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ABC is a right-angled isosceles triangle, right-angled at B. AP, the bisector of ∠BAC, intersects BC at P. Prove that AC 2 = AP 2 + 2(1+√2)BP 2 Ans: AC = √2AB (Sinc
A solid is formed by cutting the top off of a cone with a slice parallel to the base, and then cutting a cylindrical hole into the resulting solid. Determine the volume of the holl
Players and spectators enter a ballpark according to independent Poisson processes having respective rates 5 and 20 per hour. Starting at an arbitrary time, compute the probability
An unbiased die is tossed twice .Find the probability of getting a 4,5,6 on the first toss and a 1,2,3,4 on the second toss
statement of gauss thm
Example of Fractional Equations: Example: Solve the fractional equation (3x +8)/x +5 =0 Solution: Multiply both sides of the equation by the LCD (x). (x) ((3x
The tenth term in the binomial expansion of (1-1/4)(1-1/5)(1-1/6)...(1-1/n+3) is equal to
Graph y = tan ( x ). Solution In the case of tangent we need to be careful while plugging x's in since tangent doesn't present wherever cosine is zero (remember that tan x
Let {An} be sequence of real numbers. Define a set S by: S={i ? N : for all j > i, ai
The total ticket sales for a soccer game were $1,260; 210 tickets were purchased. If all the tickets are the similar price, what was the cost of a ticket? Divide the total sale
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