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At each point P of a curve for which x > 0 the tangent cuts the y-axis at T, and N is the foot of the perpendicular from P to the y-axis. If T is always 1 unit below N and the curve passes through the point (1,0), find the Cartesian equation of the curve.

When faced with a problem like this, it is always a good idea to draw a rough sketch of what might be going on. With the help of a diagram, we notice that PNT is a right angled triangle w...

Answered by Siddharth P. • Maths tutor

2764 Views

A triangle has sides of length 8 cm, 10 cm and 14 cm. Work out the size of the largest angle of the triangle. Give your answer correct to 1 decimal place.

Utilising the cosine rule: c² = a² + b² - 2abcosC, substitute in the given lengths. We therefore get that 14² = 10² + 8² − 2 × 10 × 8 × cosA . Expanding this expression we then get that 196 = 164 - 160cos...

Answered by Josephine K. • Maths tutor

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3 teas and 2 coffees have a total cost of £7.80. 5 teas and 4 coffees have a total cost of £14.20. Work out the cost of one tea and the cost of one coffee.

Make x= Tea and y= CoffeeTherefore 3x + 2y = 7.80 (1) and 5x + 4y = 14.20. (2)Want either x or y to be equal for both equations- therefore make (1) 6x + 4y = 15.60 (3)“Same signs subtract” so do (3) - (2)...

Answered by Adaeze C. • Maths tutor

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A curve C has equation: x^3+2xy-x-y^3-20=0. Find dy/dx in terms of x and y.

First we need to make sure we understand implicit differentiation. As we are differentiating with respect to x, y has to be treated differently, this is because it could be anything from a constant to a f...

Answered by Martin M. • Maths tutor

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Find the inverse of the function g(x)=(4+3x)/(5-x)

For simplicity first rewrite as y=(4+3x)/(5-x). Now swap any x for a y, and any y for an x. This leaves the equation x=(4+3y)/(5-y). Our goal is to make y the subject of the formula. Multiply both sides b...

Answered by Martin M. • Maths tutor

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