raja harishchandra

This page lists questions and answers that were posted by visitors named raja harishchandra.

Questions

The following questions were asked by visitors named raja harishchandra.

Find the sum of all positive integers m such that 2^m can be expressed as sums of four factorials (of positive integers).

The integers from 1 through 10 (inclusive) are divided into three groups, each containing at least one number. These groups satisfy the additional property that if x is in a group and 2x≤10, then 2x is in the same group. How many different ways are there...

Find the positive integer value of n such that n^3−3/n^3+n^3−4/n^3+n^3−5/n^3+…+4/n^3+3/n^3=169.

The complex number [2[cos(π/10)+isin(π/10)]]^5 can be written as a+bi. What is the value of a+b?

The sum of squares formula is given by 1^2+2^2+3^2+…+n^2=n(n+1)(2n+1)/6. The sum of odd squares can be expressed as 1^2+3^2+5^2+…+(2n−1)^2=An^3+Bn^2+Cn+D. The value of A can be expressed as ab, where a and b are positive coprime integers. What is the valu...

A trapezoid with area 417/16 has three of its sides on the x-axis, the line x=3, and the line x=6. The fourth side is contained in the line y=mx+5/2. The value of m can be written as a/b where a and b are coprime positive integers. Find a+b.

Two congruent circles Γ1 and Γ2 each have radius 213, and the center of Γ1 lies on Γ2. Suppose Γ1 and Γ2 intersect at A and B. The line through A perpendicular to AB meets Γ1 and Γ2 again at C and D, respectively. Find the length of CD.

If you watch little kids try to open doors, they will often just push anywhere on the door, rather than on the edge like adults do. This is because they don't understand that it's easier to open a door if you push on the edge. But how much easier? Conside...

Tarzan is often portrayed as swinging through the jungle from vine to vine. Each of Tarzan's vines are 30 meters long and Tarzan catches each vine when it is at rest 15 degrees to the left of the (downwards) vertical, swings on it until it stops at an ang...

The number 27+200−−−√−−−−−−−−−√ can be simplified to the form a+b√, where a and b are positive integers. Find the product ab.

Noah wants to swim across a river 10 m wide, flowing from north to south. He swims so his velocity with respect to the river is 2 m/s due east, and the river moves at 4 m/s. How far downstream in m from his starting point will he reach the other side?

What is the sum of all possible real values of x, such that there exists a real value y which satisfies the equation (x+y−40)^2+(x−y−18)^2=0?

Answers

The following answers were posted by visitors named raja harishchandra.

In a monic polynomial, the leading coefficient is 1 So let f(x) = x^4 + ax^3 + bx^2 + cx + d f(1) = 1 +a+b+c+d = 10 a+b+c+d = 9 , #1 f(2) = 16 + 8a + 4b + 2c + d = 20 8a + 4b + 2c + d = 4 , #2 f(3) = 81 + 27a + 9b + 3c + d = 30 27a + 9b + 3c + d = -51 , #...

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