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Find D when 8x^3-12x^2-2x+D is divided by 2x+1 when the remainder is -2

8x 3 -12x 2 -2x+D...(1) 2x+1...(2) Assume 2x+1=0 so x=-1/2 8x 3 -12x 2 -2x+D=-2... when divided by (2) substitute -1/2 into all X values rearrange to find D
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Answered by Shaun W. • Maths tutor
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How would you differentiate ln(sin(3x))?

To answer this question we require the chain rule, which states that dy/dx=(dy/du)*(du/dx) To use this formula in our question, we can let y=ln(sin(3x))=ln(u) where u=sin(3x) Firstly, using a standard result...
HD
Answered by Hannah D. • Maths tutor
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Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

First, write the line in vector form r =(1 1 1) + t(1 2 -1). Consider a point P on the line such that the line connecting P and A is perpendicular to L. The vector P->A is (2 3 4) - (1 1 1) - t(1 2 -1) = ...
ZT
Answered by Zac T. • Maths tutor
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Simplify (3x^2-x-2)/(x^2-1)

This is an algebraic fraction. There is more than one way of solving this expression, but the simplest is to factorise both the top and the bottom quadratic expressions.Firstly we shall simplify the top expr...
VL
Answered by Venetia L. • Maths tutor
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Differentiate the equation y = x^2 + 3x + 1 with respect to x.

A simple way to differentiate an equation with respect to x is to reduce each x components power by one and multiply each x component by their original power. Looking at the equation y = x^2 + 3x + 1, the co...
JB
Answered by Jake B. • Maths tutor
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