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Write x^2 + 8x + 7 in the form (x + a)^2 + b

We work from right to left (x + a)² = x² + 2ax + a² 2a = 8 [coefficients of x must match] a = 4 (x + 4)² = x² + 8x + 16 [substitute in a = 4] x^2...

Answered by Will M. • Maths tutor

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How do I do definite integrals?

A definite integral is an indefinite integral with set limits. If we consider integration as a way of calculating the area under a curve, a definite integral calculates the area under the curve between tw...

Answered by Charlie J. • Maths tutor

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A Curve has parametric equation x=2sin(t), y= 1+cos(2t), -pi/2<=t<=pi/2. a) Find dy/dx when t=pi/3. b) Find the Cartesian equation for the curve in form y=f(x), -k<=x<=k. c) Find the range of f(x)

x=2sin(t), y=1+cos(2t)

a) By chain rule, dy/dx = (dy/dt)/(dx/dt)
dy/dt = -2sin(2t), dx/dt= 2cos(t)
dy/dx= -sin(2t)/cos(t)
dy/dx=-2sin(t)cos(t)/cos(t)
dy/dx=-2sin(t)

Answered by Max B. • Maths tutor

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Find the first and second derivatives of: y = 6 - 3x -4x^-3, and find the x coordinates of the line's turning points

dy/dx = -3 +12x^-4 d^2y/dx^2 = -48x^-5

Answered by Matthew S. • Maths tutor

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What is £23 increased by 4%?

There are two steps to solving this problem. First, we want to find out how much the increase itself is, so we want to calculate 4% of £23. Then, we want to add the result to the £23. That will give us th...

Answered by Giulia B. • Maths tutor

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