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Mashutka [201]
3 years ago
9

Perform the indicated operation. Write the sum as a fraction, whole number, or mixed number in lowest terms.

Mathematics
1 answer:
Readme [11.4K]3 years ago
7 0

Answer:

Fraction = 10625/72

Decimal = 147.5694

Mixed Number = 147 41/72

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We need to optimize f(x, y, z) = x + 2y subject to the constraints g(x, y, z) = x + y + z = 8 and h(x, y, z) = y2 + z2 = 4. To f
Evgesh-ka [11]

The Lagrangian is

L(x,y,z,\lambda,\mu)=x+2y+\lambda(x+y+z-8)+\mu(y^2+z^2-4)

with critical points where the partial derivatives vanish:

L_x=1+\lambda=0\implies\lambda=-1

L_y=2+\lambda+2\mu y=0\implies\mu=-\dfrac1{2y}

L_z=\lambda+2\mu z=0\implies\mu=\dfrac1{2z}

L_\lambda=x+y+z-8=0

L_\mu=y^2+z^2-4=0

The second and third equations tell us z=-y, so that in the last equation we find

y^2+(-y)^2=2y^2=4\implies y=\pm\sqrt2\implies z=\mp\sqrt2

and from the fourth equation we get

x+y+z=x=8

So we have two critical points, (8,\sqrt2,-\sqrt2) and (8,-\sqrt2,\sqrt2), which give respective extreme values of f(8,\sqrt2,-\sqrt2)=8+2\sqrt2 (maximum) and f(8,-\sqrt2,\sqrt2)=8-2\sqrt2 (minimum).

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3 years ago
I need help on this question.
BartSMP [9]

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The expression sin x (cos x cot x - sin x) simplifies to?
nikdorinn [45]
◆ Trigonometric Identities ◆

Hey !!

Check the attachment.
Hope it helps you :)

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The answer would be 14,000 dollars because, Turn the fraction into in improper fraction = to 125
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