All Answers 358108 Answers

My very first wrap is on that same thread so you can look for yourself.    

i do all u have to do is wait and try it again it should work but recently ive had no luck so

The pictures are not being uploaded or displayed properly for me tonight.

I wrote this in my wrap.  I thought that you read the wrap :)

It is a nuicance.      

Yep! You are correct, my friend!

amazing I can't explain my feeling =D  ... 

points P and R in the first picture ( x - t ) is a turning point but how did you know that p is the maimum velocity and R is minimum ? 

Alan, is yours simplified?

I know, but I wasn't so sure...

There are many answers:

Since  71 x 1 = 71       71 / 1 = 71

Since  71 x 2 = 144     144 / 2 = 71

Etc.

Fixed Gino is correct. (So am I now)

$$\\1+4^{34}+7^{35}\\
4^n=4,16,64,256,.... $ when n is even it ends in 6$\\
7^n=7,49,343,2401, 16807, $ So the last digits are 7,9,3,1,7,...$\\
35=4*8+3$ so the last digit of $ 7^{35}$ is 3 (3 is the third number in the sequence)$\\
$Edited: Geno is right, these three digits need to be added$\\\\
$ The last digit will be hte last digit of $ 6+3+1 $ Which is zero $$$

Let's attack  4^34  first:

   4^1 = 4

   4^2 = 16

   4^3 = 64

   4^4 = 256   --->  This indicates that if the exponent is odd, the last digit will be a  4; if the exponent is even,                               the last digit will be a  6.

Now  7^35:

   7^1 = 7                         7^5 = 16807

   7^2 = 49                       7^6 = 117649

   7^3 = 343                     7^7 = 823543

   7^4 = 2401                   7^8 = 5764801

This indicates that it cycles in groups of 4, so you can keep doing this until you get to 7^35. (You really don't have to keep doing the multiplications.)

Another way is to divide the exponent by 4:

  if the remainder is 1, the answer ends in a 7;

  if the remainder is 2, the answer ends in a 9;

  if the remainder is 3, the answer ends in a 3; and

  if the remainder is 0, the answer ends in a 1.

Dividing 35 by 4, the remainder is 3; therefore the last digit is a  3.

Now, the problem is reduced to adding 1 to a number whose last digit is  6 to another number whose last digit is  3. So what is the last digit of  1 + 6 + 3? 

But, unicorns can fly too!

Melody, I think that EVERY answer comes with guarantee. I am always bored, so I read your wrap. When did you start doing your wraps? Curiosity question, my queen.

Curiosity can lead to new discoveries, or to more danger...

You are mistaken.

$$1+3=4$$

$$10+9=19$$

To add the fractions  1/2  and  1/4  get a common denominator.

Since  2  can be divided evely into  4, make the common denominator  4.

Since 2 x 2 = 4, multiply both the numerator and denominator of 1/2 by 2:

     (1/2) x (2/2)  =  (1 x 2) / (2 x 2)  =  2/4

---> 9 1/2  +  3 1/4  =  9 2/4  + 3 1/4

Now, add the whole numbers together (9 + 3  = 12)

and add the fractions (2/4  + 1/4  = 3/4)

So the answer is:  12 3/4

(When you add fractions with the same denominator together, add the numerators (2  + 1  = 3) and write this answer over the common denomintor. (Don't add the denominators together!) This is how  2/4  +  1/4 becomes 3/4.)   

The main ones that we use is Desmos, it makes beautiful graphs but it does have limitations.

then we use wolfram|alpha

there are others that we pull out very occasionally.

I do not know what I could use for those graphs I drew for you this afternoon - that is why I drew them free hand.

Let  x  represent the measure of the angle.

Supplementary angles are angles that sum to 180°. Thus, if one angle is  x  the other angle will be  180° - x.

"An angle" becomes  x.

"measures" is a verb so it becomes  =.

" 104° less than" means subtract 104° from what follow those words.

"the measure of a supplementary angle" becomes 180° - x.

Replacing the original words with these symbols, we have:  x  =  (180° - x) - 104°

Combining  180° - 104°, this becomes 76°.

--->  x  =  -x + 76°

--->  2x  =  76°

--->  x = 38°

Then, find the supplement. 

@@ End of Day Wrap       Mon 29/9/14        Sydney, Australia      Time 11:15 pm      ♬  

Hi all,

Today our favulous answerers were NathanDeAlien, Quinn, CPhill, NinjaDevo, Geno3141, DragonSlayer554, Alan and Kitty<3.  Thank you all.    

The site is playing up tonight.  Pictures are not displaying properly and for some reason i couldn't give 
Alan points on one of his posts, sorry Alan.  Hopefully these problems won't last long.  

Now for the interest posts:

1) Do donkeys fly?  What a silly question.

the wording is rather strange but supplementary angles add to 180 degrees

so the angles are   104 and 180-104 degrees

Tues 29/9/14

1) Finding last digit

Thanks Geno,

I am just going to work through my version of your logic.  :)

$$\\x^{15}+x^5+2=0\\\\
Let\;\;y=x^5\\\\
y^3+y+2=0\\\\
y(y^2+1)=-2\\\\
y^2+1 $ must be positive so $y$ must be negative. Hence$\\\\
x^5$ must be negative, hence $\\\\
x $ must be negative$\\\\
$Therefore, no positive roots exist.$$$

Alan, I have tried to give you points for your last answer but the system is playing up and it will not allow it.

Sorry.    

$$8.6\times 10^3$$

Hi Alan,

I didn't understand the middle one partly because I didn't/don't understand what is happening.

I assume the glider is getting pulled up the slope with constant Force. 

Since force = mass  x  acceleration

The mass is constant so the acceleration is constant.  That makes sense, at least as far as the formula goes.

So even if the velocity is constant there is still acceleration??

I am afraid this does not make sense to me.

Could you please attempt to explain this to me Alan?

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Once the slider is at the top, it is then moved back down again.  Was this meant to be considered in this problem.  I thought it was and that completely threw me because I don't know what force it returns with.  Maybe gravity ??

Maybe I was not suppose to consider the downward motion??

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