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First expand out the brackets: 5x-15 = 4y -3xy Then re-arrange to bring all the x terms to one side: 5x+3xy = 4y +15 Now factorise: x(5+3y) = 4y + 15 Now we have isolated the x term, we can divide both si...

we have dy/dx = -x/y , so we treat the differentials as fractions and write y dy = -x dx. Now integrating the left side with respect to y and the right side with respect to x, we have y²/2 = -x...

Here, we must consider Newton's Law of Universal Gravitation. This states that the gravitational force acting between two bodies is proportional to the masses of each body and inversely proportional to th...

First you need to understand what an index (or power) is. It’s just a compact way of writing a number multiplied by itself a number of times. For example:

 3^4...

When you differentiate a function which has only one parameter, like f(x), you are finding a new function, f'(x), which gives the gradient of your original function at every point. You'll probably remembe...