All Answers 358150 Answers

The diagonals form right angles......so we have

[(1/2) the shorter diagonal]^2 + [(1/2) the longest diagonal]^2  = [(1/4) perimeter]^2

6^2  + d^2  = 9^2      where d is 1/2 the length of the longer diagonal......so.....by the Pythagorean Theorem, we have

√[9^2 - 6^2]  = √[81 - 36 ] = √45  =  3√5 = d   ......   and twice this = 6√5 = about 13.416

Take logs of both sides and use the fact that log(a^b) = b*log(a):

x*ln(2) = (x-9)*ln(9)

9*ln(9) = x*(ln(9) - ln(2))

x = 9*ln(9)/(ln(9) - ln(2))

$${\mathtt{x}} = {\frac{{\mathtt{9}}{\mathtt{\,\times\,}}{ln}{\left({\mathtt{9}}\right)}}{\left({ln}{\left({\mathtt{9}}\right)}{\mathtt{\,-\,}}{ln}{\left({\mathtt{2}}\right)}\right)}} \Rightarrow {\mathtt{x}} = {\mathtt{13.147\: \!608\: \!785\: \!565\: \!331\: \!8}}$$

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Yeah, Alan......I hadn't noticed that....72°  is definitely not correct.....it would mean that the shortest side would be opposite the intermediate angle....impossible.....!!!

(x + 1)^2 + (y - 3)^2  = 36

There is something odd about the diagram.

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{72}}^\circ\right)} = {\mathtt{0.951\: \!056\: \!516\: \!295}}$$

$${\frac{{\mathtt{6}}}{{\mathtt{15}}}} = {\frac{{\mathtt{2}}}{{\mathtt{5}}}} = {\mathtt{0.4}}$$

!!!

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I think this is supposed to be

2^x=9^(x-9 )  

Yes that could be :)

I think they meant this, Melody......

3^(1/2) * 3^(5/2)  =    3^(1/2 + 5/2)  = 3^(6/2) = 3^(3)  = 27

The produse causes the Sun god to produce extra sunshine (energy). 

Yes Rosala, you should not have the % sign in your answer :)

1/2 + 1/3 +......+ 1/x  > 3/2

5/6 + 1/4 + 1/5 +.......+ 1/x > 3/2

1/4 + 1/5 +......+ 1/x > 2/3

9/20 + 1/6 + 1/7 > 2/3

1/6 + 1/7 > 13/60

1/7 > 1/20

So.....7 is the smallest integer

Agreed!  This is one of those questions that makes you ask yourself: what did a poet want to say...?

When it works, what does it do anon?

it means "to the power of"

Sometimes it is called a 'hat'   It's real name is  a 'caret'

do not confuse this with carrots that rabbits like to eat

or carats that is a weight measure for gems      

3 and 5/2 is not a proper mixed numeral.  Perhaps I do not understand your question!

I do it like this

180 degrees = pi radians                This is all that I remember

so

1 degree = pi/180    radians

so

220 degrees must = 220 *  pi/180   radians       

Unless you want to ask questions on these, would you like to start fresh?  

(Take a look at my previous posts first though)

Can you simplify this one for me ?  Do it with cancelling.  

Can you remember how to do that or do you want me to show you?

$$\frac{21x}{y}\times \frac{8y^2x}{14t}$$

Perhaps you should copy this over to a new thread :)

Thanks Civonamzuk   

or

$${\frac{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{tan}}^{\!\!\mathtt{-1}}{\left({\mathtt{70}}\right)}}{{\mathtt{10}}}} = {\mathtt{8.918\: \!154\: \!453\: \!831\: \!1}}$$

tan-1 70 over 10

70/10=7

tan^-1 (7) = 81.87^o

LOL!!!!!

My GOD CPhill that took you more than 8 minutes.  

AWESOMEEE will cut your pay by 90%  How will you be able to live on just 10% of nothing!!

AND IT SERVES YOU RIGHT.

WHAT YOU THINK THAT BEING IN HOSPITAL WITH PNEUMONIA AND A TRIPLE HEART BIPASS IS ANY EXCUSE!

NO IT IS NOT!!

I COULD HAVE DONE IT WITH 2 FINGERS UP MY NOSE.

I COULD HAVE DONE IT BEFORE AWSOMEEE KNEW IT WAS GOING TO BE HIS QUESTION.

SO NEXT TIME CPHILL YOU JUST SHAPE UP OR YOU WILL HAVE TO LIVE ON 0% OF NOTHING  !!!!!

(a) One possibility is 8.45

Rounded to the nearest integer = 8

Rounded to the nearest tenth = 8.5

And rounding this to the nearest integer = 9

(b) The possible numbers are 8.45 to 8.49, inclusively

It depends on how large the apples are. If the apples are about 80 mm then about 7.115 MJ or 7115 kJ.

You will have to do the Umbrella Sun Dance for it to work.

.12........ = 12/99

.345...... = 345/999

So......   12/99 + 345/999  = [999(12) + 99(345)] / [99 *999] = 46143 / 98901 = .446557..........

So....the sum of the integers in the repeating part is  31