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A circle with centre C has equation: x^2 + y^2 + 20x - 14 y + 49 = 0. Express the circle in the form (x-a)^2 +(y-b)^2=r^2. Show that the circle touches the y-axis and crosses the x-axis in two distinct points.

Firstly we rearrange the expression to the required form:x 2 + y 2 + 20x - 14y + 49 = 0 which gives (x + 10) 2 - 100 + (y - 7) 2 - 49 + 49 = 0 and so (x - (-10)) 2 + (y -7) 2 = 10 2 Hence a = -10, b = 7 and ...
JI
Answered by John I. • Maths tutor
8027 Views

Integrate ln(x/7) with respect to x

Firstly split up the ln(x/7) = ln(x) - ln(7) using rules of logarithms learnt in your first year of A-levels, as this will reduce any likely error.Secondly, recognise that the -ln(7) term is constant, and so...
AS
Answered by Arjun S. • Maths tutor
3851 Views

A curve passes through the point (4, 8) and satisfies the differential equation dy/dx = 1/ (2x + rootx) , Use a step-by-step method with a step length of 0.3 to estimate the value of y at x = 4.6 . Give your answer to four decimal places.

h dy/dx (4) = 0.03y(4.3) = 8+0.03 = 8.03y(4.6) = y(4.3) + 0.3 dy/dx(4.3) = 8.0581 to 4 d.p
KW
Answered by Keni W. • Maths tutor
4082 Views

Express 2(x-1)/(x^2-2x-3) - 1/(x-3) as a fraction in its simplest form.

The answer is 1/(x+1)I began by factorising the denominator of the first fraction:2(x-1)/(x^2-2x-3) - 1/(x-3) = 2(x-1)/(x-3)(x+1) - 1/(x-3) Next, I multiplied both the numerator and the denominator of the se...
DR
Answered by Devan R. • Maths tutor
9862 Views

There are 11 counters in a bag. 8 of them red, 3 of them green. Neville takes 2 counters from the bag. Work out the probability that Neville takes one counter of each colour.

8/11 3/10=24/110=12/553/11 8/10=24/110=12/55 Probability = 24/55
KH
Answered by Kieran H. • Maths tutor
13985 Views