Question

Find the missing value. y is directly proportional to x and inversely proportional to the square of z. y = 20 when x = 50 and z = 5. Find y when x = 3 and z = 6.

Answer 1

x=y/z^2

50=20/25

Answer 2

You're very close. Proportional means that there's a constant, k, there.
\[ y = k \frac{x}{z^2} \]

Answer 3

buht i thought that y would be k?

Answer 4

This can't be the case because k is a constant and y is a variable.

Answer 5

oh

Answer 6

You have to use the given information (y=20, x=50, z=5) to solve for k. THEN find y when x=3 and z=6. Does that make sense?

Answer 7

yes

Answer 8

so then 20=50/2500

Answer 9

wait nvm i got that wrong i thought it said x^2 oops

Answer 10

Also, I noticed you switched x and y in your original equation. A tip to avoid this next time: when it says "is," that's when you know to add an equals sign! So "y is direction proportional to x" would give you y=kx :)

Answer 11

oooooooooooo i see :3 thank you

Answer 12

20=50/25

Answer 13

50/25 is 2 so 20=2 10=k

Answer 14

You're forgetting the constant k again! lol
\[ 20 = k \frac{50}{25} \]
What is k?

Answer 15

10 is k?

Answer 16

Yup. So your new equation relating x, y, and z is
\[ y = 10 \frac{x}{z^2} \]

Answer 17

y=10*3/36

Answer 18

correct :)

Answer 19

5/6 is the answer?

Answer 20

Mhmm, because that's what y equals when x=3 and z=6.

Answer 21

hue yay could I do one more?

Answer 22

Sure!

Answer 23

Find the missing value. x varies inversely as y . x = 5 when y = 50. Find x when y = 20.

Answer 24

How do you think you should set that up?

Answer 25

well it cant be like last time so x=k/y?

Answer 26

well we have to have squared thing T-T i dont know

Answer 27

What squared thing? If the statement is "x varies inversely with y," you did it correctly

Answer 28

i mean what we did with the last one z^2

Answer 29

i thought there is always a squared variable so iset it up correctly then?

Answer 30

There's only a squared variable if it says so in the statement, as in "x varies with the square of y," but there's no square in this problem, so you did it correctly.

Answer 31

hokay

Answer 32

5=k/50

Answer 33

Good

Answer 34

(5*50) x= k/20

Answer 35

Not quite. Remember you want to use the first set of information (x=5, y=50) to solve for k! Then plug this k value into x=k/y again

Answer 36

im confused can you show me how you plug them in is it like 5=k/50*20

Answer 37

Before you plug in for y=20 and try to solve for x, you need to find k. This is because if we went straight to plugging in, you'd have \[ x = k/20 \] and you can't solve that!

Therefore, you're using the equation you just came up with, \[5=k/50\] to solve for k. What is the value of k?

Answer 38

k=5*50?

Answer 39

Yup, which is 250. Now that you have \[k=250\] you can plug k into \[x=k/20\] to get the answer you were looking for!

Answer 40

5=250/20

Answer 41

5=125

Answer 42

Do you mean x instead of 5?

Answer 43

I think I see where you're getting confused. You have two pairs of numbers:
1. x=5, y=50
2. x=?, y=20

You can't mix up these pairs because the value of x depends on y. So you used to first pair to solve for k. Now use the second pair to solve for x.

Does this help?

Answer 44

ohhhhh

Answer 45

x=250/50 x=12.5

Answer 46

Nice! You're correct lol

Answer 47

buht thats not an answer T-T

Answer 48

xD what is the answer?

Answer 49

Oh. You got the answer right. How would you write 12.5 as a fraction? Or think about how do you reduce the fraction \[ \frac{250}{20}\]

Answer 50

25/2

Answer 51

There you go!

Answer 52

alright lol i just realized one more may i do it with you and see if i can get it without helps :p

Answer 53

haha of course

Answer 54

Find the missing value. y varies inversely as x. y = 10 when x = 5. Find y when x = 2.

Answer 55

y=k/x

10=k/5
k=50

Answer 56

Good

Answer 57

y=50/2
y=25

Answer 58

Yup. Easy!

Answer 59

ohmai thank you I can dothem on my own nows :D

Answer 60

10/10 heuheueheueheuehue

Answer 61

haha you're very welcome :)