The shape of a container is obtained by rotating the curve y = x^2 over the interval 0 ≤ x ≤ 2 about the y-axis. If the tank is full of water, the work required for pumping all water to the top of the...
The shape of a container is obtained by rotating the curve y =
x^2 over the interval 0 ≤ x ≤ 2 about the y-axis. If the tank is
full of water, the work required for pumping all water to the top
of the tank can be expressed as an integral W = f(b,a) f(y)dy. Use
trapezoidal rule on four subintervals of equal length to estimate
the work. (Assume that water density is ρ kg/m3, and gravity
acceleration g m/s2.)
(a) 6πρg (b) 8πρg (c) 10πρg (d) 12πρg (e) 14πρg
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The shape of a container is obtained by rotating the curve y = x^2 over the interval 0 ≤ x ≤ 2 about the y-axis. If the tank is full of water, the work required for pumping all water to the top of the...
5 1.) A storage container has the shape obtained by revolving the curve y = 1x4...
5 1.) A storage container has the shape obtained by revolving the curve y = 1x4 (shown on the right) from x = 0 to x = 2 about the y-axis, where x and y are measured in meters. 4 4 3 The tank is partially filled with coconut oil, up to a height of 1 meter. 2 1 kg : 900 = and the (The density of coconut oil is p acceleration due to gravity is g m3, т...
9. (9 points) Suppose we have a triangular tank full of water. The tank is 2 meters long, half a meter tall and a meter wide (see below). Set up an integral for how much work is done when pumping...
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Create a bucket by rotating around the y-axis the curve y=5ln(x−4) from y = 0 to y = 6. If this bucket contains a liquid with density 720 kg/m3 filled to a height of 2 meters, find the work required to pump the liquid out of this bucket (over the top edge). Use 9.8 m/s2 for gravity. Work =_____ Joules
(2) The work required to pump the fluid from a tank (between a units and b...
(2) The work required to pump the fluid from a tank (between a units and b units above the bottom of a tank) of constant mass-density p out to a height h above the bottom of the tank is given by W- pg(cross-sectional area at y)(distance fluid at y needs to be lifted) dy where g is the acceleration due to gravity and y is the distance from bottom of the tank. Note: Water has a mass-density of p 10...
2) A tank is created by revolving the region enclosed by y=Vx,x=0, and y= 2 about...
2) A tank is created by revolving the region enclosed by y=Vx,x=0, and y= 2 about the y-axis. The tank is filled with a liquid of weight-density 70 lb/ft? . 3 3 o Setup the integral that would give the work done in pumping the liquid to a height 1 ft. above the top of the tank. (Setup Only) o Give the units the answer would have.
Simpson's rule for a volume problem
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Consider the following. x = 3 sin y , 0 ≤ y ≤ π, x = 0; about y = 4 (a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified...
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Please help with 1-10 and please show all work thanks. Show all of your work neatly,...
Please help with 1-10 and please show all work thanks.
Show all of your work neatly, and express solutions as exact answers unless otherwise requested. No credit will be given to solutions that have no work shown! BOX or CIRCLE your final answer. 1. Sketch a graph and shade the area of the region bounded by the following equations. Set up an integral that would give this area. 2x + y2 = 6 and y=x+1 2. Sketch a graph and...
5 1.) A storage container has the shape obtained by revolving the curve y = 1x4 (shown on the right) from x = 0 to x = 2 about the y-axis, where x and y are measured in meters. 4 4 3 The tank is partially filled with coconut oil, up to a height of 1 meter. 2 1 kg : 900 = and the (The density of coconut oil is p acceleration due to gravity is g m3, т...
9. (9 points) Suppose we have a triangular tank full of water. The tank is 2 meters long, half a meter tall and a meter wide (see below). Set up an integral for how much work is done when pumping water out of the top of the tank. Use p for the density of water and g for the acceleration due to gravity. Do not evaluate the integral. 0.5 m 1 m
9. (9 points) Suppose we have a triangular...
(2) The work required to pump the fluid from a tank (between a units and b units above the bottom of a tank) of constant mass-density p out to a height h above the bottom of the tank is given by W- pg(cross-sectional area at y)(distance fluid at y needs to be lifted) dy where g is the acceleration due to gravity and y is the distance from bottom of the tank. Note: Water has a mass-density of p 10...
2) A tank is created by revolving the region enclosed by y=Vx,x=0, and y= 2 about the y-axis. The tank is filled with a liquid of weight-density 70 lb/ft? . 3 3 o Setup the integral that would give the work done in pumping the liquid to a height 1 ft. above the top of the tank. (Setup Only) o Give the units the answer would have.
Please help with 1-10 and please show all work thanks.
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