anonymous
  • anonymous
Solve: 2y^(-1/2)=10
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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JamesJ
  • JamesJ
What do you think is a good first step?
anonymous
  • anonymous
umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]
JamesJ
  • JamesJ
If the problem \[ 2y^{-1/2} - 10 \] or \[ (2y)^{-1/2} = 10 \]

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