Melody

$${\mathtt{9.884}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{6}}} = {\mathtt{9\,884\,000}}$$

just move the decimal point over 6 places in the direction to make the number bigger.

(Bigger because the 6 is positive so $${{\mathtt{10}}}^{{\mathtt{6}}}$$   is a big number.)

Can I have a decoder ring too please Chris?

Good effort notthebestmathmaster 😀

I am on my phone and not checking properly but I think you have determined that 15755.5 shoe strings are needed.

The question actually asked how many moles of shoe strings ard needed.

 I do not know how many shoe strings are in a mole but you would need to divide the answer by this number.  ☺

Thank you David that is really lovely of you.

That post sure took me back.  That seems like 100 years ago.  As far a current posters go, only you, me and Kitty were on the forum then, and maybe jedithious.  I love it when i see Jedithious on the forum it reminds of old times.  Of course it is always great to see you and Kitty and all the new people as well.  Maybe you could retire and then you could spend more time with us.  Just joking, sort of. 

Thank you.  You have made my day.    : D

$${\sqrt{{\frac{\left({\mathtt{\,-\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}\right)}{\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}}}}$$

Well the domain is all possible values of x so lets look at this.

you  cannot divide by 0 so x cannot be -2

You cannot find the square root of a neg number so

$$\frac{(-x+3)}{(x+2)}\ge0$$

now I want to get rid of the fraction but I need to know if I am multiplying by a neg or a positive

so instead of mult by (x+2) to get rid of the fraction I am going to multiply by  $${\left({\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}^{{\mathtt{2}}}$$   because I know that is positive.

$$\\(x+2)^2\times\frac{(-x+3)}{(x+2)}\ge0 \times (x+2)^2\\\\
(x+2)(-x+3)\ge0 \\\\
-(x+2)(x-3)\ge0$$

Now if I let   

y=-(x+2)(x-3)

then the statement above will be true when y is positive.

Now I can see straight off that  y=-(x+2)(x-3)   is a concave down parabola

It is a parabola because the degree is 2 (the highest power of x is 2)

and it is concave down because the coefficient of x^2 is -1.  i.e the leading coefficient is negative.

Since it is concave down, y will be positive in the middle ,   not at the ends.

The roots  are  x=-2 and x=3

so     $$y\ge0$$     when        $$-2\le x\le 3$$

so what do we have here.

$$x\ne -2\qquad and \qquad -2\le x \le3$$

So the domain is      $$-2< x \le 3$$       this can also be written as    Domain (-2,3]

this is the graph - All makes perfect sense (to me anyway)

Feel free to ask questions  

This video should help you.

Follow the example on the veideo clip properly

THEN apply this knowledge to your question.

$${\frac{{\mathtt{3\,572}}}{{\mathtt{12}}}} = {\frac{{\mathtt{893}}}{{\mathtt{3}}}} = {\mathtt{297.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

So there are 297 dozen eggs with some left over.

There are a number of different ways of determining the number left over.

1) 0.666666.. = 2/3 and 2/3 of 12 eggs is 8 eggs so there will be 8 eggs left over.

or if that is confusing that you couold say

2) $${\mathtt{297}}{\mathtt{\,\times\,}}{\mathtt{12}} = {\mathtt{3\,564}}$$    that is how many eggs are in the 297 containers.

to find the left overs just subtract this answer from the original number of eggs.

$${\mathtt{3\,572}}{\mathtt{\,-\,}}{\mathtt{3\,564}} = {\mathtt{8}}$$

pi is just a postive number, it is bigger than one too although I don't think this makes any difference.  

The answer it infinity.

20/100*200

there is a calc on the home page

or

$$\\\frac{20}{100} \times 200\\\\
=\frac{20}{1\not{0}\not{0}}\;\times \frac{\;2\not{0}\not{0}}{1}\\\\
=\frac{2}{1}\times \frac{2}{1}\\\\
=2\times 2\\\\
=4$$

Sat 3/1/15

1) Interesting domain question.