A solar water heater is made from a long sheet of metal bent so that the cross sections are parabolic. A long tube of water is placed inside the curved surface so that the height of the tube is equal to the focal length of the parabolic cross section. In this way, water in the tube is exposed to maximum heat. a. Determine the focal length of the parabolic cross sections so that the engineer knows where to place the tube. b. Use a coordinate system with origin at the vertex of a parabolic cross section and write an equation of the parabola.
A solar water heater is made from a long sheet of metal bent so that the cross sections are parabolic. A long tube of water is placed inside the curved surface so that the height of the tube is equal to the focal length of the parabolic cross section. In this way, water in the tube is exposed to maximum heat. a. Determine the focal length of the parabolic cross sections so that the engineer knows where to place the tube. b. Use a coordinate system with origin at the vertex of a parabolic cross section and write an equation of the parabola.
Solution Summary: The author calculates the focal length of the parabolic cross section of a solar water heater.
A solar water heater is made from a long sheet of metal bent so that the cross sections are parabolic. A long tube of water is placed inside the curved surface so that the height of the tube is equal to the focal length of the parabolic cross section. In this way, water in the tube is exposed to maximum heat.
a. Determine the focal length of the parabolic cross sections so that the engineer knows where to place the tube.
b. Use a coordinate system with origin at the vertex of a parabolic cross section and write an equation of the parabola.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
The correct answer is Ccould you show me how to do it by finding a0 and and akas well as setting up the piecewise function and integrating
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7. Fill in the blanks to write the calculus problem that would result in the following integral (do
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Find the volume of the solid obtained when the region under the curve
on the interval
is rotated about the
axis.
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solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x|
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and the curve y
y =
about the line
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A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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