A cylindrical tank has a height of 10 feet and a radius of 4 feet. Jane fills the tank with water at a rate of 8 cubic feet per minute. At this rate, how many minutes will it take Jane to completely fill the tank without overflowing it?

Given:

A cylindrical tank has a height of 10 feet.

The radius of the cylindrical tank is 4 feet.

Jane fills the tank with water at a rate of 8 cubic feet per minute.

We need to determine the time it will take for Jane to completely fill the tank without overflowing it.

Volume of the cylinder:

The volume of the cylinder can be determined using the formula,

Substituting the values, we have;

Thus, the volume of the cylinder is 502.4 cubic feet.

Time taken:

The time taken can be determined using the formula,

Substituting the values, we have;

Thus, Jane takes 62.8 minutes to completely fill the tank without overflowing it.

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>

the system of inequity is

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

the solid line passing through the points (0,4) and (4,0).

the related equation of solid line is .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

the related equation of dashed line is

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be . the required inequality is

similarly, check the second related equation.

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is