A direct and inverse proportion to question

bumblebee123

New member
Joined
Jan 3, 2018
Messages
20
Hi All,

Doing Direct and inverse proportion still. Got the hang of it until I saw this question: ( I have used ^ show a square)

Y is directly proportional to x^2. When x=2, y=36


A)
Express y in terms of x

The answer here is y=9x^2

I got the answer correct but the next bit beats me, I do not know where to begin.

z in inversely proportional to x. When x = 3, z= 2

B)
Show that z = cy^n, where c and c are numbers and c > 0 . (you must find the values c and n)

So, I have managed to find the formula z=6/x but I do not know how to find c or n. I thought about using answer to A for the y value but this doesn't help me. It's probably staring me in the face but I just don't see it.
I could use the answer I got for z and insert this into the z=cy^n to read:
6/x = cy^n
but I don't see how that will get me answers.

If it helps the answer book says c=18 and n = -1/2

Thank you in advance.
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,052
Y is directly proportional to x^2. When x=2, y=36

A)
Express y in terms of x

The answer here is y=9x^2

I got the answer correct but the next bit beats me, I do not know where to begin.

z in inversely proportional to x. When x = 3, z= 2

B)
Show that z = cy^n, where c and c are numbers and c > 0 . (you must find the values c and n)

So, I have managed to find the formula z=6/x but I do not know how to find c or n. I thought about using answer to A for the y value but this doesn't help me. It's probably staring me in the face but I just don't see it.
I could use the answer I got for z and insert this into the z=cy^n to read:
6/x = cy^n
but I don't see how that will get me answers.

If it helps the answer book says c=18 and n = -1/2

Thank you in advance.
You have found that y = 9x^2, and that z = 6/x. You want to find the relationship between z and y, which means combining the two known equations to eliminate x. You can solve either equation for x, and "plug" that into the other. Then you can solve the resulting equation for z, and hope it will have the form cy^n.

Give that a try, so we can see how close you are.
 

bumblebee123

New member
Joined
Jan 3, 2018
Messages
20
You have found that y = 9x^2, and that z = 6/x. You want to find the relationship between z and y, which means combining the two known equations to eliminate x. You can solve either equation for x, and "plug" that into the other. Then you can solve the resulting equation for z, and hope it will have the form cy^n.

Give that a try, so we can see how close you are.
Rearranging both equations for x I get:

y/9=x^2
I don't know how to write square root here but I know that I can go one step further and do the square root to leave x on its own.

and

x= 6/z

I put the two equations together as they both now equal x but still I can not find the form z = cy^n. I seem to always find that I am either dividing by z or dividing by y, neither of which is what I am trying to get. My closest so far is:
z^2=324/y

Can you offer any more pointers?
Thanks again
 

mmm4444bot

Super Moderator
Staff member
Joined
Oct 6, 2005
Messages
10,251
You posted this answer:

z = 18 y^(-1/2)

Do you know what it means, when an exponent is 1/2?

How about when an exponent is negative?
 

bumblebee123

New member
Joined
Jan 3, 2018
Messages
20
You posted this answer:

z = 18 y^(-1/2)

Do you know what it means, when an exponent is 1/2?

How about when an exponent is negative?
For this equation z = 18 y^(-1/2) I understand that a negative exponent can be written as this:

z = 18/ y^(1/2)

I know that a fraction exponent means in this case the square root:

z = 18/√y

I now have an equation which looks a lot like what I have with the

√y/9=6/z when I rearrange for z

z√y/9=6


z√y=54

z=54/√y

But still this is not right as I know the answer is z = 18 y^(-1/2)

Where am I going wrong?
 

Dr.Peterson

Elite Member
Joined
Nov 12, 2017
Messages
3,052
z = 18/√y

I now have an equation which looks a lot like what I have with the

√y/9=6/z when I rearrange for z

z√y/9=6


z√y=54

z=54/√y

But still this is not right as I know the answer is z = 18 y^(-1/2)

Where am I going wrong?
You just left out parentheses: √(y/9)=6/z .

The left side simplifies to (√y)/3=6/z.

Take it from there!
 
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