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Let x = degree of arc

x/360  *  pi * d  = arc length

                            Now increase x  by 1.2   and  d by 1.25     (20% and 25% respectivley)

x/360 (1.2) * pi * d 1.25 = 1.5 arc length        The arc length increases 50%      

I don't know what you mean by "standard form". It is already in standard form. 

If you want it as a regular number, it would be 1,080,000,000

Ahhha...OK....   Thanx !  Got it ..... 

As you can see, just distribute as these range by increasing power. The answer should be -15. \(144x^7+108x^6+114x^5+84x^4\boxed{-15}x^3-20x^2-43x-20\)

We have  2* pi *5=10pi cm in 12 hours, so in 24 hours, that would be 20pi cm. For the minute hand, we have 2 * pi *  10= 20 pi cm. That is only for one revolution, so 20pi*24=480 pi. Thus, the answer is  \(480\pi+20]pi=500\pi\approx\boxed{1570.796}.\) So, that is 15.708 meters.

no.. 3333 means each bracelet is assigned to person 3

Another way of writing it is (0,0,4,0)

Hey good to see you!!!

I might be wrong, but I think the guest is trying to ask the same question. 

Is this question even complete? How many ways are there to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among  4 people if each person can receive any number of bracelets, including ? Each bracelet must be given to someone. Including what? 

A quick search gives web2.0calc link to the same question. Look at part (b). The full question is, "How many ways are there to divide a red bracelet, a yellow bracelet, a green bracelet, and a black bracelet among 4 people if each person can receive any number of bracelets, including 0? Each bracelet must be given to someone." 

CPhill correctly answered the question by using distinguishability, where it is \(n^k\) with duplicates and  \(k^n\) without duplicates. This does require duplicates, CPhill is correct.

OK, synth....and you  ???

Thank you, CPhill! I just learned this a few days ago... 

It was a great problem.

It had a few of us in a head spin!  

Thanks again for your great solution Alan :)

Thanks, tertre.....your method is better than mine...I even forgot that my final fraction could be simplified even more!!!

Good job  !!!

Thanks, tertre.....not sure how that person knew that adding 35 to both sides would produce a "workable" problem, but....it was a good insight  .....!!!!

We can also use our handy formula: \(\frac{n}{1-r}.\) Since the series has a first term of \(\frac{3}{2}\) and a common ratio of \(\frac{-4}{9}\), we attain \(\cfrac{\frac{3}{2}}{1-\left(\frac{-4}{9}\right)}=\boxed{\frac{27}{26}}.\)

Looks like it was posted here: https://www.reddit.com/r/cheatatmathhomework/comments/weka3/6xyz30xy21xz2yz105x10y7z_812_find_x_y_z/

Maybe some method to solve this, but I certainly do not know what it might be....

WolframAlpha  gives   (x, y, z)  =  (2, 2, 6)

I'm skeptical about this problem.

Where did you get it?

Let the numerator  =  x      and the denominator = y

So.....we have this system

[ x + 6 ] / y   =  [ x / y] + 1        

[ x ] / [ y + 36]  =  [ x / y] - 1  

Looking at the first equation, we can write

[ x + 6]  /  y  =  [ x + y ] / y          multiply through by y

x + 6     =  x +  y       implies that y = 6

Subbing this into the second equation, we have that

 [ x] /  [ 6 + 36]  =  [ x / 6]  - 1

[x ] / 42   =  [ x - 6] / 6         cross-multiply

6x  =  42 [ x - 6]

6x = 42x - 252

-36x = - 252

x = 7

So  the original fraction   is    x / y   =      7 / 6

Here's one way to do this

Just  set this = 0   and   multiply through by  4t - 2   and we get that

t (3t - 2)  =  0

Setting each factor to  0    and solving, we get that 

t = 0      or     t = 2/3 

And since the denominator of the original fraction cannot = 1/2....we have these  possible intervals

(-inf, 0]  ( 0, 1/2)  (1/2, 2/3 ]  and ( 2/3, inf )

Picking a point in each interval  shows that the intervals   (-inf, 0 ]  and (1/2, 2/3]  solve the inequality

can anyone help?

anyone?

We have this

(t + 1) (3t - 3) =  (3t - 5) (t + 2) + 2       simplify

3t^2 - 3  =  3t^2 + t  - 10  + 2        subtract 3t^2 from both sides  and simplify

-3  =  t   - 8        add  8 to both sides

5  =  t