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You are shown a diagram of a right angled triangle, with the hypotenuse labelled c and the other sides labelled a and b. If a is 7m long and c is 10m long, what is the length of b?

A simple implementation of Pythagoras' Theorem a 2 +b 2 =h 2 , and as in the question c is the hypotenuse, a 2 +b 2 =c 2 . (Side Note - in exams, the question may not specify which length is the hypotenuse -...
WH
Answered by William H. • Maths tutor
4540 Views

Solve the simultaneous equations: 2x - y = 4 and x + 2y = 7

Solve: 2x - y = 4 and x + 2y = 7 There are two methods to solve this, you can either calculate one of the variables from either equations and then substitute to the second one or try to multiply one of the e...
EK
Answered by Eliza K. • Maths tutor
16736 Views

Work out the value of 2a^2 + b^3 when a = 5 and b = –3

It is best to approach this question in parts, then combine the parts to find your solution. This question may be split into parts, as follows: Firstly, if a = 5, then a 2 = 5 2 = 5 x 5 = 25. So a 2 = 25 Sec...
TD
Answered by Tutor51449 D. • Maths tutor
14984 Views

Consider the functions f and g where f (x) = 3x − 5 and g (x) = x − 2 . (a) Find the inverse function, f^−1 . (b) Given that g^−1(x) = x + 2 , find (g^−1 o f )(x) . (c) Given also that (f^−1 o g)(x) = (x + 3)/3 , solve (f^−1 o g)(x) = (g^−1 o f)(x)

(a) Start with f(x)= 3x − 5; y=3x - 5, and switch x and y before rearanging to get y in terms of x again: y=3x - 5 x=3y - 5 (x+5)/3=y Therefore f^−1(x)=(x+5)/3 (b) Start with f(x)= 3x − 5 and and sub result ...
IB
Answered by Isobel B. • Maths tutor
20276 Views

5 students are in a maths class and 10 students are in a physics class. The mean mark of the maths class is 90 and the mean mark of the physics class is 85. Work out the mean mark of both classes.

To find the mean mark the formula is mean = ∑marks /number of students Therefore the mean for maths is 90 and so ∑marks = mean number of students = 90 5 = 450 and the ∑marks for the physics class is 85*10= 8...
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Answered by Ryan S. • Maths tutor
3920 Views