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maw [93]
3 years ago
9

What is the value of x?

Mathematics
1 answer:
leva [86]3 years ago
4 0
THE ANSWER IS D 8 BECAUSE I DID THE MATH
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Find all points on the portion of the plane x+y+z=5 in the first octant at which f(x, y, z) = xy2z2 has a maximum value.
irina1246 [14]
Lagrange multipliers:

L(x,y,z,\lambda)=xy^2z^2+\lambda(x+y+z-5)

L_x=y^2z^2+\lambda=0
L_y=2xyz^2+\lambda=0
L_z=2xy^2z+\lambda=0
L_\lambda=x+y+z-5=0

\lambda=-y^2z^2=-2xyz^2=-2xy^2z

-y^2z^2=-2xyz^2\implies y=2x (if y,z\neq0)

-y^2z^2=-2xy^2z\implies z=2x (if y,z\neq0)

-2xyz^2=-2xy^2z\implies z=y (if x,y,z\neq0)

In the first octant, we assume x,y,z>0, so we can ignore the caveats above. Now,

x+y+z=5\iff x+2x+2x=5x=5\implies x=1\implies y=z=2

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of f(1,2,2)=16.

We also need to check the boundary of the region, i.e. the intersection of x+y+z=5 with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force f(x,y,z)=0, so the point we found is the only extremum.
4 0
3 years ago
Matt he bought five book he needed 9 how many more he needed
Dimas [21]

Answer:

5

Step-by-step explanation:

4 0
3 years ago
Find a positive angle less than 360° that is coterminal with the given angle.
olya-2409 [2.1K]

Answer:

3(360⁰)-335⁰

=1080⁰-335⁰

=745⁰ is a positive angle.

6 0
3 years ago
Which of the following is equal to √^3√5<br>5^1/3<br>5^1/6<br>5^2/3<br>5^3/2​
svlad2 [7]
I think it’s number 3
5 0
3 years ago
A 25-foot tall flagpole casts a 42-foot shadow. What is the angle (to the neasrest tenth of degree) that the sun hits the flagpo
Maurinko [17]
Tan^-1 (tan x) = 42/25
x=tan^-1 42/25

x= 59.237 degrees.
8 0
3 years ago
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