Question

Rearrange the following to make y the subject t = √3y 2 – 5

Answer 1

\[\sqrt{3y} * 2 - 5\]?

Answer 2

@joshhhunt if you're just going to use a square root character like that, at least put parentheses around the stuff under the square root sign so there is no question about what the problem is...

Answer 3

Better yet, click on the Equation button and format it nicely...make it easier to help you.

Answer 4

Hi, I'm trying to learn how to get the answer. My bad on not making it clear: t = \[\sqrt{3y ^{2}-5}\] (Im new)

Answer 5

Not a problem, just trying to help you help us help you :-)

Answer 6

so you have
\[t=\sqrt{3y^2-5}\] and you want to solve for \(y\) in terms of \(t\), correct?

Answer 7

The task is to rearrange it so that y is the subject if that helps.

Answer 8

I would square both sides of the equation. Remember that \((\sqrt{x})^2=x\)

Answer 9

What do you get after squaring both sides?

Answer 10

I should know this but how do I go about that.. the previous questions like k = 2y + 15 – 4y I didn't need to square either sides to get the answer

Answer 11

I understand how to do them but the square root throws me off for this question

Answer 12

If we square both sides, we have this:
\[t^2 = (\sqrt{3y^2-5})^2\]but as I said, if you square the square root, when the dust settles, you just have what was under the square root sign:
\[t^2=3y^2-5\]

Answer 13

So I assume the next step would be to add 5 to both sides, right?

Answer 14

That's what I would do.

Answer 15

Ok so now I have \[t{^2} + 5=3y{^2}\] Then I would divide both sides by 3 and end up with this \[7t \div 3=y2\] Am I on the right track?

Answer 16

Wait I've done something wrong, hold up.

Answer 17

\[t{^2}+5 \div 3=y2\] ?

Answer 18

\[t^2+5 = 3y^2\]\[\frac{t^2+5}{3} = y^2\]

Answer 19

Or if you prefer, \[\frac{t^2}{3} + \frac{5}{3} = y^2\]

Answer 20

But neither of those is equivalent to \[t^2+5/3 = y^2\]because division has a higher priority than addition. Remember PEMDAS?

Answer 21

Ahh wrong symbol, so what do I do with the 2 so that I am left with just y? \[y{^2}\]

Answer 22

Now you take the square root of both sides:
\[\sqrt{\frac{t^2+5}{3}} = y\]And then switch sides
\[y=\sqrt{\frac{t^2+5}{3}}\]
I assume that's what your instructor wants when saying "make y the subject"

Answer 23

That looks right to me, thank you very much for your help.