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Mademuasel [1]
2 years ago
8

Whitney goes into Rodger’s Pizza-Toy store and buys a toy for $14. She gives Rodger a $20 bill. Rodger doesn't have any change,

so he takes the $20 bill across the street to Kevin, the clerk in Plato’s Gym. Plato trades Rodger’s $20 bill for twenty $1 bills. Rodger comes back and gives Whitney $6 in change. Whitney takes the toy and the $6 chance and leaves town forever. Half an hour later Plato comes over to Rodger’s gym, furious. He has discovered that the $20 bill he gave him is counterfeit. Rodger, gives Plato a genuine $20 bill he has in the till from an earlier sale.
Question:
Now that it is all over, who came out behind? And by how much? Explain.
Mathematics
1 answer:
Shtirlitz [24]2 years ago
7 0

Answer:

I think Roger $40

Step-by-step explanation:

He got scammed by Whitney for $20 then had to give Plato an actual $20 bill

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First find the critical points of <em>f</em> :

f(x,y)=2x^2+3y^2-4x-5=2(x-1)^2+3y^2-7

\dfrac{\partial f}{\partial x}=2(x-1)=0\implies x=1

\dfrac{\partial f}{\partial y}=6y=0\implies y=0

so the point (1, 0) is the only critical point, at which we have

f(1,0)=-7

Next check for critical points along the boundary, which can be found by converting to polar coordinates:

f(x,y)=f(10\cos t,10\sin t)=g(t)=295-40\cos t-100\cos^2t

Find the critical points of <em>g</em> :

\dfrac{\mathrm dg}{\mathrm dt}=40\sin t+200\sin t\cos t=40\sin t(1+5\cos t)=0

\implies\sin t=0\text{ OR }1+5\cos t=0

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t=\pi\implies f(-10,0)=235

t=2\pi-\cos^{-1}\left(-\dfrac15\right)\implies f(-2,-4\sqrt6)=299

So <em>f</em> has a minimum of -7 and a maximum of 299.

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