much. I have one more question and ill let you be.
x^2-5x+6
is (x-3) a factor?

Answer 13

yes, another factor is x-2

Answer 14

Oh ok. Thank you so much. For all your help. I have so many more questions. I have finals next week. But i dont wanna ask too many tonight.

Answer 15

alright, you're welcome, good luck on your finals

Answer 16

Thank you!