Simultaneous eqns: 0.5Ax^-0.5=0.1, 0.5Ay^-0.5=z, x=100y, A is a constant

heinmac

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Apr 17, 2016
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Hi all,

Currently doing some work for university for my economics degree and have encountered a problem when trying to derive a variable for z given a few other equations. I'm so stuck with it right now that I thought i'd give this a try?

I know the below:

0.5Ax-0.5=0.1
0.5Ay-0.5=z
x=100y
A is a constant

I'm pretty sure I need to solve them simultaneously, and in doing so I've got the answer of z=0.001, however this doesn't seem to fit with the rest of my workings and so I think I may have gone wrong with the maths.

My maths is a little rusty when it comes to this, so any help would be greatly appreciated, thanks!
 
Hi all,

Currently doing some work for university for my economics degree and have encountered a problem when trying to derive a variable for z given a few other equations. I'm so stuck with it right now that I thought i'd give this a try?

I know the below:

0.5Ax-0.5=0.1 ......................(1)
0.5Ay-0.5=z ......................(2)
x=100y ......................(3)
A is a constant

I'm pretty sure I need to solve them simultaneously, and in doing so I've got the answer of z=0.001, however this doesn't seem to fit with the rest of my workings and so I think I may have gone wrong with the maths.

My maths is a little rusty when it comes to this, so any help would be greatly appreciated, thanks!

If we divide (2) by (1), we get:

(10 z)2 = x/y

from (3) we get

x/y = 100

Now continue.....
 
If we divide (2) by (1), we get:

(10 z)2 = x/y

from (3) we get

x/y = 100

Now continue.....

So (10z)2=100, therefore 10z=10, meaning z=1?

I think I see where I was going wrong. I was trying to substitute (3) into (1) and then divide the two equations rather than just dividing straight away.

Thank you so much!
 
So (10z)2=100, therefore 10z=10, meaning z=1?
No, but close. Do the steps, like they showed you. When you're at this point:

. . . . .\(\displaystyle (10z)^2\, =\, 100\)

...how do you "solve" the square on the left-hand side? What do you do to each side of the equation? And what must you remember to put in front of the square-root sign on one side of the equation? (here) ;)
 
No, but close. Do the steps, like they showed you. When you're at this point:

. . . . .\(\displaystyle (10z)^2\, =\, 100\)

...how do you "solve" the square on the left-hand side? What do you do to each side of the equation? And what must you remember to put in front of the square-root sign on one side of the equation? (here) ;)

So you square root both sides of the equation?

10z = ±10

Therefore z = ±1 ?
 
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