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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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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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A triangle has sides of 4cm and 5cm with the hypotenuse unknown. What is the length of the unknown side?

Pythagorus' theorem a^2 + b^2 = c^2 4^2 + 5^2 = c^216+25 = c^241 = c^2Root 41 or 6.403 = c
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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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Answered by Charles H. • Maths tutor
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A teacher gives her students a maths test and they receive the scores: 4, 4, 7, 3, 9, 10, 5, 8. What was the mean score of the class?

To work out the mean, we first add up all of the scores so 4+4+7+3+9+10+5+8= 50. We then divide by the number of student who took the test, or the number of scores given, which is 8. Divide 50 by 8 to give u...
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Answered by Carmen L. • Maths tutor
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