A builder uses the coordinate plane below to plan the location of a rectangular plot of land for a new house. The length of one
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Answer:
the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;
or 10.036
Step-by-step explanation:
Given the data in the question;
y = , y = 0, x = 1, x = 2.
Now, using the integration capabilities of a graphing utility
y = , y = 0
Volume =
Volume =
Volume =
Volume =
Volume =
Volume =
Volume = or 10.036
Therefore, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is;
or 10.036
The height of the screw = 16 inches.
<h3>How do you determine the number of revolutions in a circle?</h3>The total distance covered in one revolution will be equal to the perimeter of the wheel. Finally, to find the total number of revolutions, divide the total distance by distance covered in one revolution.
Given that,
Diameter of a bicycle = 16 inches
The distance the bike moves (forward) after the screw punctures the tire = 56π inches
We note that the circumference of the bicycle = π·D = π × 16 = 16π inches
Therefore,
= 3.5
Showing that the bicycle moves three and half complete turns (revolution) where after each complete turn, the screw starts from the bottom of the tire.
The height, h of the screw in the final half turn is given by the relation;
h = A cos(Bx - C) + D
Where
A = Amplitude of the motion = Diameter/2 = 16/2 = 8
P = The period of the motion 2π/B
Bx = The angle described by the motion = Half of one revolution = π = 180°
C = Phase shift = π
D = The mid line = Diameter/2 = 8 inches
Therefore;
h = 8×cos(π - π) + 8 = 16 inches
Hence, After the bike moves forward another 56π inches the height of the screw = 16 inches.
To learn more about number of revolution from the given link:
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