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In a triangle ABC, side AB=10 cm, side AC=5cm and the angle BAC=θ, measured in degrees. The area of triangle ABC is 15cm(sq). Find 2 possible values for cosθ and the exact length of BC, given that it is the longest side of the triangle.

To find cosθ, use the formula for the area of a triangle i.e. AREA=1/2 x a x b x sinC.=> For this case: 15= 1/2 x 10 x 5 x sinC to find sinC.=> SinC = 3/5 thus, Arcsin(3/5)=+- 4/5 or +-0.8
To f...

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How do rearrange y to make it the subject of an equation?

The general principle is to collect all of the values with y in on one side using adding, subtracting, multiplication and division. Then, you take y out as a factor and divide the other side by the values...

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Find the antiderivative of the function f(x)=(6^x)+1

F(x)= ((6^x)/ln(6))+ x + C

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Prove by contradiction that sqrt(3) is irrational. (5 marks)

To the contrary assume that sqrt(3) is a rational number. Thus we can write sqrt(3) = a/b where a and b are coprime integers and b is non-zero. (1 mark for this or equi...

Answered by Dan S. • Maths tutor

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Curve C has equation x^2 - 3xy - 4y^2 + 64 = 0. a) find dy/dx in terms of x and y. b) find coordinates where dy/dx=0.

a) This is no standard differentiate question. You will need identify the fact that the equation contains both x and y terms and thus you will need to differentiate with respect to both. This involves ap...

Answered by Emma D. • Maths tutor

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