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Find two positive numbers whose sum is 100 and whose product is a maximum.

Call the two numbers x and y. The constraint is that x + y =100, and we need to maximise A=xy. Rearrange the constraint to y = 100 - x, and substitute into the product equation. A = x(100-x) = 100x - x 2 Dif...
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Dónde se come mejor en España?

Es de saber común que la comida en la Península Ibérica es de calidad suprema. Sin embargo la gente no tiende a ponerse de acuerdo sobre cuál es la región española con la mejor gastronomía. Los valencianos e...
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Solve the integral: int(x^3+4x^2+sinx)dx.

First, since there are terms with different factors of x summing together, we can separate these into three individual integrals as follows:int(x 3 dx) + 4int(x 2 dx) + int(sinx dx)Then using the rules of in...
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Explain the effect on economic growth if a government increases income tax (ceteris paribus).

An increase in taxation reflects tighter fiscal policy, reducing the take home pay of those employed. This will reduce the amount of income that households are willing to spend on goods and services in the e...
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A curve C has equation: y = x^2 − 2x − 24x^1/2, x > 0; Find (i) dy/dx (ii) d^2y/dx^2

i) let dy/dx = ans, where ans = y, where you multiply the coefficients of each constant of x by the power and reduce the power by 1 in the equation ytherefore dy/dx = 2x - 2 - 12x -1/2 ii) repeat the process...
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