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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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What do you think is a good first step?
umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]
If the problem \[ 2y^{-1/2} - 10 \] or \[ (2y)^{-1/2} = 10 \]

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\[2y ^{-1/2}=10\]
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
How did you get 5?
oh wait never mind. You just divided by 2
C'mon. Look at the expression before hand. I divided both sides by 2.
then we should turn y^(-1/2) into \[\sqrt{1/y}\] right?
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.
Ok. \[\sqrt{1/y}=5\] I square both sides right? so 1/y =25
yes and hence y = ...
25?
If 1/y = 25, then it can NOT be the case y = 25.
I'm not sure
If 1/x = 2, then x = 1/2. If 1/z = 1/3, then z = 3
Hence if 1/y = 25 then y = ...
I don't understand how to find y. I kind of forgot how to do the reciprocal thing .Can u explain
Scary. \[ 2 \times \frac{1}{2} = 1 \] Agreed?
two times one half equals one, yes?
yes
Suppose now that 2x = 1. What does x equal?
1/2
but i mean in the form of 1/y=25. I don't understand this one
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 = ... ?
If 1/y = a, then y = 1/a
If 1/y = 25, then y = ... ?
ummm
I thought I would just times y/1 to both sides
well \[ y \times \frac{1}{y} = 1 \] So if 1/y = 25, then \[ y \times 25 = 1 \] i.e., \( 25y = 1 \). Hence y = ...
If 1/y = a, then y = 1/a
Hence if 1/y = 25, then y = ....
1/y=25 times by y/1 to both sides... 25y???
No. You are not reading what I am writing. \[ \frac{1}{y} \times y = 1 \] Do you agree with that statement?
yes
Now suppose 1/y = 25, then \[ 25 \times y = 1 \] That is \[ 25y = 1 \] Agreed so far?
ok. 25y=1 Oh then divide by 25 so I get 1/25
thank you!
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

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