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Question
1 Find all solutions of the following equations in the interval [0, 2π)
(a) sin(2x) = √2 cos(x).
(b) 2 cos2(x) + 3 sin(x) = 3.
2. Sketch the graph of the circular function
F(Θ) = 1- 2cos (3Θ +π)
i. State clearly the amplitude, phase shift, period and the equation of the midline.
ii. Show working for all Θ- and y-intercepts for the function y = f(Θ).
iii. Show at least two periods for the graph of y = f(Θ), and label the axes clearly.
(b) Prove the following identity
2sin(1/2 (x+y))cos (1/2(x-y))= sin(X) +sin(y)
Make sure you show all working and give clear explanations.
The acceleration of an oscillating particle is defined by the relation a = -kx Determine the value of k such that v = 15 in./s when x = 0 and x = 3 in. and v = 0, the speed of the
procedure of tracing a closed loop
(i) Test for the existence of regression (the F-test). Carefully de ne the null and alternative hypothesis, and explain the result of any R output you obtain. (ii) Which of the
r u there?
Determine the missing entries in the following divided difference table and use the result to estimate f(1/2).
First systems were described as systems that had one method of storing energy. Second order systems; wait for it.... have two methods of storing energy. Using a similar mechanica
a. Explain the Integrated Circuits? What are the benefits of ICs as compared to standard printed circuits? b. Explain in brief, the various steps included in fabrication of ICs.
discussion
1. what is the formula of the sequence by three?
Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0
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