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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 - ...
Answered by • Maths tutor
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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 (b 2 - 4ac) in the quadratic formula is equal to zero. Comparing terms a = (k+1), b = (5k -3) and c = 3k, ...
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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. Howev...
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Answered by Joss O. • Maths tutor
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Differentiate y=x^2+4x+12

y=x^2+4x+12dy/dx=2x+4
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Answered by Robert H. • Maths tutor
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Calculate (7-i*sqrt(6))*(13+i*sqrt(6))

We expand the parentheses to get to the equation: 7 13-13 i sqrt(6)+7 i sqrt(6)-i i sqrt(36) which after some further calculations equals to: 91-6 i sqrt(6)+sqrt(36) [We got +sqrt of 36 because i i*=sqrt(-1)...
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