All Answers 358514 Answers

with one million

                                          +

                                          |   .      +

                                          |      .            +

                                 x/2    |          .                +

                                          |            r                      +

                                          |                .                         +

                                          |           60      .                              +

            arc     (<----r/2---->+<----r/2----> C <------------r--------->) arc

                       <-      h   -> | <-   r - h    ->                            +

                                          |                                          +

                                          |                                   +

                              x/2       |                            +

                                          |                     +

                                          |            +

                                          |      +

                                          +

Your question does not make any sense  

5 only goes into numbers that end in 0 or 5 so therefore I can see straight of that the remainder will be 4

the question you can pur into ANY calculator.  Just take the whole number part and ignore the decimal part.  

the remainder will be 4

In English,

+ = Add / Plus (Addition)

-  = Subtract / Minus (Subtraction)

x  = Multiply / Times (Multiplication)

% = Percentage (Percentage)

^    / = Divide (Division)

@@ End of Day Wrap    Wed 28 /1/15     Sydney, Australia      Time 10:55 pm

Hi everyone,

Thurs 29/1/15

Thanks Alan,

A note to anon,

I already answered this question many hours ago!

If you want to repost please follow the intructions.

We do not have time to answer the same question twice when there is nothing to be gained from this!

Please read this post !!!  

I do not understand Heureka.   

One can turn the equilateral triangle, thus one side is vertical, then the height (h) of the curve (chord) is half the radius.

1,4,10,28,?,244

 I am going for    $$3^n+1$$

.

okay I have looked at CPhill's answer and I decided to reproduce it - but it is still CPhill's answer.

I left labelling the same as CPhill's except that I called the side length 2x inches.  

First I want to find AH in terms of x

$$\\AH^2=4.5^2-x^2\\
AH^2=20.25-x^2\\
AH=\sqrt{20.25-x^2}\\$$

Now consider the big right angled triangle DEH

$$\begin{array}{rll}
DH^2&=&DE^2-EH^2\\
(DA+AH)^2&=&(2x)^2-x^2\\
(4.5+\sqrt{20.25-x^2})^2&=&4x^2-x^2\\
(4.5+\sqrt{20.25-x^2})^2&=&3x^2\\
\sqrt{(4.5+\sqrt{20.25-x^2})^2}&=&\sqrt{3x^2}\\
4.5+\sqrt{20.25-x^2}&=&\sqrt{3}\;x\\
\sqrt{20.25-x^2}&=&\sqrt{3}\;x-4.5\\
(\sqrt{20.25-x^2})^2&=&(\sqrt{3}\;x-4.5)^2\\
20.25-x^2&=&3x^2-2*4.5\sqrt{3}\;x+4.5^2\\
20.25-x^2&=&3x^2-9\sqrt{3}\;x+20.25\\
-4x^2&=&-9\sqrt{3}\;x\\
x^2&=&\frac{9\sqrt{3}\;x}{4}\\
x&=&\frac{9\sqrt{3}}{4}\\
2x&=&\frac{9\sqrt{3}}{2}\\
\end{array}$$

So each side is exactly   $$\frac{9\sqrt{3}}{2}$$    inches long

What is the side length of an equilateral triangle that fits exactly inside a circle with a 9 inch diameter ?

I.

$$\cos{(60\ensurement{^{\circ}})}=\frac{r-h}{r}=\frac{1}{2} \quad | \quad \small{\text{h = the height of the chord}} \\
\Rightarrow \boxed{h=\dfrac{r}{2}}$$

II.

Intersecting chord theorem:

$$\small{\text{
$
h*(d-h)= (\frac{x}{2})*(\frac{x}{2}) = (\frac{x}{2})^2
$
}}\\
\Rightarrow \boxed{x = d* \frac{ \sqrt{3} } {2}= 4.5* \sqrt{3}}$$

The answer is x=43

My solution below is basically the same as Chris's, but laid out slightly differently:

.

15 x 10 / 2

150 / 2

=75 

Hi Chris,

I was coaching a student yesterday and I tought him this method of yours.

He seemed to think that it would work for him.  I had never thought of it that way before.

So thank you 

Although  when they first start learning addition and subtraction of directed numbers it is nice for them to understand the numberline and how it works properly

21m , 20m , 29m.

(29-21)(29+21) = 20^2

8*50 = 20*20

8*50 = 400  equal!

Yes, it is a right triangle

Let x = 0.63333....

Multiply x by 100:  100x = 63.3333....

Multiply x by 10:      10x = 6.3333....

Subtract 10x from 100x:  90x = 63 - 6 or 90x = 57 

Divide both sides by 90:   x = 57/90

Simplify by dividing top and bottom by3:  x = 19/30

.

If it's a right-angled triangle the sum of the squares of the two shorter sides will equal the square of the longest side (Pythagoras).

$${{\mathtt{7}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{{\mathtt{9}}}^{{\mathtt{2}}} = {\mathtt{130}}$$

$${{\mathtt{15}}}^{{\mathtt{2}}} = {\mathtt{225}}$$

So, clearly not a right-angled triangle

.

What is biggest 4 digit number in base 23 ?

$$\small{\text{
The biggest 4 Digit number in base 23 is:
}} \\
\small{\text{
$
22*23^3+22*23^2+22*23^1+22*23^0 = 23^4-1 = 279840
$
}} \\\\
\small{\text{
Geometric sequence:
$
s_4 = \dfrac{ a * (r^4-1) } { (r-1) }
\quad a = 22, \ \quad r = 23 \qquad s_4 = \frac{ 22 * (23^4-1) } { ( 23-1) } = \frac{ 22 * (23^4-1) } { ( 22 ) } = (23^4-1)
$
}}$$