Melody

Thanks for the points Chris.   

It was an interesting question.  :)

30 * 30 *30 = 27000cm^3

= 27,000ml

= 27Litres

 Use the method of completing the square to solve,

x2 + bx+ c = 0

where b and c are real numbers.

\(x^2+bx+c=0\\ x^2+bx=-c\\ x^2+bx+(\frac{b}{2})^2=-c+(\frac{b}{2})^2\\ (x+\frac{b}{2})^2=-c+\frac{b^2}{4}\\ (x+\frac{b}{2})^2=\frac{b^2-4c}{4}\\ x+\frac{b}{2}=\pm \sqrt{\frac{b^2-4c}{4}}\\ x+\frac{b}{2}=\frac{\pm\sqrt{b^2-4c}}{2}\\ x=\frac{-b}{2}\pm\frac{\sqrt{b^2-4c}}{2}\\ x=\frac{-b\pm \sqrt{b^2-4c}}{2}\\ \)

And there we have the quadratic formula for when a=1

Hi Asinus,

You are very lucky to be able to edit your answers - I wish I could edit mine  

Hi asinus,

It appears we have different answers    

A carrot has 120mg of vitamin c per 100g. if the average carrot weighs 250 gram. how many carrots do i need to eat to get 2grams of vitamin c?

\( \frac{120 mg (of\; vitamin )}{100g (carrot) },\qquad \frac{ 250g (of\; carrot) }{1carrot} \qquad, 2grams\; of\; vitC, \quad ?Carrots\\ \frac{120 mg (of\; vitamin )}{100g (carrot) },\qquad\frac{1carrot}{ 250g (of\; carrot) }\qquad, 2grams\; of\; vitC, \quad ?Carrots\\ \mbox{Carrot must be first and on the top}\\ \frac{1carrot}{ 250g (of\; carrot) }\times\frac{100g (carrot) }{120 mg (of\; vitamin )}\times 2grams\; of\; vitC\\ =\frac{1carrot}{ 250g (of\; carrot) }\times\frac{100g (carrot) }{120 mg (of\; vitamin )}\times 2000mg\; of\; vitC\\ \mbox{Now I can cancel all the units out except for the carrots}\\ =\frac{1carrot}{ 250}\times\frac{100 }{120}\times 2000\\ =\frac{1carrot}{ 5}\times\frac{1 }{3}\times 100\\ =\frac{20carrot}{ 3}\\ =6\frac{2}{3}\;carrots \)

Hi again Gibsonj338,

\(|5|>|\sqrt{-x+x^2}|\)

\(5>\sqrt{-x+x^2}\\ \qquad \mbox{For real solutions }\\ \qquad -x+x^2\ge0\\ \qquad x(x-1)\ge0\\ \qquad x\le0\quad or \quad x\ge1\\~\\ 25>x^2-x\\ 0>x^2-x-25\\ x^2-x-25<0\\ \mbox{This is a concave up parabola so this will be true between the roots}\\~\\ roots:\\ x=\frac{1\pm\sqrt{1+100}}{2}\\ required \;\;region:\\ \frac{1-\sqrt{101}}{2}<x<\frac{1+\sqrt{101}}{2}\\ BUT\\ \mbox{The region is also restrained by }\quad x\le0\quad and \quad x\ge 1\\ so\\~\\ \mbox{The region where this is true is }\\ \frac{1-\sqrt{101}}{2}<x\le0 \quad \cup \quad 1\le x < \frac{1+\sqrt{101}}{2}\\~\\ \mbox{This can also be expressed as} \\ (\frac{1-\sqrt{101}}{2},\; 0 ] \quad \cup \quad [1,\; \frac{1+\sqrt{101}}{2}) \)

Another look

Hi max :)   your teacher is right.

But 2/3 can be written on scientific notation.

2/3

= 0.666666..

= 6.66666... ×10^(-1)

I have not disayed the repeater notation properly because I am on my phone. :(

The range of a number does not make sense.  

You can have the range of a set of scores - that is the highest score minus the lowest score.

Or

You can have the range of a function.  That is all the possible y values.

What do you mean?