Reference no: EM131100277
1. Question
Solve the following Integrals,
1. ∫cos7x sin4x dx
2. ∫cos5x sin6x dx
2. Question
a. A circle with co-ordinates (0,2), (0,-2), (2,0), (-2,0) is rotated 360 degrees about the y-axis, what is the volume of the solid formed by this rotation.
b. Rotate a curve defined by the function y = x2, between x = 2 and x = 4, about the,
i. x - axis
ii. y - axis
3. Question
Solve the integral U(x) = ∫tanθdθ.
4. Question
Solve the integral ∫cos(ln(x)).
5. Question
Two stiff parallel wires a distance d apart in a horizontal plane act as rails to support a light metal rod of mass m (perpendicular to each rail). A magnetic field →B, directed vertically upward acts throughout.
At t = 0, a constant current I begins to flow through the system. Determine the speed of the rod, which starts from rest at t = 0, as a function of time
(a) assuming no friction between the rod and the rails,
(b) if the coefficient of friction is μk
(c) In which direction does the rod move, east or west, if the current through it heads north?
6. Question
Write a program which takes in an input(number of alphabets) and prints out the alphabets such that a diamond shape is created at the core of the arrangement of the alphabets.
For example, if you enter 6, the program takes the alphabets A,B,C,D, E and F and arranges them in the manner shown below.
ABCDEFEDCBA
ABCDE EDCBA
ABCD DCBA
ABC CBA
AB BA
A A
AB BA
ABC CBA
ABCD DCBA
ABCDE EDCBA
ABCDEFEDCBA
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Create virtual options within petville
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Determine the minimum power requirement for the pump
: determine the minimum power requirement for the pump.
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People from their own community
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Shown in the graph for the indicated exercise
: Determine the values of x for which the function, as represented by the graphs in Fig. 23.12, is continuous. If the function is not continuous, determine the reason.
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What is the volume of the solid formed
: Determine the speed of the rod, which starts from rest at t = 0, as a function of time assuming no friction between the rod and the rails.
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What is the final volume of the cylinder
: What is the final volume of the cylinder? Does this process violate the second law of thermodynamics?
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Details of the implementation environment
: Present your results in the form of a research paper of more than ten pages in length. Illustrate data in tabulated and/or graphical form and give full details of the implementation environment.
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Determine the velocity of the water when it exits at a
: Water is drawn from the well at B through the 3-in. -diameter suction pipe and discharged through the pipe of the same size at A . The pump supplies 1.5 kW of power to the water. The water has the specific weight of 62.4 lb/ft3 .
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Determine the values of x
: Determine the values of x for which the function, as represented by the graphs in Fig. 23.12, is continuous. If the function is not continuous, determine the reason.
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