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Consider the forced spring mass system (dy2/dt2) + 5y = 6 sin(αt). Where α is a parameter.
1. For which value of α does the system exhibit a resonance?
2. Find the general solution for the value of α found in (a)
Assignment 1. A cycle in a graph is Hamiltonian if it goes through all vertices. Suppose G is a graph on n vertices with the property that for every pair of vertices u, v that are not adjacent, deg(u) + deg(v) ≥ n. Prove that G has a Hamiltonian c..
A liberal arts college has 1000 students. The numbers studying various languages are: English (E) 780; French (F) 220; and Spanish (S) 52.
At noon, ship A is 65 km due north of ship B. Ship A is sailing south at 14 km/hr and ship B is sailing east at 16 km/hr. How fast are the the two ships approaching each other 5 hours later at 5:00?
Which of the two sets are equivalent
Two adjacent sides of a regular hexagon are given as the vectors u? and v? in Figure. Label the remaining sides in terms of u? and v?.
What is the proof of Pythagoras Theorem ?
An investment in a certain machine is expected to earn a profit of $400 000 each year.
Plot a histogram of the variable age. Include an appropriate title to your histogram. Explain the plot.
The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan.
A stone is tossed into a pond creating a circular ripple whose radius increases at a rate of 3 feet per second. In square feet per second, how fast is the area of the ripple increasing 15 seconds after the stone hits the water?
Calculate the maximum radius of curve no. 2 that will maintain 125' between p.t. 1 and p.c. 2. Calculate the curve stakeout information for half (50') stations at 17.5' left (outside) of curve center line. Include long & short chords.
let f be the function defined by f(x) = 12x^(2/3) - 4x. a) find the intervals on which f is increasing. b) Find the x and y coordinates of all relative maximum points.
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