All Answers 358460 Answers

Just remember Zac,

If you need to find a power you can always resort to logs.

Thanks Heather,

Yes, give it a go and then we will check or help you find any errors.

Great answer Zac :)

two ways to do the same thing.  Thanks DarkBlaze and CPhill  

Thanks Alan  

Thanks DarkBlaze  

It is exactly the same thing but I would multiply both sides by -5/3

$$\\28-7x\\
=\textcolor[rgb]{0,0,1}{7}*4-\textcolor[rgb]{0,0,1}{7}*x\\
=\textcolor[rgb]{0,0,1}{7}(4-x)$$

$$\\\\$Yes HeadingNorth is right$\\\\
\\\frac{1}{6}\;is\;the\;answer\;\mathbf{simplified}\\\\
\\$To be precise, 6\times400=2400 and 1\times400=400$\\
\\$So\; \frac{400}{2400}$$

I always like these questions

Thanks CPhill and Awesomeee  

The propability to get one specifik number with a dice is   $${\mathtt{P}} = {\frac{{\mathtt{1}}}{{\mathtt{6}}}}$$   because there is one specifik number out of 6 possible. the propability for even numbers is 3/6 because there is 3 "whished" numbers outof 6 possible.

However, if you roll the dice 2400 we can expect that 1/6 of all rolls would be  a four.

So you just multiplie 2400 with 1/6.

I hope you find this helpfull! :)

Nice work Zacismyname!!!

But is it possible that  there is a couple of brackets missing?

$${\frac{\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)}{{\mathtt{2}}}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}$$       multiplie all terms with 2 in order to remove the denominator on the left side.

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}} = {\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}$$     get all x to the left side and all terms without x on the other side.

$$\left({\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right){\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}} = \left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}\right){\mathtt{\,-\,}}{\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{2}}$$

Good luck

my day is awful cuz im in school

$${\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{53}}{\mathtt{\,-\,}}{\mathtt{6}} = {\frac{{\mathtt{35}}}{{\mathtt{3}}}} = {\mathtt{11.666\: \!666\: \!666\: \!666\: \!666\: \!7}}$$

It´s just to replace the a with 4 and the b with 3

$${\mathtt{c}} = {\sqrt{{{\mathtt{a}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{b}}}^{{\mathtt{2}}}}}$$

$${\mathtt{c}} = {\sqrt{{{\mathtt{4}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{3}}}^{{\mathtt{2}}}}}$$

Alan is much too polite.

Consider the number

$$\displaystyle N=30.29.28.(36.27!+25)=36.30!+30.29.28.25$$

Working mod 31,

$$\displaystyle 36\equiv5,\quad \text{and}\quad 30!\equiv -1,$$ 

( the second of those being Wilson's theorem with p = 31, )

so, multiplying,

$$\displaystyle 36.30! \equiv 5.(-1)=-5.\quad ...........(1)$$

Also,

$$30 \equiv (-1), \: 29 \equiv (-2), \: 28\equiv (-3)\: \text{and}\: 25\equiv (-6),$$

so, again multiplying,

$$\displaystyle 30.29.28.25\equiv (-1).(-2).(-3).(-6)=36\equiv 5.\quad ...............(2)$$

Adding (1) and (2),

$$\displaystyle N\equiv -5+5\equiv 0,$$

which says that N is divisible by 31.

Looking back at the definition of N, since 30.29.28 is not divisible by 31 (which is prime), it follows that the expression within the brackets must be divisible by 31.

$$tan(\theta/2)=2/(36*5)$$

awesome awesome

56

(eight weeks *7 days in a week)

Where is your working Beary ?

Continuing from zacismyname's analysis:

Take logs of both sides:

log(1.15ⁿ) = log(20/9)

Because log(aⁿ) = n*log(a) we can write

n*log(1.15) = log(20/9)

so

n = log(20/9)/log(1.15)

$${\mathtt{n}} = {\frac{{log}_{10}\left({\frac{{\mathtt{20}}}{{\mathtt{9}}}}\right)}{{log}_{10}\left({\mathtt{1.15}}\right)}} \Rightarrow {\mathtt{n}} = {\mathtt{5.713\: \!341\: \!433\: \!638\: \!366\: \!8}}$$

n ≈ 5.7 years

.

 Lol it's not too hard.

365 days = a year

10 years = a decade

365*10=3650 days in a decade.

If you use the calculator on this site, you can type in log(16,4) to get the log to base 4 of 16.  More generally, to get log to base b of x type in log(x,b)

.

linear velocity = circumferential distance*number of revolutions per minute so:

linear velocity = 15*pi*3 metres/minute = (15*pi*3/1000)*60 km/hour

You can crunch the numbers.

.