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Show that for odd positive integer to be a perfect square, it should be of the form 8k +1. Let a=2m+1 Ans: Squaring both sides we get a2 = 4m (m +1) + 1 ∴ product of two
Graph y = cos (x) Solution: There actually isn't a whole lot to this one. Given the graph for -4 ? ≤ x ≤ 4 ? . Note that we can put all values of x in cosine (that wo
4/(x+7)(x+4)
a triangle with side lengths in the ratio 3:4:5 is inscribed in a circle of radius 3.what is the area of the triangle.
Area between Curves In this section we will be finding the area between two curves. There are in fact two cases that we are going to be looking at. In the first case we des
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
Show that the radius of the circle,passing through the centre of the inscribed circle of a triangle and any two of the centres of the escribed circles,is equal to the diameter of t
Your friends have opened an ocean fishing operation that requires their fishing vessel to cross a channel, where the depth of the water (measured in metres) varies with time, and i
Find out where the following function is increasing & decreasing. A (t ) = 27t 5 - 45t 4 -130t 3 + 150 Solution As with the first problem first we need to take the
Descrbe about Arithmetic and Geometric Sequences? When numbers are listed according to a particular pattern, we call the list a sequence. In a sequence, the numbers are separat
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