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Prove that a simple graph is connected if and only if it has a spanning tree. Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G.
a) The distance d that can be seen from horizon to horizon from an airplane varies directly as the square root of the altitude h of the airplane. If d = 213 km for h = 3950
Utilizes the second derivative test to classify the critical points of the function, h ( x ) = 3x 5 - 5x 3 + 3 Solution T
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1. For a function f : Z → Z, let R be the relation on Z given by xRy iff f(x) = f(y). (a) Prove that R is an equivalence relation on Z. (b) If for every x ? Z, the equivalenc
#question when equation of tangent T=0 and why
Andy earned the subsequent grades on his four math quizzes: 97, 78, 84, and 86. What is the average of his four quiz grades? To ?nd out the average, you must add the items (97
x 4 - 25 There is no greatest common factor here. Though, notice that it is the difference of two perfect squares. x 4 - 25 = ( x 2 ) 2 - (5) 2 Thus, we can employ
what is fraction?
In a right triangle ABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that 9AQ 2 = 9AC 2 +4BC 2
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