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f (x) = (x^2 + 4)(x^2 + 8x + 25). Find the roots of f (x) = 0

firstly, x²+ 4 = 0 x² = -4 x = 2i x = -2iSecondly, x² + 8x + 25 = 0 using the quadratic formulae: x = (-b +- sqrt(b² - 4ac))/2a x = (-8+-sqrt(64-100))/2 x = -8...

Answered by Laura S. • Maths tutor

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The curve C has equation y = 3x^4 – 8x^3 – 3. Find dy/dx.

To find dy/dx, the differential, of any function... you must times the coefficient of each variable of x by its power, then reduce the power by one. Using this information we can work out that 3x^4 turns ...

Answered by Joseph C. • Maths tutor

4054 Views

How do I determine the domain and range of a composite function, fg(x) ?

Firstly I would state the rule that for any composite function fg, its domain is always the domain of g. If the student would like to know why this is the case, I would simplify the expression fg(x) to f(...

Answered by Rhys S. • Maths tutor

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The curve C has equation: (x-y)^2 = 6x +5y -4. Use Implicit differentiation to find dy/dx in terms of x and y. The point B with coordinates (4, 2) lies on C. The normal to C at B meets the x-axis at point A. Find the x-coordinate of A.

We start off by differentiating the equation implicitly which will give us:2(x-y) -2(x-y)dy/dx = 6 + 5dy/dxThen we rearrange to get dy/dx on it's own:dy/dx = (2x-2y-6)/(2x-2y+5)
For the second part o...

Answered by Jake M. • Maths tutor

2953 Views

A circular table has a diameter 140 cm. Calculate the area of the table in cm^2, leaving your answer as a multiple of pi.

The equation for a circle is pi x radius x radius. So,first we need to find the radius which is half the diameter, 140 divided by 2 equals 70 cm. As the question asks for the answer as a multiple of pi th...

Answered by Fraser S. • Maths tutor

6358 Views