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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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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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Solve: 3X - 5 = Y 2X +2 = Y +3

2X +2 = Y + 3 2X -1 = Y3X -5 = Y3X -5 = 2X -1 X -5 = -1 X = 43X -5 =Y 3(4) -5 = Y12 - 5 = Y7 = Y
X = 4 Y = 7

Answered by Tutor516653 D. • Maths tutor

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If f(x)=(x-2)^2, determine the gradient of the tangent to the curve f(x) at x=-2.

Firstly, we will need to determine f'(x) which is the derivative of the function and will give us the gradient at a point. This is easiest done but multiplying out the brackets of f(x) to get the function...

Answered by Cameron G. • Maths tutor

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How would I find the formula for the nth term of a sequence such as 3, 7, 11, 15, 19?

This is an example of a linear sequence which will always have the formula: u_n=an+b.Where 'a' is the common difference between each term and 'b' is ...

Answered by Tommy G. • Maths tutor

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