## Decipher this: Supermaniam?

Answer Supermaniam = superman + i + am So answer = i am superman.

## How do you solve the question 8 8’s = 1000?

Answer It’s classic one and usually people only know “one way” to solve it. There are two ways … and here they are: 888 + 88 + 8 + 8 + 8 = 1000 (8888 – 888) / 8 = 1000

## Quadratic equations

Question 1) A number exceeds four times its reciprocal by 3. find the number forming a quadratic equation. 2) A cyclist travels 40km at a speed of x km/h. Find the time taken in terms of x. Find when his speed is reduced by 2 km/h. If the difference between the times is one...

## How can I show that gcd(a,b) =gcd(b,r) ? Euclidean algorithm? given a=bq+r?

Comments Off on How can I show that gcd(a,b) =gcd(b,r) ? Euclidean algorithm? given a=bq+r?Answer Let gcd(a,b) = t. … (1) So in a = bq + r, let a = ct and b=dt, with gcd(c,d) = 1. so ct = dtq + r. Thus t divides r. Let r = te. We get, c = dq + e. …(2) Now let gcd ( d,e) = h. (...

## Parametric equations … ellipse?

Question The ellipse ((x^2)/(2^2) + (y^2)/(3^2))=1 can be drawn with parametric equations. If x=rcos(t). Then r=? and y=? Answer ((x^2)/(2^2) + (y^2)/(3^2))=1 How to define our x,y and r? The “idea” is to compare it and “equalize” appropriately to the tigonometric identity below : [cos x]^2 + [sin x]^2 = 1 Thus, “equating” we...

## Please prove this formula?

Question Prove 1*2+2*3+3*4+4*5+…+n*(n+1) =1/3*n*(n+1)*(n+2) Don’t use induction. I need to know how someone wrote that formula. Answer This is “deduction” 1*2+2*3+3*4+4*5+…+n*(n+1)=? Let S = 1*2+2*3+3*4+4*5+…+n*(n+1) … ( 1) Use. 1 + 2 + … + n = n*( n + 1 ) / 2 and 1^2 + 2^2 + … + n^2 = [...

## What is logic?

Answer Logic is a method of argument in which we check for consistency. A lot of people do not understand the difference between “logic” and “truth”. Logic is a test of consistency. “Relative truth” is a true statement which is dependent on certain conditions. “Absolute truth” is a true statement that is independent of...

## Discrete math proof needed

Question It is asking for the proof for lemma X. According to the discussion in class we know that when you have something like a mod j. that translate into: a = jq + r where 0 <= r < j also r has to be the smallest number possible. I just don’t know...

## Find n in terms of K if K=3n+1/n+2

Answer k=3n+1/n+2 k = ( 3n^2 + 1 +2n ) /n kn =3n^2 + 1 +2n 3n^2 + 1 +2n -kn =0 3n^2 + (2-k)n + 1 = 0 Just ‘complete the square’. as folows : 3n^2 + (2-k)n + 1 = 0 3 [ n^2 + (2-k)n/3 + 1/3 ] = 0 [...

## A Cylinder Problem

Question A circular cylinder is to fit inside a sphere of radius 10 cm. Calculate the maximum possible volume of the cylinder.(It is probably best to take as your independent variable the height,or half the height of the cylinder.) Answer Volume of the sphere is 4*pi*r^3 = 4*pi*10^3 =4000*pi Now, volume of a cylinder...

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