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Calculate the area of a sector which has an acute angle of 30 degrees and a radius of 5cm.

Sector area = (angle/360) + πr 2 Therefore the answer would be: Area = (30/360) + (π x 5 2 ) = 78.62 degrees to 2dp
PH
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P (–1, 4) is a point on a circle, centre O which is at the origin. Work out the equation of the tangent to the circle at P. Give your answer in the form y = mx + c

A tangent makes an angle of 90 degrees with the radius of a circle.Using this fact, we find the gradient of the radius going through P = -4Therefore gradient of the tangent to the circle at P is -1/-4 = 1/4T...
CG
Answered by Charlie G. • Maths tutor
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n is an integer greater than 1. Prove algebraically that n^2-2-(n-2)^2 is always an even number

We want to show that this gives an even number, so we need to get it into a form that it is 2 multiplied by some positive integer. We start by expanding the (n-2) 2 out, remember that (n-2) 2 =(n-2)(n-2). Th...
JC
Answered by Jacob C. • Maths tutor
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Find the length of the hypotenuse of a right-angled triangle using i) Pythagoras Theorem ii) Trigonometry. The triangle has sides of lengths 3cm and 4cm and an acute angle of 30 degrees.

Part i Pythagoras Theorem states a 2 = b 2 + c 2 , where a is the hypotenuse.Using this the lengths can be substituted into the equation as b and c, a 2 = 3 2 + 4 2 a 2 = 25a = sqrt(25) = 5cm Part ii Trigono...
ZS
Answered by Zaakir S. • Maths tutor
2555 Views

Differentiate y = x^2 - 2x-3 + e^3x + 2ln(x)

The above function has several components with different rules on how to differentiate each of them. For each:(1) y = x 2 dy/dx = 2x This follows the general rule of differentiating polynomials: y = x n , dy...
JH
Answered by Jim H. • Maths tutor
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