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(a) A graph has six vertices every two of which are joined by an edge. Each edge is colored red or white. Show that the graph contains a monochromatic triangle.
(b) Is the result of (a) true for a graph with five vertices? Explain.
Find the derivatives of the following functions (Do not simplify): f(x) = 20x^(11/5) - 13x^(5/4) - 4x(-7/2)
Assume that a watermelon dropped from a tall building falls y=16t^2 in t sec. Find the watermelon's average speed during the first 3 sec of fall and the speed at the instant t=3sec.
For each of the following sequences a0, a1, a2, . . . , determine a closed form for the generating series A(x) = a0 + a1x + a2x2 + · ·
a hot air balloon rises and moves away from you. the total distance it travels is 1382 feet. the angle of elevatin from you to the balloon
How much money has been borrowed in the energy sector by smaller companies hoping to capitalize on the oil market in the last two years
using a trigonometric substitution, find the transformed integral but do not integrate.
Where should Steve cut the wire so that the total area of the circle and square combined is as small as possible? What is this minimal area? What should Steve do if he wants the combined area to be as large as possible?
data gathered by the u.s department of transportation show the number of miles that residents of the 75 largest
In each case make a conjecture about a possible generalisation, and explore it (i.e. attempt to prove your conjectures true or false).
The normal stress acting at the end of the bar varies according to s = E(x - x1)/x1 , where x is the position of the end of the bar, x1 is the initial length, and E is a material constant (Young's modulus). For E = 2 * 107 kPa, determine the work..
What price will generate the greatest profit for the airline?
The rocket is tracked through a telescope by an observer located 11 km from the launching pad. Find the rate at which the angle between the telescope and the ground is increasing 3 min after lift-off.
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