Question

Solve:
2y^(-1/2)=10

Answer 1

What do you think is a good first step?

Answer 2

umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]

Answer 3

If the problem
\[ 2y^{-1/2} - 10 \]
or
\[ (2y)^{-1/2} = 10 \]

Answer 4

*Is

Answer 5

\[2y ^{-1/2}=10\]

Answer 6

Right. So you want y by itself. That is, you want y^1 by itself equal to something.

So first step I would use is to at least get y^something by itself first

\[ 2y^{-1/2} = 10 \]
implies
\[ y^{-1/2} = 5 \]

Yes? If you're ok with that step, then suggest what to do next. Remember you want y^1 = y = something

Answer 7

How did you get 5?

Answer 8

oh wait never mind. You just divided by 2

Answer 9

C'mon. Look at the expression before hand. I divided both sides by 2.

Answer 10

then we should turn y^(-1/2) into \[\sqrt{1/y}\] right?

Answer 11

There are lots of ways to solve the problem. Writing y^(-1/2) that way is one way. Write now the rest of the solution and then I'll show you another way.

Answer 12

Ok.
\[\sqrt{1/y}=5\] I square both sides right? so 1/y =25

Answer 13

yes and hence y = ...

Answer 14

25?

Answer 15

If 1/y = 25, then it can NOT be the case y = 25.

Answer 16

I'm not sure

Answer 17

If 1/x = 2, then x = 1/2. If 1/z = 1/3, then z = 3

Answer 18

Hence if
1/y = 25
then
y = ...

Answer 19

I don't understand how to find y. I kind of forgot how to do the reciprocal thing .Can u explain

Answer 20

Scary.
\[ 2 \times \frac{1}{2} = 1 \]
Agreed?

Answer 21

two times one half equals one, yes?

Answer 22

yes

Answer 23

Suppose now that 2x = 1. What does x equal?

Answer 24

1/2

Answer 25

but i mean in the form of 1/y=25. I don't understand this one

Answer 26

Yes 2x = 1 implies x = 1/2.
Now take 2x = 1 and divide both sides by x; we have
\[ \frac{2x}{x} = \frac{1}{x} \]
Hence
\[ 2 = \frac{1}{x} \]

I.e., x = 1/2 if and only if 1/x = 2.

So if 1/y = 25, what does y = ... ?

Answer 27

If 1/y = a, then y = 1/a

Answer 28

If 1/y = 25, then y = ... ?

Answer 29

ummm

Answer 30

I thought I would just times y/1 to both sides

Answer 31

well
\[ y \times \frac{1}{y} = 1 \]
So if 1/y = 25, then
\[ y \times 25 = 1 \]
i.e., \( 25y = 1 \). Hence y = ...

Answer 32

If 1/y = a, then y = 1/a

Answer 33

Hence if 1/y = 25, then y = ....

Answer 34

1/y=25
times by y/1 to both sides... 25y???

Answer 35

No. You are not reading what I am writing.

\[ \frac{1}{y} \times y = 1 \]
Do you agree with that statement?

Answer 36

yes

Answer 37

Now suppose 1/y = 25, then
\[ 25 \times y = 1 \]
That is
\[ 25y = 1 \]
Agreed so far?

Answer 38

ok. 25y=1
Oh then divide by 25 so I get 1/25

Answer 39

thank you!

Answer 40

Yes y = 1/25

If 1/y = 25, then y = 1/25

In general,
if 1/y = a, then y = 1/a
if 1/x = 1/b, then x = b