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How do I simplify (1 / [1 + cos(x) ] ) + (1 / [1 - cos(x) ] )?

In order to add the fractions together, we must have a common denominator of the fractions. The simplest way to do this is to make the denominators of the equations the product of the original two denomniato...
SC
Answered by Simon C. • Maths tutor
14896 Views

A curve has the equation: x^4 + 2x -xy - y^3 - 10=0. Find dy/dx in terms of x and y.

We need to differentiate all values with respect to x. Therefore for the first two terms, multiply by the power and then subtract 1 from the original power. Therefore 4(x 4-1 ) + (2)(2x 2-1 ) which gives 4x ...
JG
Answered by John G. • Maths tutor
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A conical vase of base radius 5cm and height 20cm is filled with 200ml of water, how high is the water level? Give your answer to 3 significant figures.

Answer: 2.96 cm Equations used: Volume of a cone = (base area x height) / 3 ; Base Area = pi x radius 2 Volume of whole vase = (pi x 5 2 x 20)/3 = 523.6 cm 3 (4sf) therefore Volume of air in vase with 200ml ...
IC
Answered by Ian C. • Maths tutor
3880 Views

A curve has equation y = e^x + 10sin(4x), find the value of the second derivative of this equation at the point x = pi/4.

Firstly, differentiate y with respect to x once to obtain the equation dy/dx = e^x + 40cos(4x). Then differentiate this resultant expression, with respect to x, to acquire a solution for (d^2)y/d(x^2) = e^x ...
JI
Answered by Joe I. • Maths tutor
3698 Views

Factorise the following equation: 2x^2 + 8x + 8

The first step in factorising is to look for a 'common factor'. A common factor is a number or letter that all the values have in common. All the integers (numbers) in this equation can be divided by 2. Ther...
EK
Answered by Ellen K. • Maths tutor
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