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Simplify 125^(-2/3)

Simplify 125^-2/3
A negative indices means that we need to reciprocate the number or "flip it":
125^-2/3 = (1/125)^2/3
A fractional indices can be sp...

Answered by Bethan H. • Maths tutor

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The finite region S is bounded by the y-axis, the x-axis, the line with equation x = ln4 and the curve with equation y = ex + 2e–x , (x is greater than/equal to 0). The region S is rotated through 2pi radians about the x-axis. Use integration to find the

formula for volume of solid generated = 2pi x integral between limits of y²expand ( e^x + 2e^-x)²= e^2x+4+4e^-2xintegrate e^2x+4+4e<...

Answered by Kit T. • Maths tutor

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I’m having some trouble understanding functions. Mainly concerning how to know what the input and outputs are. Could you give me an explanation?

The best way to think about a function is to see it as a machine. Your input is the item you put into the machine, the function is what the machine does, and then when you get out of the other side is you...

Answered by Chelsie J. • Maths tutor

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Integrate the function xsin(4x^2) with respect to x, using the integration by substitution method.

Heres our integral: int(xsin(4x²)dx)The first decision to make is what to use as our substitution. We're going to go for the term tied up in the sine function: 4x²Set u = 4x²

Answered by Benjamin C. • Maths tutor

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Find the 1st derivative of y = x^2 + 7x +3 and hence find the curves minima.

Firstly, we differentiate y = x²+7x+3 . This gives dy/dx = 2x+7.The minimum value occurs when dy/dx = 0. So find x and y when dy/dx=0. 2x+7=0 implies x= -3.5, which from the first equation mean...

Answered by Connor W. • Maths tutor

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