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

1. JamesJ

What do you think is a good first step?

2. sparky16

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

3. JamesJ

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

4. JamesJ

*Is

5. sparky16

$2y ^{-1/2}=10$

6. 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

7. sparky16

How did you get 5?

8. sparky16

oh wait never mind. You just divided by 2

9. JamesJ

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

10. sparky16

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

11. 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.

12. sparky16

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

13. JamesJ

yes and hence y = ...

14. sparky16

25?

15. JamesJ

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

16. sparky16

I'm not sure

17. JamesJ

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

18. JamesJ

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

19. sparky16

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

20. JamesJ

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

21. JamesJ

two times one half equals one, yes?

22. sparky16

yes

23. JamesJ

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

24. sparky16

1/2

25. sparky16

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

26. 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 = ... ?

27. JamesJ

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

28. JamesJ

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

29. sparky16

ummm

30. sparky16

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

31. JamesJ

well $y \times \frac{1}{y} = 1$ So if 1/y = 25, then $y \times 25 = 1$ i.e., $$25y = 1$$. Hence y = ...

32. JamesJ

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

33. JamesJ

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

34. sparky16

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

35. JamesJ

No. You are not reading what I am writing. $\frac{1}{y} \times y = 1$ Do you agree with that statement?

36. sparky16

yes

37. JamesJ

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

38. sparky16

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

39. sparky16

thank you!

40. 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