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Write x^2+4x-12 in the form (x+a)^2+b where a and b are constants to be determined.

This method is known as completing the square. To find the constant a, we must halve the coefficient of x, which in this case is 4. This is to compensate for the double term when expanding the brackets. So a...
PG
Answered by Priya G. • Maths tutor
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A curve (a) has equation, y = x^2 + 3x + 1. A line (b) has equation, y = 2x + 3. Show that the line and the curve intersect at 2 distinct points and find the points of intersection. Do not use a graphical method.

a) y = x 2 + 3x + 1b) y = 2x + 3At points of intersection (a) = (b).2x + 3 = x 2 + 3x + 1Note this is a quadratic expression which will solve for 2 unique solutions, providing the discriminant (b 2 - 4ac, wh...
JC
Answered by Joseph C. • Maths tutor
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Find the inverse of: f(x) = (2x + 3)/(x - 4)

To find the inverse of a function, f -1 (x):1) set f(x) as y: y = (2x + 3)/(x - 4)2) swap x and y: x = (2y + 3)/(y -4)3) solve the new equation for y: x(y -4) = 2y + 3 = xy -4x2y - xy = -4x - 3y(2 - x) = -4x...
SI
Answered by Sophie I. • Maths tutor
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a) Find the indefinite integral of sec^2(3x) with respect to x. b) Using integration by parts, or otherwise, find the indefinite integral of x*sec^2(3x) with respect to x.

a) First deduce that problem can be solved by inspection. Then use the fact that the derivative of tan3x equals 3sec^2(3x) and adjust for the constant. (Note this fact should be given in a formula booklet).b...
ER
Answered by Ebrahim R. • Maths tutor
4031 Views

Can you explain when we flip the inequality direction when solving inequalities.

We solve inequalities exactly like normal equations except for Dividing by a Negative Coefficient where we Change the inequality directionE.gx+2>4 is ... x>2 (ask second sim example)x-1>1 is ... x&g...
MM
Answered by Matthew M. • Maths tutor
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