## Ash90 one year ago i need help solving this replace r and g with the following and find the time-out. r=91-7* sqrt(t) g=14*t

1. Ash90

@AkashdeepDeb

2. Ash90

idk what to do with this?

3. AkashdeepDeb

Do we just have to find the time in this question? And is any other equation given? :)

4. Ash90

yes we just need to find the time in this equation but I have to write it out by showing my work. let me check and see if anything else is given...

5. Ash90

that's all nothing else is need right now.

6. Ash90

what this is is a programm that when you do the calculations the colors are set up to do what you need them to.

7. AkashdeepDeb

That's cool! Well, if you have to find the value of t in terms of r or in terms of g, you can do that. But if you want to find the value of t, in terms of real numbers, [Although, I don't think it is possible] I suggest you tag someone else. The equations you have posted are called Parametric equations, you can also express r in terms of g here but I am not sure how to go about calculating the sole value of 't'. :)

8. Ash90

could i show you what i have and maybe you can help from there?

9. Ash90

|dw:1397796459525:dw|

10. Ash90

|dw:1397796552699:dw|

11. AkashdeepDeb

Yes, I can help you from there! But is it given that r=g ? Because you have equated it over there! :D

12. Ash90

well i think what i had to do was set them equal to each other if i'm not mistaking i think thats what the teacher wanted.

13. AkashdeepDeb

Okay. So if r=g $$91-7 \sqrt{t} = 14t$$ $$91-14t = 7\sqrt{t}$$ $$Squaring ~~both ~~sides ~~we~~ get:$$ $$(91-14t)^2 = 49t$$ $$196t^2 + 8281 - 2548t = 49t$$ $$196t^2 - 2597t + 8281$$ $$~~~~~~~~~~~~Where~~[a = 196, ~b = -2597,~c = 8281]$$ Use the quadratic equation below to solve for $$t$$: $\frac{-b \pm \sqrt{b^2-4ac}}{2a}$ Got it? :)

14. Ash90

$t=\frac{ 53+\sqrt{105} }{ 8 }, t=\frac{ 53-\sqrt{105} }{ 8 }$

15. AkashdeepDeb

Yes, if you got that by calculating the above equation, then yes. :)

16. Ash90

yay!

17. Ash90

can we do one more?

18. AkashdeepDeb

Sure!

19. Ash90

okay thanks.

20. Ash90

$r=7*t^2-51*t+92$

21. Ash90

for this one i thought using quadratic formula right of hand would be a good idea

22. AkashdeepDeb

You cannot always do that. The quadratic formula can only be used when f(x) = ax^2 + bx + c = 0 [And zero only] As it gives us the zeroes of the polynomial/expression. What you could do is write it like this: 7t^2 - 51t + 92 - r = 0 Now apply the quadratic formula, considering, [c = 92-r] Getting this? :) You may also try this by the completing-the-square method, although I am not a 100% sure if it'll work here.

23. Ash90

|dw:1397798167883:dw|

24. Ash90

|dw:1397798377673:dw|

25. Ash90

thanks for the help

26. AkashdeepDeb

:)