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Furkat [3]
3 years ago
15

Help me pls i will make u a brainliest

Mathematics
1 answer:
omeli [17]3 years ago
8 0

101.66 ÷ 4.42 = 23 square feet

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Use Lagrange multipliers to find the maximum and minimum values of (i) f(x,y)-81x^2+y^2 subject to the constraint 4x^2+y^2=9. (i
sp2606 [1]

i. The Lagrangian is

L(x,y,\lambda)=81x^2+y^2+\lambda(4x^2+y^2-9)

with critical points whenever

L_x=162x+8\lambda x=0\implies2x(81+4\lambda)=0\implies x=0\text{ or }\lambda=-\dfrac{81}4

L_y=2y+2\lambda y=0\implies2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1

L_\lambda=4x^2+y^2-9=0

  • If x=0, then L_\lambda=0\implies y=\pm3.
  • If y=0, then L_\lambda=0\implies x=\pm\dfrac32.
  • Either value of \lambda found above requires that either x=0 or y=0, so we get the same critical points as in the previous two cases.

We have f(0,-3)=9, f(0,3)=9, f\left(-\dfrac32,0\right)=\dfrac{729}4=182.25, and f\left(\dfrac32,0\right)=\dfrac{729}4, so f has a minimum value of 9 and a maximum value of 182.25.

ii. The Lagrangian is

L(x,y,z,\lambda)=y^2-10z+\lambda(x^2+y^2+z^2-36)

with critical points whenever

L_x=2\lambda x=0\implies x=0 (because we assume \lambda\neq0)

L_y=2y+2\lambda y=0\implies 2y(1+\lambda)=0\implies y=0\text{ or }\lambda=-1

L_z=-10+2\lambda z=0\implies z=\dfrac5\lambda

L_\lambda=x^2+y^2+z^2-36=0

  • If x=y=0, then L_\lambda=0\implies z=\pm6.
  • If \lambda=-1, then z=-5, and with x=0 we have L_\lambda=0\implies y=\pm\sqrt{11}.

We have f(0,0,-6)=60, f(0,0,6)=-60, f(0,-\sqrt{11},-5)=61, and f(0,\sqrt{11},-5)=61. So f has a maximum value of 61 and a minimum value of -60.

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3 years ago
Write the percent as a fraction or mixed number in simplest form.<br><br> 88% =
Katyanochek1 [597]
88% it equal to .88 or 88/100 
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3 years ago
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For a field trip 30 Students Rode and cars and the rest filled six buses how many students were in each bus of 264 students were
kari74 [83]

Answer:39 students in each bus.

Step-by-step explanation:

264 - 30 = 234 ÷ 6 = 39

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Which are examples of results of good credit? Check all that apply.
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A bank gives you the lowest interest rate for a personal loan

You find it easy to borrow money when you need it
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Raghav has to load 2456 cartons of apples equally in 5 trucks. how many cartons will be left unloaded in the end?​
zlopas [31]

Answer:

12,280

Step-by-step explanation:

just do 1456×5 :))

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