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What is 2/3 + 1/4?

When adding or subtracting fractions, we must always start by putting the fractions over the same denominator, that is the number on the bottom half of the fraction. To do this, we need to find ...

Answered by Catherine C. • Maths tutor

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Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?

The key concepts to apply in this question will be the product and chain rules, namely: if f(x)=g(x)h(h), then f'(x)=g(x)h'(x) + g'(x)h(x), and if h(x)=u(v(x)), then h'(x)=u'(v(x))v'(x).

Equivalen...

Answered by Bromlyn C. • Maths tutor

4909 Views

Show that: [sin(2a)] / [1+cos(2a)] = tan(a)

We start by expanding out the double trigonometric terms (sin(2a)) using the double angle formula, giving us: [2sin(a)cos(a)] / [1+cos^2(a) - sin^2(a)]. Next we spot that on the denominator (bottom half o...

Answered by George H. • Maths tutor

8763 Views

What does it mean when I get a negative value when I do a definite integral?

The definite integral gives the value of the area bounded between the curve at the given limits, and the x-axis (if we are integrating with respect to x!) If this value is negative, it means that the area...

Answered by Callum L. • Maths tutor

13675 Views

Callum mixes a drink such that the Fruit Juice and Water is a ratio of 1:4 respectively. Calculate how much of both the Fruit Juice and the Water Callum will need in order to make 2 litres of juice. (Water: ml, Fruit Juice: ml )

A ratio of 1:4 means there are 5 parts to the mixture.
2 litres of drink divided into 5 parts means there are 400 ml per part (2000ml/5 parts).
As Fruit Juice has 1 part, Callum would need 400...

Answered by Charlotte M. • Maths tutor

22649 Views