Alan

The n'th root of x is a number which, when multiplied by itself n times, equals x.

No.  If \(x^2=-1\) then \(x=\pm \sqrt{-1}\) 

However \(\sqrt{-1} = i\)

The following article might be of some use:

http://mathforum.org/library/drmath/view/55563.html

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No, it assumes the father's starting speed is V and the son's is v.  It also assumes the son's speed doesn't change when the father's does (indeed, it assumes the son's speed doesn't change at any time).

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Upper case = father, lower case = son

(1/2)MV² = (1/2)*(1/2)mv²

m = M/2.  So. V² = v²/4.   

(1/2)M(V+1)² = (1/2)mv²  So (V+1)² = v²/2, or  V² + 2V + 1 = v²/2

So. V² + 2V + 1 = 4V²/2. 

V² - 2V - 1 = 0

V² - 2V + 1 = 2

(V-1)² = 2

V = 1 + √2.   (Since only the positive V is needed) This is the father's original speed (in m/s)

Use the fact that v² = 4V² to find the son's speed.

A field is an algebraic structure with certain properties.

It is a set of mathematical objects on which are defined two binary operations, namely addition and multiplication. 

The operations are commutative (e.g. x*y = y*x) and associative (e.g. (x+y)+z = x+(y+z)) and have identity elements (e.g. 0 for addition and 1 for multiplication). 

They have inverse elements (e.g. x and -x for addition; x and 1/x for multiplication). Multiplication is distributive over addition (i.e. x*(y+z) = x*y + x*z).

A finite field is a set with these properties, but it only has a finite number of elements.

Hope this helps!

Use the 2nd button.  asin is the same as sin^-1

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Oops!  Yes you can.

(a) 4.791 * 10^-6 → 1*10^-6 → 10^-6

(b) 6.239 * 10¹⁰ → 10*10¹⁰ → 10¹¹

(c) 1.96237 * 10³ → 1*10³ → 10³

(d) 9.2 * 10^-2 → 10*10^-2 → 10^-1

It's possible this question is looking for the cube root of the expression in brackets, in which case we have:

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