sparky16
Solve:
2y^(-1/2)=10
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JamesJ
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What do you think is a good first step?
sparky16
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umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]
JamesJ
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If the problem
\[ 2y^{-1/2} - 10 \]
or
\[ (2y)^{-1/2} = 10 \]
JamesJ
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*Is
sparky16
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\[2y ^{-1/2}=10\]
JamesJ
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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
sparky16
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How did you get 5?
sparky16
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oh wait never mind. You just divided by 2
JamesJ
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C'mon. Look at the expression before hand. I divided both sides by 2.
sparky16
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then we should turn y^(-1/2) into \[\sqrt{1/y}\] right?
JamesJ
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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.
sparky16
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Ok.
\[\sqrt{1/y}=5\] I square both sides right? so 1/y =25
JamesJ
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yes and hence y = ...
sparky16
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25?
JamesJ
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If 1/y = 25, then it can NOT be the case y = 25.
sparky16
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I'm not sure
JamesJ
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If 1/x = 2, then x = 1/2. If 1/z = 1/3, then z = 3
JamesJ
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Hence if
1/y = 25
then
y = ...
sparky16
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I don't understand how to find y. I kind of forgot how to do the reciprocal thing .Can u explain
JamesJ
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Scary.
\[ 2 \times \frac{1}{2} = 1 \]
Agreed?
JamesJ
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two times one half equals one, yes?
sparky16
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yes
JamesJ
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Suppose now that 2x = 1. What does x equal?
sparky16
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1/2
sparky16
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but i mean in the form of 1/y=25. I don't understand this one
JamesJ
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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 = ... ?
JamesJ
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If 1/y = a, then y = 1/a
JamesJ
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If 1/y = 25, then y = ... ?
sparky16
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ummm
sparky16
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I thought I would just times y/1 to both sides
JamesJ
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well
\[ y \times \frac{1}{y} = 1 \]
So if 1/y = 25, then
\[ y \times 25 = 1 \]
i.e., \( 25y = 1 \). Hence y = ...
JamesJ
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If 1/y = a, then y = 1/a
JamesJ
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Hence if 1/y = 25, then y = ....
sparky16
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1/y=25
times by y/1 to both sides... 25y???
JamesJ
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No. You are not reading what I am writing.
\[ \frac{1}{y} \times y = 1 \]
Do you agree with that statement?
sparky16
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yes
JamesJ
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Now suppose 1/y = 25, then
\[ 25 \times y = 1 \]
That is
\[ 25y = 1 \]
Agreed so far?
sparky16
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ok. 25y=1
Oh then divide by 25 so I get 1/25
sparky16
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thank you!
JamesJ
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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