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The fact that y is directly proportional to x gives us that y=kx, where k is some constant.Firstly, we need to find the value of this constant, using the pair of values we are given in the question. We su...

Solving the above question means to find a value of x and y that satisfies both equations. To solve this we first have to look at the x terms and y terms and decide which terms are the easiest to cancel o...

We know that f'(x) = x^3 + 2*x^0.5 + 8, and we can integrate both sides. This gives us f(x) = (1/4)*x^4 + (4/3)x^(3/2) + 8x + c, remembering to add the constant of integration. Now, we are almost...

= (4/3)x³ - (10/2)x² + x^1/2/(1/2) + C = (4/3)x³ - 5x² + 2x^1/2 + C

Let's look at what makes this question more difficult than, say, 0.5 or 0.01: as the decimal is recurring, you can't just multiply and divide by a big number to get a fraction. Example: multiply 0.01 time...