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

- anonymous

- chestercat

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- anonymous

- anonymous

idk what to do with this?

- AkashdeepDeb

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

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## More answers

- anonymous

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...

- anonymous

that's all nothing else is need right now.

- anonymous

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

- 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'.
:)

- anonymous

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

- anonymous

|dw:1397796459525:dw|

- anonymous

|dw:1397796552699:dw|

- AkashdeepDeb

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

- anonymous

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.

- 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? :)

- anonymous

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

- AkashdeepDeb

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

- anonymous

yay!

- anonymous

can we do one more?

- AkashdeepDeb

Sure!

- anonymous

okay thanks.

- anonymous

\[r=7*t^2-51*t+92\]

- anonymous

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

- 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.

- anonymous

|dw:1397798167883:dw|

- anonymous

|dw:1397798377673:dw|

- anonymous

thanks for the help

- AkashdeepDeb

:)

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