Top answers

A particle of mass M is being suspended by two ropes from a horizontal ceiling. Rope A has a tension of 15N at 30 deg and rope B has a tension of xN at 45 deg, find M assuming the particle remains stationary.

This is a classic "picture frame" resolving forces question. By resolving horizontally we can use the "assuming the particle remains stationary" meaning the forces must cancel out, so, xC...
Answered by • Maths tutor
3772 Views

Integrate (x+2)/((x+5)(x-7)) using partial fractions between the limits 5 and -2, giving your answer to 3sf

First, we're going to split this 1 fraction into 2 fractions. Let (x+2)/((x+5)(x-7)) = A/(x+5) + B/(x-7) then multiplying by (x+5)(x-7) gives A(x - 7) + B(x + 5) = x + 2 multiplying this out we achieve Ax - ...
Answered by • Maths tutor
3335 Views

The quadratic equation (k+1)x^2 + (5k-3)x + 3k = 0 has equal roots, find the possible values of the real number k.

Given that the equation is quadratic and has two distinct roots , this implies that the discriminant (b 2 - 4ac) in the quadratic formula is equal to zero. Comparing terms a = (k+1), b = (5k -3) and c = 3k, ...
AL
Answered by Adam L. • Maths tutor
5343 Views

Water is flowing into a rightcircular cone at the rate r (volume of water per unit time). The cone has radius a, altitude b and the vertex or "tip" is pointing downwards. Find the rate at which the surface is rising when the depth of the water is y.

Always a good first step to a problem like this, is to draw a diagram, making sure to label any lengths. The unknown in this question, is the rate at which the surface of water, in the cone, is rising. Howev...
JO
Answered by Joss O. • Maths tutor
3520 Views

Differentiate y=x^2+4x+12

y=x^2+4x+12dy/dx=2x+4
RH
Answered by Robert H. • Maths tutor
3524 Views