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sparky16
 2 years ago
Solve:
2y^(1/2)=10
sparky16
 2 years ago
Solve: 2y^(1/2)=10

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JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0What do you think is a good first step?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0umm maybe..\[\sqrt{2}\times \sqrt{1/y}=10\]

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0If the problem \[ 2y^{1/2}  10 \] or \[ (2y)^{1/2} = 10 \]

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Right. 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
 2 years ago
Best ResponseYou've already chosen the best response.0oh wait never mind. You just divided by 2

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0C'mon. Look at the expression before hand. I divided both sides by 2.

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0then we should turn y^(1/2) into \[\sqrt{1/y}\] right?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0There 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
 2 years ago
Best ResponseYou've already chosen the best response.0Ok. \[\sqrt{1/y}=5\] I square both sides right? so 1/y =25

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0If 1/y = 25, then it can NOT be the case y = 25.

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0If 1/x = 2, then x = 1/2. If 1/z = 1/3, then z = 3

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Hence if 1/y = 25 then y = ...

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0I don't understand how to find y. I kind of forgot how to do the reciprocal thing .Can u explain

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Scary. \[ 2 \times \frac{1}{2} = 1 \] Agreed?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0two times one half equals one, yes?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Suppose now that 2x = 1. What does x equal?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0but i mean in the form of 1/y=25. I don't understand this one

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Yes 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
 2 years ago
Best ResponseYou've already chosen the best response.0If 1/y = a, then y = 1/a

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0If 1/y = 25, then y = ... ?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0I thought I would just times y/1 to both sides

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0well \[ y \times \frac{1}{y} = 1 \] So if 1/y = 25, then \[ y \times 25 = 1 \] i.e., \( 25y = 1 \). Hence y = ...

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0If 1/y = a, then y = 1/a

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Hence if 1/y = 25, then y = ....

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.01/y=25 times by y/1 to both sides... 25y???

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0No. You are not reading what I am writing. \[ \frac{1}{y} \times y = 1 \] Do you agree with that statement?

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Now suppose 1/y = 25, then \[ 25 \times y = 1 \] That is \[ 25y = 1 \] Agreed so far?

sparky16
 2 years ago
Best ResponseYou've already chosen the best response.0ok. 25y=1 Oh then divide by 25 so I get 1/25

JamesJ
 2 years ago
Best ResponseYou've already chosen the best response.0Yes 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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