All Answers 358149 Answers

Circle    $${\mathtt{A}} = {{\mathtt{r}}}^{{\mathtt{2}}}{\mathtt{\,\times\,}}{\mathtt{\pi}}$$        =>     $${\mathtt{r}} = {\sqrt{{\frac{{\mathtt{A}}}{{\mathtt{\pi}}}}}}$$

r =  $${\sqrt{{\frac{{\mathtt{63.6}}}{{\mathtt{\pi}}}}}} = {\mathtt{4.499\: \!389\: \!820\: \!996\: \!742}}$$   feet

Tues 9/6/15

If you would like to comment on other site issues please do so on the Lantern Thread.  Thank you.    

Interest Posts: 

FTJ means 'For the juniors' 

Equate the exponents

$$\\y=3y+2\\
-2y=2\\
y=-1$$

One way as follows:

In decimal:  (4*6 + 3)*(5*6 + 1) = 837

Convert to base 6: 3513₆

(Though this might be considered to be a cheat if the workings are all supposed to be done in base 6!)

.

When $555_{10}$ is expressed in this base, it has 4 digits, in the form ABAB, where A and B are two different digits. What base is it?

Let the base be X

$$\\A*X^3+B*X^2+A*X+B=555\\\\
AX^3+BX^2+AX+B=555\\\\
X^2(AX+B)+(AX+B)=555\\\\
(X^2+1)(AX+B)=555\\\\
So\;\;X^2+1\;\;$must be a factor of 555$\\\\$$

$${factor}{\left({\mathtt{555}}\right)} = {\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{37}}$$

factors of 555 are   3,5,37,15,111,185,555

5  and 37 would both work so far

5 would  be base 2 And base 2 is to little,  37 would give base 6 (X=6) so that is probably correct.

Lets see

$$\\(X^2+1)(AX+B)=555\\\\
(6^2+1)(6A+B)=555\\\\
37(6A+B)=555\\\\
6A+B=15\\\\
If A=1 B=8 \qquad $no good A and B cannot be more than 5$\\\\
If A=2 B=3 \qquad $Great$\\\\
$so our number is $ 2323_6$$

Check

$${\mathtt{2}}{\mathtt{\,\times\,}}{{\mathtt{6}}}^{{\mathtt{3}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{6}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{6}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}} = {\mathtt{555}}$$

And that is excellent

So               $$555_{10}=2323_6$$

what is the sum of the interior angles of a polygon with 30 sides ?

Total energy emission is given by:

$$E=A\sigma \epsilon T^4$$

where A is area, σ is the Stefan-Boltzmann constant ( ≈ 5.670373×10⁻⁸ W m⁻² K⁻⁴), ε is the emissivity and T is the absolute temperature.

I'll leave you to plug in the numbers.

.

Divide 6 feet by the golden ratio, which is (1 + √5)/2 to get the width.

.

On this calc you use asin   it is the same as inverse sin

Let the number be XYZ       XY and Z are all 1 digit numbers between 0 and 6 inclusive

X and Z cannot by 0

Z must be smaller than X

So Y could possible be 0,12,3,4,5,6

So X could possible be 2,3,4,5,6

So Z could possible be 1,2,3,4,5

$$\\X*7^2+Y*7+Z=Z*9^2+Y*9+X\\\\
49X+7Y+Z=81Z+9Y+X\\\\$$

I might just use trial and error Mellie

Try Z=1

49X+7Y+1=81*1+9Y+X

48X-2Y=80

24X-Y= 40                   Multiples of 24 are 24,48,  Neither of these - an allowed y =40

so Z is not 1 

Try Z=2

49X+7Y+2=81*2+9Y+X

48X-2Y=160        

24X-Y=80                 Multiples of 24 are 24,48,72,96  Neither of these - an allowed y =80

so Z is not 2

Try Z=3

49X+7Y+3=81*3+9Y+X

48X-2Y=240          

24X-Y=120              The first multiple of 24 that is BIGGER than or equal to 120 is 120

SO Z can be 3, X=5 and Y=0

$$\\\mathbf{503_7=305_9}$$  

check

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{49}}{\mathtt{\,\small\textbf+\,}}{\mathtt{3}} = {\mathtt{248}}$$

$${\mathtt{3}}{\mathtt{\,\times\,}}{\mathtt{81}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{248}}$$                     (Edited: Thanks Chris )

There might be a much quicker way of doing this 

I was aware of the fact that the unknown side could've been either the adjacent side, or the hypotenuse.

I am going to try and list them.  Here goes nothing

I want all possible combinations of 4 digits from    2 2 2 4 4 7 7 8 9

I get 20 combinations of the digits    

There is another way-by table or list all possible anwser .

Hi Mellie,

See if this video helps, there are others that follow as well.

$$\\0.1_2=\frac{1}{2}\\\\
0.001_2=\frac{1}{2^3}=\frac{1}{8}\\\\
0.00001_2=\frac{1}{2^5}=\frac{1}{32}\\\\
so\\\\
0.10101_2=\frac{1}{2}+\frac{1}{8}+\frac{1}{32}\\\\$$

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{32}}}} = {\frac{{\mathtt{21}}}{{\mathtt{32}}}} = {\mathtt{0.656\: \!25}}$$

$$$$

if the rectangle is perfect, a rectangle that has 1 half the width as the length, the width is 3 feet

With the Web2.0calc on the home page you just press equals twice.

In the forum calc I don't think this works :(

Multiply the second equation by 2.

Then add the two equations together.

From that you can get the value of y.

Sub y back into any of the equations to get the value of x

There is an insert button with a drop down list.

One of the choices is Special Charcters.

The other inequalities are on the second row.   :)

Why anon ?  You need to give an explanation.

The area is given by L*L

so

L*L=5.76

Find length from that formala and then you can find the perimeter.     

Your brackets are not paired properly.

I would use the quadratic formula to solve this  

https://www.youtube.com/watch?v=O8ezDEk