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First the number of children that travel by train can be found by dividing 45 by 9 to give 5. Since we know that double as many take the bus, as 2/9 is the double of 1/9,5x2=10 children take the bus. Then...

We know x is inversely proportional to P, so immediately we know their relationship is of the form x = k/P , where k is a constant. We are also given some conditions we can use to solve for k: when x = 2,...

Set the expression equal to the form required in the solution. Multiply both sides by (4x-2)(x-3) to get rid of the denominator and acquire an expression of the form: 19x-15 = A(4x+2) + B(x-3). From here ...

The important thing here is to try and find the bottom bracket in the top bracket ie the numerator

Notice that (3x-3) can be divided by 3 and therefore (3x-3) can be written as 3 multiplied by (x-1...

8x + 3. When you differentiate you must take each term separately. For the first term (4x^2) you must times the coefficent of x (4) by the power (2) and subtract one from the power. Giving an answer of 8 ...