A spherical storage tank contains oil. The tank has a diameter of 6 feet. You are...

A spherical storage tank contains oil. The tank has a diameter of 6 feet. You are asked to calculate the height at which an 8-foot-long dipstick would be wet with oil when immersed in the tank when it contains 6 ft³ of oil. The equation giving the height h of the liquid in the spherical tank for the given volume and radius is given by:

f(h) = h³−9h² + 3.8197

Use the secant method to find roots of equations to find the height at which the dipstick is wet with oil.

Perform three iterations to estimate the root of the equation above.

Find the absolute relative approximate error at the end of each iteration and the least correct number of significant digits at the end of each iteration. (h_-1= 0.5 and h₀ = 1)

Expert Solution

Colby Messinger answered 1 year ago

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is...

A water tank is spherical in shape with radius of 90 feet. Suppose the tank is filled to a depth of 140 feet with water. Some of the water will be pumped out and, at the end, the depth of the remaining water must be 40 feet. i) Set up a Riemann sum that approximates the volume of the water that is pumped out of the tank. (use horizontal slicing). You have to draw a diagram and choose a coordinate...

A facility has a waste storage tank with a capacity of 40 cubic feet. Each week...

A facility has a waste storage tank with a capacity of 40 cubic feet. Each week the tank produces either 0, 10, 20, or 30 cubic feet of waste with respective probabilities of 0.1, 0.4, 0.3, and 0.2. If the amount of waste produced in a week creates a situation where the tank would overflow, the amount exceeding the tank’s capacity can be removed at a cost of $3 per cubic foot. At the end of each week, a contracted...

A conical tank, point down, has a radius of 6 feet and a depth of 9...

A conical tank, point down, has a radius of 6 feet and a depth of 9 feet. Water is filling the tank and thus the volume of water in the tank is changing with time, as is the depth of the water and the radius of the surface of the water. Suppose that at the instant the depth of the water is 4 feet, the depth of the water is changing at an instantaneous rate of0.125 feet per minute. How...

A conical tank extends from two foot in diameter at the discharge to twelve feet in...

A conical tank extends from two foot in diameter at the discharge to twelve feet in diameter at the top with sides 30 degree from the vertical. Water flows into the tank at 100 lbm/min. How long does it take to fil the tank to 80 percent full?

An oil company installs a new pipeline to connect a storage tank to an existing pump...

An oil company installs a new pipeline to connect a storage tank to an existing pump 1,000 feet away. Three possible diameters are being considered to make the pipeline, the related costs of which are presented below: pipeline diameter 4 inch. 6 inch. 8inch. initial cost $2,000 $3,000 $4,000 maintnance cost per year 600 500 400 pumping cost per hour 2.70 1.30 1.00 residual value 100 150 300 useful life 10 10 10 The company is presumed to apply a...

A certain spherical eukaryotic cell has a diameter of 51um. If a spherical organelle has a...

A certain spherical eukaryotic cell has a diameter of 51um. If a spherical organelle has a diameter of 860nm, how many of these organelles can the cell hold.

A rigid tank A is connected to a spherical and elastic balloon B. Each contains air...

A rigid tank A is connected to a spherical and elastic balloon B. Each contains air at an ambient temperature of 25 ° C. The volume of tank A is 0.1 m3 and the initial absolute pressure is 300 kPa. The initial diameter of the balloon is 0.5 m and the internal absolute pressure is 100 kPa. The tap connecting A and B is opened and left open. It can be assumed that the pressure inside the balloon is directly...

A steel storage tank 20m in diameter will be used to hold liquid petroleum product. When...

A steel storage tank 20m in diameter will be used to hold liquid petroleum product. When filled, the tank causes a bearing pressure of 150kPa. The soil underlying the tank has a unit weight of 16.5kN/m3 above the water table and 19.8kN/m3 below the water table. For a depth of 10m below the base of the tank, compute the effective vertical stress when the tank is empty and when it is full, for points under the center and the edge....

A storage tank contains ethanol. As liquid ethanol is taken from the lower part of the...

A storage tank contains ethanol. As liquid ethanol is taken from the lower part of the tank, nitrogen is fed into the upper part of the tank so that the pressure above the liquid in the tank is always 780 mmHg. Currently the depth of the liquid ethanol in the tank is 1.2 m. It is a summer day. The temperature in the tank is 50 OC. (a) If you took a sample of the vapor in the tank, what...

A storage tank at STP contains 21.6 kgkg of nitrogen (N2)(N2). a. What is the volume...

A storage tank at STP contains 21.6 kgkg of nitrogen (N2)(N2). a. What is the volume of the tank? b.What is the pressure if an additional 32.7 kgkg of nitrogen is added without changing the temperature?

Question