zacismyname

The circumference of a circle is $${\mathtt{C}} = {\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{D}}$$

So the circumference is 8.4 pi

Thanks :)

2/5t just immediately jumps out to me as $${\frac{{\mathtt{2}}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}}$$ :/

I'm not sure if it's right, but I ended up with a quadratic by the end. Here goes:

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{2}}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}}{\mathtt{\,-\,}}{\mathtt{1}} = {\frac{{\mathtt{1}}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}}{\mathtt{\,\small\textbf+\,}}{\mathtt{t}}$$ Take the 1/5t off both sides.

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{t}}$$ Multiply everything by 10t.

$${\frac{\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{\left({\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}\right)}}{\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{t}} = {\mathtt{10}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$ Simplify.

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,-\,}}{\mathtt{10}}{\mathtt{\,\times\,}}{\mathtt{t}} = {\mathtt{10}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}$$

$${\mathtt{10}}{\mathtt{\,\times\,}}{{\mathtt{t}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{t}}{\mathtt{\,-\,}}{\mathtt{2}} = {\mathtt{0}}$$ Now using the quadratic formula,

$$t=\frac{-b+\sqrt{b^2-4ac}}{2a}$$ or $$t=\frac{-b-\sqrt{b^2-4ac}}{2a}$$

a=10, b=-5, c=-2

$$t=\frac{5+\sqrt{5^2-4\times{10}\times{-2}}}{2\times{10}}$$ or $$t=\frac{5+\sqrt{5^2-4\times{10}\times{-2}}}{2\times{10}}$$

$$t=\frac{5+\sqrt{25+80}}{20}$$ or $$t=\frac{5-\sqrt{25+80}}{20}$$

$$t=\frac{5+\sqrt{105}}{20}$$ or $$t=\frac{5-\sqrt{105}}{20}$$

which works out to $$\approx$$ 0.76235 or -0.26235.

P.S. I don't know how to say "plus minus" something.

$$(x+12)\times{4}=x+60$$

$$4x+48=x+60$$

$$3x=12$$

$$x=4$$

I can only make some sense of your question. I'm assuming he can paint a room with 3 fiths of a can of paint.

P=paint cans, r=rooms

$$\frac{3}{5}p:1r$$  Now we need to make p=1. We can do this by dividing both sides by 3/5.

(Note that $$\frac{3}{5}p:1r$$ can also be written as $$3p:5r$$)

$$1p:1\frac{2}{3}r$$ So if we have 33 paint cans (multiply both sides by 33), he can paint. . .

$$33p:55r$$

55 rooms.

I'm assuming this is what you mean . . .

$$19x=2+55000$$

$$19x=55002$$ 

Now divide each side by 19 to make x the subject.

$$x=2894.842$$ (3 decimal places) or $$2894\frac{16}{19}$$

The oldest it is possible to live plus 10 years ;)

Width of to after 5 minutes = 2*2*2*2*2*2 = 64 inches

$$66\frac{2}{3}%$$% of 96

$$=\frac{66\frac{2}{3}}{100}\times{96}$$

$$=\frac{2}{3}\times{96}$$

$$=64$$

Not the worst way to spend eternity.