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yKpoI14uk [10]
2 years ago
6

If a = -35, b = 10 cm and c = -5, verify that:

Mathematics
1 answer:
Murljashka [212]2 years ago
7 0

Step-by-step explanation:

(i). a+(b+c) = (a+b)+c

-35+(10-5) = (-35+10)+(-5)

-35+5 = -25-5

-30 = -30

(ii). a×(b+c) = a×b + a×c

-35 × [10+(-5)] = -35×10 + -35×-5

-35 × (10-5) = -350 + 175

-35 × 5 = -350 + 175

-175 = -175

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

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f(1,0)=-7

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

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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

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t=0\implies f(10,0)=155

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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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