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What is the distance between two points with x-coordinates 4 and 8 on the straight line with the equation y=(3/4)x-2

Firstly, to be able to find the distance between the two points we must find the y-coordinates of each point by substituting in the x values. For x=4y=3/4x4-2=1For x=8y=3/4x8-2=4Now that we know the coordina...
LD
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Let I(n) = integral from 1 to e of (ln(x)^n)/(x^2) dx where n is a natural number. Firstly find I(0). Show that I(n) = -(1/e) + n*I(n-1). Using this formula find I(1).

For the first part this is a standard polynomial integral whereby we can follow the power rule for anti-differentiation. In part ii), if we look at the question we see that we're trying to get I(n-1) in our ...
MP
2893 Views

A curve has the equation (5-4x)/(1+x)

Start by looking for intercepts.x=0, y= 5. Therefore the curve crosses the y axis at y=5y=0, x= 5/4these are the only two intercepts. Now look for asymptotes.3. at x= 1, y becomes undefined, looking at eithe...
HH
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l1 and l2 are tangents of a circle. l1 intersects the circle at (3-√3,5) with a gradient of √3, and l2 intersects the circle at (3+√2,4+√2) with a gradient of -1. Find the centre of the circle, and hence find the radius of the circle.

To first find the centre of the circle, the key fact to remember is that the radius of a circle is normal (perpendicular) to any tangent. This means if you take the normals to both of these tangents at their...
JB
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Evaluate the following product of two complex numbers: (3+4i)*(2-5i)

Answer : 26-7iMethod : Expanding the brackets will result in the sum, 6 -15i + 8i - 20i 2 by assessing this you can see that you can evaluate -15i + 8i to be equal to -7i which is the imaginary part of the c...
CB
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