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Given the points P(-1,1) and S(2,2), give the equation of the line passing through P and perpendicular to PS.

First, we can find the slope of the line PS , with the help of the formula m = (y 2 - y 1 )/(x 2 - x 1 ) or if we substitute for the given points m PS = (2 - 1)/(2 - (-1)) = (-1)/(3)= -1/3. Since the line l ...
KS
Answered by Kalina S. • Maths tutor
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Find the integral of (2(3x+2))/(3x^2+4x+9).

Start by expanding out the bracket on the top of the fraction to get (6x+4)/(3x 2 +4x+9). Then using the trick of identifying that the fraction is in the form [g(x)]/[f(x)] where f’(x)=g(x), the solution is ...
EN
Answered by Elise N. • Maths tutor
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Factorise completely x − 4 x^3

= x(1-4x^2)From difference of two squares method,= x(1-2x)(1+2x)
CT
Answered by Christopher T. • Maths tutor
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Relative to a fixed origin O, the point A has position vector (8i+13j-2k), the point B has position vector (10i+14j-4k). A line l passes through points A and B. Find the vector equation of this line.

The vector equation of any line is composed of the addition of a point on the line and some distance in the direction of the line, in the form y=(x,y,z) +d(x_1, y_1, z_1), where (x,y,z) is any point on the l...
CS
Answered by Carlota S. • Maths tutor
8478 Views

What is the indefinite integral of xlog(x)?

The integral can be split into two different functions of x which is a hint that we must use the integration by parts method. The method is defined as ∫ uv’ dx = uv - ∫ u’v dx . If we let u = log(x) and v’ =...
WH
Answered by William H. • Maths tutor
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