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A fox and an eagle lived at the top of a cliff of height 6m, whose base was at a distance of 10m from a point A on the ground. The fox descends the cliff and went straight to the p
Find out the length of y = ln(sec x ) between 0 x π/4. Solution In this example we'll need to use the first ds as the function is in the form y = f (x). So, let us g
After a lot of effort, 8-year-old Hari worked out 2 x 88 = 176. When asked to say what 2 x 89 was, after a lot of hard work, he produced the answer 178. How would you help him to r
If e were rational, then e = n/m for some positive integers m, n. So then 1/e = m/n. But the series expansion for 1/e is 1/e = 1 - 1/1! + 1/2! - 1/3! + ... Call the first n v
3x+y=9 5x-y=7
In this theorem we identify that for a specified differential equation a set of fundamental solutions will exist. Consider the differential equation y′′ + p (t ) y′ + q (t
Determine dy & Δy if y = cos ( x 2 + 1) - x as x changes from x = 2 to x = 2.03 . Solution Firstly let's deetrmine actual the change in y, Δy . Δy = cos (( 2.03) 2
Find the volume of a cylinder of radius r and height h. Solution : Here, as we mentioned before starting this illustration we actually don't require using an integral to get t
1. What is the probability that the two beverages will be of the same kind? 2. What is the probability that the two beverages will be different? 3. What is the probability
Suppose S = {vi} and T = {ti} are "easy" sets of knapsak weight. Also, P and q are primes p > ?Si and q > ?ti. We can combine S and T into a signle set of knapsack weight as follow
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