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A scalene triangle has side lengths a=xcm, b=10cm and c=15cm. The angle A=105 degrees is opposite side a. Using the cosine rule, find the value of x to 3 s.f.

The cosine rule= a² = b²+c²-2bcCos(A)a²= 10²+15²-(2x10x15xCos(105))a²= 402.65...Square root of ans.a= 20.07x=20.1cm

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The relationship between Beatrice and Benedick is described as ‘a merry war’ in the play. Starting with this conversation, explore how Shakespeare presents the relationship between Beatrice and Benedick.

This extract from Act 1 Scene 1 serves as the establishment of Beatrice and Benedick's relationship arc in the play. In their first moments alone, we see both characters adamantly denying that they are ca...

Answered by Dougie B. • English Literature tutor

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For all values of x, f(x) = (x + 1)^2 and g(x) = 2(x-1). Show that gf(x) = 2x(x + 2) and find g^-1(7)

gf(x) means you are applying the function f to x (giving you f(x)) and then you are applying the function g to f(x). Since g(x) = 2(x-1), g(f(x)) =2(f(x)-1). This means after substitution, gf(x) = 2((x+1)...

Answered by Arya P. • Maths tutor

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