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M=37.5e^kt 52=37.5e^k5 52/37.5=e^5k ln(52/37.5)=5k (1/5)(ln(52/37.5))=k k≈0.06538 when t=9, M=37.5e^9*0.06538 M=67.54

B:G --> 9:7

Expressed as fractions of the whole group, boys are 9/16 of the group and girls are 7/16 of the group.

We can use algebra to work out the total group number. For our working, ...

This question is looking at integration by parts. Therefore, we need to split the integral into two parts.

Part A will be x³ and Part B will be e^x .

Draw 2 columns putt...

Firstly, let (x-2)/((x+1)(x-1)²) = A/(x+1) + B/(x-1)+C/(x-1)², where A,B and C are to be calculated. 

Then, multiply both sides of the equation by (x+1)(x-1)^2<...

The ratio given tells us that our paint mixture of 18 litres consists of 3 + 2 = 5 parts.

Each part therefore consists of 18/5 = 3.6 litre...