A cylindrical glass of water with diameter 3.5 in . sits on a horizontal counter top. a. Write an equation of the circular surface of the water. Assume that the origin is placed at the center of the circle. b. If the glass is tipped 30 ° , what shape will the surface of the water have? c. With the glass tipped 30 ° , the waterline makes a slope of 1 2 with the coordinate system shown. Determine the length of the major and minor axes. Round to 1 decimal place.
A cylindrical glass of water with diameter 3.5 in . sits on a horizontal counter top. a. Write an equation of the circular surface of the water. Assume that the origin is placed at the center of the circle. b. If the glass is tipped 30 ° , what shape will the surface of the water have? c. With the glass tipped 30 ° , the waterline makes a slope of 1 2 with the coordinate system shown. Determine the length of the major and minor axes. Round to 1 decimal place.
Solution Summary: The author explains the equation of the circular surface of water in a cylindrical glass of diameter 3.5in that sits on the horizontal counter top.
A cylindrical glass of water with diameter
3.5
in
.
sits on a horizontal counter top.
a. Write an equation of the circular surface of the water. Assume that the origin is placed at the center of the circle.
b. If the glass is tipped
30
°
,
what shape will the surface of the water have?
c. With the glass tipped
30
°
,
the waterline makes a slope of
1
2
with the coordinate system shown. Determine the length of the major and minor axes. Round to 1 decimal place.
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.
23. Network Analysis The figure shows the flow of traffic
(in vehicles per hour) through a network of streets.
200
100-
-100
200
(a) Solve this system for i = 1, 2, 3, 4.
(b) Find the traffic flow when x = 0.
(c) Find the traffic flow when x = 100.
(d) Find the traffic flow when x, = 2x₂.
2\int_{-3/2}^{3/2} \sqrt{4u^2+2} du
2. Consider the following:
Prove that x, x2, and 1/x are the solutions to the homogeneous equation
corresponding to x³y"" + x²y" + 2xy' + 2y = 2x4.
b. use variation of parameters to find a particular solution and complete the general
solution to the differential equation. I am interested in process. You may use a
computer for integration, finding determinants and doing Kramer's.
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