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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...

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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...

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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 (b² - 4ac) in the quadratic formula is equal to zero. Comparing terms a = (k+1), b = (5k -3)...

Answered by Adam L. • Maths tutor

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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. Ho...

Answered by Joss O. • Maths tutor

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