explanation of example: from 1-1/k^2=0.36 to 1/k^2=0.64

[hsing]

Hi,

I was given this example as a solution. But I'm not sure what was done to get from the solution of 0.36 to 0.64. Thanks for any help you can give. Dan

1-1/k[sup:3u6plc4q]2[/sup:3u6plc4q]=0.36

1/k[sup:3u6plc4q]2[/sup:3u6plc4q]=0.64

 

[Denis]

Re: explanation of example

Hint: multiply each term by k^2 : k^2 - 1 = .36k^2 : OK?

 

[stapel]

1-1/k[sup:19ycl0ch]2[/sup:19ycl0ch]=0.36

1/k[sup:19ycl0ch]2[/sup:19ycl0ch]=0.64

You moved the 1/k[sup:19ycl0ch]2[/sup:19ycl0ch] to the right-hand side, subtracted 0.36 from either side, and simplified. What did you get instead of their answer?

Please be complete. Thank you!

 

[hsing]

This was the entire problem. It is supposed to be an explanation of how to solve a business statistics problem on aleks.com But I don't seem to remember my basic algebra. I'm trying to understand how they got from the step that has the solution of .36 to the next step - solution of .64 Thanks for the help.

[100(1-1/k[sup:g55wow8r]2[/sup:g55wow8r])]% = 36%

100(1-1/k[sup:g55wow8r]2[/sup:g55wow8r]) = 36

1-1/k[sup:g55wow8r]2[/sup:g55wow8r] = 0.36

1/k[sup:g55wow8r]2[/sup:g55wow8r] = 0.64

k[sup:g55wow8r]2[/sup:g55wow8r] = 1/0.64

k = + 1.25

 

[DrMike]

This was the entire problem. It is supposed to be an explanation of how to solve a business statistics problem on aleks.com But I don't seem to remember my basic algebra. I'm trying to understand how they got from the step that has the solution of .36 to the next step - solution of .64 Thanks for the help.
<snip>
1-1/k[sup:2ijwdnls]2[/sup:2ijwdnls] = 0.36

1/k[sup:2ijwdnls]2[/sup:2ijwdnls] = 0.64

First, remember that 1-1/k[sup:2ijwdnls]2[/sup:2ijwdnls] means "one minus (one over k squared)". It doesn't mean "(one minus one) over k squared" Forgive me if this was already obvious.

Now, if 1-X = 0.36, and you add X to both sides, you get 1-X+X = 0.36+X, that is, 1 = 0.36 + X.

Then, if you subtract 0.36 from both sides, you get 1-0.36 = 0.36+X-0.36, that is, 1-0.36 = X

But 1-0.36 is just 0.64. So this just means 0.64 = X, or X = 0.64. Yay!

In general, the following are equivalent :

A - B = C
A - C = B
A = B + C

eg

9 - 3 = 6,
9 - 6 = 3 and
9 = 3 + 6 are all saying the same thing.

I'm sure you knew that, but somehow it didn't "click" when you saw

1-1/k[sup:2ijwdnls]2[/sup:2ijwdnls] = 0.36 mysteriously transmogrify into 1/k[sup:2ijwdnls]2[/sup:2ijwdnls] = 0.64

Am I right?