Alan

Alternatively, use the menu system as shown below:

Enter 125^(1/3) to get OneNote to calculate the cube root.

Here's another way of looking at 1).

I suspect this is meant to be "What two numbers when multiplied equal 4 and when added equal -9?"

If so, from x*y = 4 and x+y = -9, we find the two numbers to be:  (√(65) - 9)/2  and (-√(65) - 9)/2.

Numerically, this seems to converge (very quickly) to 9/32.  This is such a simple result I suspect there is a way of finding it analytically. However, I have so far failed to do so!!

As follows:

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"What is the derivative of (3x)/(2x^2-18)?"

Let u = 3x and v = (2x²-18)^-1

Use the chain rule:  duv/dx = udv/dx + vdu/dx:

du/dx = 3      dvdx = -(2x²-18)^-24x

d(3x(2x²-18)^-1)/dx = -12x²(2x²-18)^-2 + 3(2x²-18)^-1 

or  (3(2x²-18) - 12x²)/(2x²-18)²   →  -(6x² + 54)/(2x²-18)² → -(3/2)(x² + 9)/(x² - 9)²

Volume of sphere: \(\frac{4}{3}\pi r^3\)    r = 4cm

Volume of cone:  \(\frac{1}{3}\pi r^2h\)   r = 3cm   h = 12cm

Plug in the numbers to see which is larger.

You could use the x^y key.  eg.  5x^y-1=

"One town is directly north of another. From a point 20 km to the west of the road joining them, the towns are at bearings 050 and 120. How far apart are the towns?"

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