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# Find the time until a tank with a hole is empty

Consider a water tank shaped like a right circular cone with its point up. Find the amount of time necessary for the tank to completely drain if there is a hole in its base. Express the time as a function of the dimension of the water tank and the area of the hole in the tank.

Incomplete.

# Find the depth of water in a leaky tank as time goes to infinity

Consider a water tank with vertical sides and with cross-section a square of area 4 feet. Water exits the tank through a hole which as area equal to \frac{5}{3} square inches, and water is added to the tank at a rate of 100 cubic inches per second. Show that the water level approaches the value of feet above the hole no matter what the initial water level was.

Incomplete.

# Find the time required for the water level in a tank to drop 1 foot

Consider a water tank with vertical sides and with cross-section a square of area 4 feet. Water exits the tank through a hole which as area equal to square inches. The water level is initially 2 feet above the level of the hole. Find the time required for the water level to drop 1 foot.

Incomplete.

# Find a function whose graph has given properties

Let be a function such that the points and are on the graph of . Assume that for every point on the graph of , the graph is above the line segment joining to . Further, assume that the area of the region bounded by the graph of and the line segment is . Find a formula for the function .

Incomplete.

# Find a function whose graph has given properties

Let be a function on the interval that is nonnegative and differentiable, and such that . If for each in the open interval the line given by the equation divides the ordinate set of into regions and where denotes the leftmost region. If the areas of the two regions obey the equation

where is a constant that does not depend on , find and .

Incomplete.

# Find a function whose ordinate set generates a solid of revolution with volume x2 f(x)

Let be a nonnegative, differentiable function whose graph passes through both points and . For every real number , the ordinate set of on the interval generates a solid of revolution when rotated about the -axis whose volume is given by

Find the formula for the function .

Incomplete.

# Find a function which divides a rectangle into pieces with given properties

Consider a curve whose Cartesian equation is given by , and which passes through the origin. A rectangular region is drawn with one corner at the origin, and the other corner on the curve of the graph of . The curve then divides the rectangle into two pieces and . These two pieces of the rectangle then generate solids of revolution when rotated about the -axis. If the volume of one solid of revolution is always times the volume of the other solid of revolution, find the equation for .

Incomplete.

# Find a function which divides a rectangle into pieces with given properties

Consider a curve whose Cartesian equation is given by , and which passes through the origin. A rectangular region is drawn with one corner at the origin, and the other corner on the curve of the graph of . The curve then divides the rectangle into two pieces and such that one of the regions has area times the area of the other for every such rectangle. Find the equation of .

Incomplete.

# Find a Cartesian equation for the pursuit path for given parameters

Let Q be a point which moves upward along the positive y-axis and let P be a point which starts at (1,0) and pursues Q according to an equation which stipulates that the distance from P to the y-axis is exactly \frac{1}{k} times the distance from Q to the origin for a positive number. Find the Cartesian equation for the path of pursuit the point P traces out.

Incomplete.

# Find a Cartesian equation for the pursuit path of given parameters

Let be a point which moves upward along the positive -axis and let be a point which starts at and pursues according to an equation which stipulates that the distance from to the -axis is exactly the distance from to the origin. Find the Cartesian equation for the path of pursuit the point traces out.

Incomplete.