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6 divided by 678
ABCD is a rectangle. Δ ADE and Δ ABF are two triangles such that ∠E=∠F as shown in the figure. Prove that AD x AF=AE x AB. Ans: Consider Δ ADE and Δ ABF ∠D = ∠B
Calculate the Probability A bag contains 80 balls of such 20 are red, 25 are blue and 35 are white. A ball is picked at random what is the probability that the ball picked is
solve the differential equation dy/dx=f(y)x^n+g(y)x^m by finding a one-parameter group leaving it invariant
The value of y that minimizes the sum of the two distances from (3,5) to (1,y) and from (1,y) to (4,9) can be written as a/b where a and b are coprime positive integers. Find a+b.
Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have, f ( x )≤ h (
The index of industrial production This is a quantity index compiled by the government. This measures changes in the volume of production in main industries. The index is a ex
Any point on parabola, (k 2 ,k) Perpendicular distance formula: D=(k-k 2 -1)/2 1/2 Differentiating and putting =0 1-2k=0 k=1/2 Therefore the point is (1/4, 1/2) D=3/(32 1/2
Consider a person's decision problem in trying to decide how many children to have. Although she cares about children and would like to have as many as possible, she knows that chi
How may six digit numbers can be made in which the sum of the digits is even? Ans = 9*10*10*10*10*5
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