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Crazy boy [7]
3 years ago
5

Х = Зу 2x + 4y = 10 Substitution

Mathematics
1 answer:
ki77a [65]3 years ago
5 0

Answer:

y=1

x=3

Step-by-step explanation:

Multiply 2x by three because if you substitute to y, you would have the multiply.

Write what is left. 6y+4y=10

Combine like terms   10y=10

y=1

x=3

Check      3=3(1)

                     6+4=10

So this solution is correct

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Find the extreme values of f subject to both constraints f(x,y) = 2x^2+3y^2-4x-5, x^2 + y^2 <=16
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f(x,y)=2x^2+3y^2-4x-5
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f(x(t),y(t))=F(t)=2(4\cos t)^2+3(4\sin t)^2-4(4\cos t)-5=32\cos^2t+48\sin^2t-16\cos t-5
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F'(t)=16\sin t+16\sin2t=16\sin t+32\sin t\cos t=16\sin t(1+2\cos t)=0
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Now, solve for x,y for both cases:

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t=\dfrac{4\pi}3\implies\begin{cases}x=4\cos t=-2\\y=4\sin t=-2\sqrt3\end{cases}

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