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A circle touches the side BC of a triangle ABC at P and touches AB and AC when produced at Q and R. Show that AQ= 1/2 (perimeter of triangle ABC) Ans: Since the length o
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
Determine y′ for xy = 1 . Solution : There are in fact two solution methods for this problem. Solution 1: It is the simple way of doing the problem. Just solve for y to
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Two sides of a picture frame are glued together to form a corner. Each side is cut at a 45-degree angle. Using the illustration provided, ?nd the measure of ∠A. a. 45° b
Let ∑ = (0, 1). Define the following language: L = {x | x contains an equal number of occurrences of 01 and 10} Either prove L is regular (by constructing a DFA/NFA or a rege
what is the graph of 2 sin x
Comparison Test Assume that we have two types of series ∑a n and ∑b n with a n , b n ≥ 0 for all n and a n ≤ b n for all n. Then, A. If ∑b n is convergent then t
Speaking Mathematically : A Class 2 teacher was explaining the concept of place value to his students, using the number eleven. He started by saying "One and one make eleven." So
Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc
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