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3 years ago

PLEASE HELPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Vladimir79 [104]3 years ago

5 0

Your answer: 4,744,473,263,806,742

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The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y, z) = 3x + 6y - 6z + 1. A bee i

madam [21]

You're looking for the extreme values of $T(x,y,z)=3x+6y-6z+1$ subject to $x^2+y^2+z^2=9$ . The Lagrangian is

$L(x,y,z,\lambda)=3x+6y-6z+1+\lambda(x^2+y^2+z^2-9)$

with critical wherever the partial derivatives vanish:

$L_x=3+2\lambda x=0\implies x=-\dfrac3{2\lambda}$

$L_y=6+2\lambda y=0\implies y=-\dfrac3\lambda$

$L_z=-6+2\lambda z=0\implies z=\dfrac3\lambda$

$L_\lambda=x^2+y^2+z^2-9=0$

Substituting the first three solutions into the last equation gives

$\dfrac9{4\lambda^2}+\dfrac9{\lambda^2}+\dfrac9{\lambda^2}=9$

$\implies\lambda=\pm\dfrac32$

$\implies x=1,y=2,z=-2\text{ or }x=-1,y=-2,z=2$

At these points, we have

$T(1,2,-2)=28$

$T(-1,-2,2)=-26$

so the highest temperature the bee can experience is 28º F at the point (1, 2, -2), and the lowest is -26º F at the point (-1, -2, 2).

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3 years ago

If you like anime comment your favorite

miv72 [106K]

Answer:

Step-by-step explanation:

my hero academia , banana fish and seven deadly sins

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2 years ago

Solve for x 510 (2x + 3) 65% 60° 64° 43 (3x - 1)º

marshall27 [118]

Answer:

2x plus 3 hope this helps. Mark as brainlist

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3 years ago

Morgan is walking her dog on an 8-meter-long leash. She is currently 500 meters from her house, so the maximum and minimum dista

Gnom [1K]

Given:
Morgan = 500 meters from her house
Length of leash = 8 meters

minimum distance of the dog from the house 500 - 8 = 492 meters.
maximum distance of the dog from the house 500 + 8 = 508 meters.

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3 years ago

X^2 - 4x - 77 = 0 Factor and check

Olenka [21]

X² - 4x - 77 = 0

( x + 7) ( x - 11)

x + 7 = 0

x - 11 = 0

x = -7
x = 11

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3 years ago