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4 years ago

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A hemisphere of radius 4 sits on a horizontal plane. A cylinder stands with its axis vertical, the center of its base at the cen

ter of the sphere, and its top circular rim touching the hemisphere. Find the radius and height of the cylinder of maximum volume.

1 answer:

spin [16.1K]4 years ago

3 0

Answer:

Sawwekei

Step-by-step explanation:

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Step-by-step explanation:

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Suppose it takes 45 hours for robot A to construct a new robot. Working together with robot B, it takes 25 hours for both robots

Len [333]

Answer:

56 hours 25 minutes

Step-by-step explanation:

Given:

Suppose it takes 45 hours for robot A to construct a new robot

It takes 25 hours for both robots to construct a new robot.

Question asked:

How long would it take robot B to construct a new robot, working alone ?

Solution:

Let the time taken by robot B to construct new robot = $x$

<u>By robot A</u>

It takes 45 hours to construct = 1 new robot

It takes 1 hour to construct = $\frac{1}{45} \ new\ robot$

<u>By robot B</u>

It takes $x$ hours to construct = 1 new robot

It takes 1 hour to construct = $\frac{1}{x}$ new robot

<u>By working together</u>

It takes 25 hours to construct = 1 new robot

It takes 1 hour to construct = $\frac{1}{25} \ new\ robot$

$\frac{1}{25}$ new robot is constructed in = 1 hour

<u><em>New robot is constructed by both working together in 1 hour = New robot is constructed by robot A in 1 hour + New robot is constructed by robot B in 1 hour </em></u>

$\frac{1}{25} =\frac{1}{45} +\frac{1}{x} \\$

Subtracting both sides by $\frac{1}{45}$

$\frac{1}{25}-\frac{1}{45} =\frac{1}{45} -\frac{1}{45}+\frac{1}{x} \\\\\frac{1}{25}-\frac{1}{45} =\frac{1}{x}\\\\ Taking\ LCM \ of \ 25\ and\ 45,\ we\ got\ 225$

$\frac{9-5}{225} =\frac{1}{x} \\ \\ \frac{4}{225} =\frac{1}{x}\\\\ By\ cross \ multiplication\\4\times x=225\\Dividing\ both\ sides\ by\ 4\\x=56.25\ hours$

Thus, robot B would take 56 hours 25 minutes to construct a new robot, working alone.

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