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Evgesh-ka [11]
3 years ago
6

The diameter of a cone-shaped storage tank is 14 feet and it's height is 9 feet. Find the volume of liquid the tank can hold. Ro

und your answer to the integer, if necessary. Use the approximate of value of /pi , that is 3.14.
Mathematics
1 answer:
NemiM [27]3 years ago
6 0

Answer:

461.6 ft³

Step-by-step explanation:

V(cone) = 1/3πr²h

= 1/3π(7²)(9)

= 49·3π

= 147(3.14)

= 461.6 ft³

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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.
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This box is a right rectangular prism. Its dimensions are 3 inches by 3 inches by 11 inches.
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Answer:

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Step-by-step explanation:

there is your anser

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2<br> 2. Evaluate (a + y)+ 2y if a = 5 and y = -3.<br> F 58<br> G -2<br> H 70<br> J 10
NARA [144]
<h3>Answer:  G) -2</h3>

=======================================================

Explanation:

I'm assuming you meant to say (a+y)^2 + 2y

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(a+y)^2 + 2y

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(2)^2 + 2(-3)

4 + 2(-3)

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So (a+y)^2 + 2y = -2 when a = 5 and y = -3.

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Answer:

The vertical line test is used to determine whether a graph line is a FUNCTION

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Step-by-step explanation:

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