#busyatmaths, Mathematics

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Find the number of ways to arrange words, Q. Find the number of ways three ...

Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution:  There are 26 ways of choosing the first lett

Show that cos - cos /sin - sin = a/b, A ladder sets against a wall at an ...

A ladder sets against a wall at an angle α to the horizontal.  If the foot is pulled away from the wall through a distance of 'a', so that is slides a distance 'b' down the wall ma

Conditional probability: independent events, Conditional Probability: Indep...

Conditional Probability: Independent Events If the probability of an event is subject to a restriction on the sample space, the probability is said to be conditional. Co

Topological spease, let X be a nonempty set. let x belong to X. show that t...

let X be a nonempty set. let x belong to X. show that the collection l={ union subset of X : union = empty or belong U

Draw the bipartite graph, The graph C n , n  ≥  3 contains n vertices and n...

The graph C n , n  ≥  3 contains n vertices and n edges creating a cycle. For what value of n is C n a bipartite graph? Draw the bipartite graph of C n to give explanation for yo

Surface area- applications of integrals, Surface Area- Applications of inte...

Surface Area- Applications of integrals In this part we are going to look again at solids of revolution. We very firstly looked at them back in Calculus I while we found the

Prove sum of squares any two sides equal twice square, Prove that in any tr...

Prove that in any triangle the sum of the squares of any two sides is equal to twice the square of half of the third side together with twice the square of the median, which bisect

How many permutations can you make of the word statistics, Q. How many perm...

Q. How many permutations can you make of the word STATISTICS? Solution:  There are 10 letters in the word STATISTICS, i.e. n=10. Three of them are S's, so n 1 =3, three are T'

Simple interest, find the simple interest on Rs. 68,000 at 50/3 per annum f...

find the simple interest on Rs. 68,000 at 50/3 per annum for 9 month

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