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A sphere and a cube have equal surface areas. Show that the ratio of the volume of the sphere to that of the cube is √6 : √π. Ans: S.A. of sphere = S.A of cube 4π r 2
What is our aim when teaching children multiplication? Firstly they should be able to judge which situations they need to multiply in, and the numbers that are to be multiplied sec
A solution to a differential equation at an interval α Illustration 1: Show that y(x) = x -3/2 is a solution to 4x 2 y′′ + 12xy′ + 3 y = 0 for x > 0. Solution : We'll
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
Let a, b, c 2 Z + . (a) Prove that if a|b, then ac|bc for all c. (b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
the variables x and y are thought to be related by a law of the form ay^2=(x+b)lnx Where a and b are unknown constants. Can a and b be found and how.
Multiply and divide by root2, then root2/root2(sinx+cosx) = root2(sinx/root2 + cosx/root2) = root2(sinx cos45+cosx sin45) = root2(sin(x+45))
We can define the conditional probability of event A, given that event B occurred when both A and B are dependent events, as the ratio of the number of elements common in both A an
The Shape of a Graph, Part I : In the earlier section we saw how to employ the derivative to finds out the absolute minimum & maximum values of a function. Though, there is many
Power Series and Functions We opened the previous section by saying that we were going to start thinking about applications of series and after that promptly spent the section
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