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Express: (x^2 + 5x - 14) / (2x^2 - 4x) as a fraction in it's simplest form.

Answer: (x+7)/(2x)
Answered by • Maths tutor
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If y = 1/x^3, find an expression for dy/dx

Write down y = 1/x 3 This can be rewritten as y = 1x -3 or just y = x -3 as if the x is on the bottom of the fraction, it can be rewritten with a negative version of the power 3. A simple way of working this...
PB
Answered by Pete B. • Maths tutor
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Prove the identity (sin2x)/(1+(tanx)^2) = 2sinx(cosx)^3

For a proof like this, I like to start with the more difficult-looking side, and aim to end up with the expression on the other side. Starting with the left hand side, the first thing to change is the sin2x,...
AC
Answered by Alice C. • Maths tutor
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The line l1 has equation 4y - 3x = 10. Line l2 passes through points (5, -1) and (-1, 8). Determine whether the lines l1 and l2 are parallel, perpendicular or neither.

To determine the answer the gradient of both lines must be found. To find the gradient of line l1 the equation can be rewritten in the form y = mx + c. 4y - 3x = 10 so y = 3/4 x + 5/2. From this equation the...
RM
Answered by Rosie M. • Maths tutor
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Evaluate the integral of cos(x)sin(x)(1+ sin(x))^3 with respect to x.

Substitution of 'u=1+sin(x)' is required.Differentiating this with respect to x gives cos(x)... therefore du=1/cos(x) dxmultiplying that through leaves the integral of sin(x)(1+sin(x))^3 which therefore can ...
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