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Work out the equation of the tangent to the curve y=x^2+5x-8 at the point (2,6)

Firstly, we know that dy/dx is the gradient of the tangent to a curve. If we know the gradient of the tangent, and the point on the curve where the tangent touches it, we can work out the equation of the tan...
AD
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In the expansion of (x-7)(3x**2+kx-3) the coefficient of x**2 is 0. i) Find the value of k ii) Find the coefficient of x. iii) write the fully expanded equation in terms of x

i) multiply out: 3x 3+kx 2-3x-21x 2-7kx+21 simplify: 3x 3+(k-21)x 2+(-7k-3)x+21 the coefficient of x 2 is 0 and therefore k-21=0 k=21. ii)from i) the coefficient of x is (-7k-3) k=21 and therefore the requir...
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What is the equation of a circle with centre (3,4) and radius 4?

The general equation of a circle is (x-a)^2 + (y-b)^2 = r^2 where the centre is (a,b) and radius r. Therefore the equation of this circle is (x-3)^2 +(y-4)^2 = 4^2 ...or 16 Sometimes its easiest to leave in ...
IL
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Find the General Second Order Differential Equation Using Substitution (A2 Further Maths)

Find the General Second Order Differential Equation 4x 2 d 2 y/dx 2 - 8x dy/dx +(8+4x 2 )y = x 4 , Transform Using y = vx. 1) Differentiate both sides of y = vx (apply Product Rule to right hand side) dy/dx ...
SC
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The equation 3x^2 – 5x + 4 = 0 has roots P and Q, find a quadratic equation with the roots (P + 1/2Q) and (Q + 1/2P)

We know the roots of the equation 3x 2 - 5x + 4 = 0 is P & Q, therefore is is equivalent to (x - P)(x - Q) = 0. Expanding the expression we get x 2 - x(P+Q) + PQ = 0 . Equating coefficents with the origi...
SC
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