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Sam and Jack share out £80 in the ratio 5:3, in that order. How much do they each get?

First, you add the 5+3 to get 8. Now you know there are 8 'portions' of the £80 needed to be shared out. So £80/8 is 10. Sam needs 5 portions so 5x10=50 and Jack needs 3 portions so 3x£10 is £30.
BP
Answered by Bradley P. • Maths tutor
28612 Views

Simplify 2^11 x 8

This would be on a non-calculator paper and so it wants an answer in the form 2^n as without a calculator it is too difficult to work out. You can only do this multiplication if you change the 8 into 2^3 as ...
SL
Answered by Samuel L. • Maths tutor
5082 Views

Differentiate e^(xsinx)

Here you need to use the formula that the differential of e^f(x), where f(x) is any function, is equal to f'(x)e^f(x). So for our function we differentiate xsinx using product rule to give sinx + xcosx. By u...
SL
Answered by Samuel L. • Maths tutor
9657 Views

Show that sin2A is equal to 2sinAcosA

This question requires you to use the trigonometric identity sin(A+B)=sinAcosB + sinBcosA. The difficulty in this problem is noticing that you need to substitute 2A for A+A and then you can simply put this i...
SL
Answered by Samuel L. • Maths tutor
39649 Views

N=2a+b, where a is a two-digit square number and b is a two-digit cube number. What is the smallest possible value of N?

Considering the smallest possible value of N will mean finding the smallest possible values of a and b to give the minimum N. As a must be a square number, let's consider the square numbers: 1 squared is 1; ...
KH
Answered by Katherine H. • Maths tutor
8808 Views