What is the smallest positive integer \(n\) such that \(n^4 + 6n^3 + 11n^2 + 6n\) is divisible by \(700\)?
\(\begin{array}{|rcll|} \hline n^4 + 6n^3 + 11n^2 + 6n = n*(n+1)*(n+2)*(n+3) \\ \hline \end{array}\)
\(\begin{array}{|r|r|r|c|} \hline n& n*(n+1)*(n+2)*(n+3) \\ \hline 1& 1*2*3*4 & 24 & \\ 2& 2*3*4*5 & 120 & \\ 3& 3*4*5*6 & 360 & \\ 4& 4*5*6*7 & 840 & \\ 5& 5*6*7*8 & 1680 & \\ 6& 6*7*8*9 & 3024 & \\ 7& 7*8*9*10 & 5040 & \\ 8& 8*9*10*11 & 7920 & \\ 9& 9*10*11*12 & 11880 & \\ 10& 10*11*12*13 & 17160 & \\ 11& 11*12*13*14 & 24024 & \\ 12& 12*13*14*15 & 32760 & \\ 13& 13*14*15*16 & 43680 & \\ 14& 14*15*16*17 & 57120 & \\ 15& 15*16*17*18 & 73440 & \\ 16& 16*17*18*19 & 93024 & \\ 17& 17*18*19*20 & 116280 & \\ 18& 18*19*20*21 & 143640 & \\ 19& 19*20*21*22 & 175560 & \\ 20& 20*21*22*23 & 212520 & \\ 21& 21*22*23*24 & 255024 & \\ 22& 22*23*24*25 & 303600 & \\ 23& 23*24*25*26 & 358800 & \\ 24& 24*25*26*27 & 421200 & \\ \color{red}25& 25*26*27*28 & 491400 & \text{divisible by 700} \\ 26& 26*27*28*29 & 570024 & \\ 27& 27*28*29*30 & 657720 & \\ 28& 28*29*30*31 & 755160 & \\ 29& 29*30*31*32 & 863040 & \\ 30& 30*31*32*33 & 982080 & \\ 31& 31*32*33*34 & 1113024 & \\ 32& 32*33*34*35 & 1256640 & \\ 33& 33*34*35*36 & 1413720 & \\ 34& 34*35*36*37 & 1585080 & \\ 35& 35*36*37*38 & 1771560 & \\ 36& 36*37*38*39 & 1974024 & \\ 37& 37*38*39*40 & 2193360 & \\ 38& 38*39*40*41 & 2430480 & \\ 39& 39*40*41*42 & 2686320 & \\ 40& 40*41*42*43 & 2961840 & \\ 41& 41*42*43*44 & 3258024 & \\ 42& 42*43*44*45 & 3575880 & \\ 43& 43*44*45*46 & 3916440 & \\ 44& 44*45*46*47 & 4280760 & \\ 45& 45*46*47*48 & 4669920 & \\ 46& 46*47*48*49 & 5085024 & \\ 47& 47*48*49*50 & 5527200 & \text{divisible by 700} \\ 48& 48*49*50*51 & 5997600 & \text{divisible by 700} \\ 49& 49*50*51*52 & 6497400 & \text{divisible by 700} \\ 50& 50*51*52*53 & 7027800 & \\ \dots & \ldots & \ldots \\ \hline \end{array}\)
Idun is rolling four ordinary six-faced dice, with the faces labelled 1 through 6.
What is the probability that her total score is divisible by 3?
\(\begin{array}{|rcll|} \hline \text{ probability } &=& \dfrac{2\cdot 6^3}{6^4} \\\\ &=& \dfrac{432}{1296} \\\\ &=& \dfrac{1}{3} \\ \hline \end{array} \)
simplify n+1 divided by n squared - n - 2 divided by n squared-1
Hello Guest!
\(\frac{n+1}{n^2}-n-\frac{2}{n^2}-1\ \)\(\ =\frac{n-1}{n^2}-n-1\)
When editing terms without parentheses, the arithmetic symbols are edited from left to right, with first the power calculation and multiplication and division being edited.
!
+2,+3,+7, +1, and lastly -1.
-2,-3,+7, +1, and lastly -1.
-2,+3,-7, +1, and lastly -1
+2,-3,-7, +1, and lastly -1.
Looks like you could be right.
Looking at your graph for the first question, I still have no clue whatsoever what the answer might be....
I appreciate the work you have done but PLEASE make your answer clearer to understand.
The answer is 16.
Bro I already tried the message board I just didn't get the help I needed, chill out man
4 * 20 = 80
oh sorry I confused it with Abraham Lincoln's gettyburg speech thats why I though it was 80.
"four score and seven years ago"
< when they say "will lay half a score", do they mean half of eighty? >
No. A score is 20, so half a score is 10.
.
factor
n^4 + 6n^3 + 11n^2 + 6n
n(n^3 + 6n^2 + 11n + 6)
n(n^2(n+6)+11(n+6))
n(n2+11)(n+6)
And i leave up to u
Is 0+1 equal to 0?
how many ways can u write 1/64 as an integer to the power of another integer
Hello notsmart!
\(\frac{1}{64}=\ {\color{blue} 2^{-6}=4^{-3}=8^{-2}=64^{-1}}\)
n = 25
25^4 + 6*25^3 + 11*25^2 + 6*25 =491,400 mod 700 =0
Artsyleilani, who do you think you are bullshitting?
Hey guys! Thanksgiving is just around the corner, and I thought... why not post some Thanksgiving questions?? (easy-ish lol & made up by me!)
Translation: I needed to delete my original question, because I’m not supposed to post them on here, and I don’t want to get into trouble with my teachers. So, I substituted this sixth-grade question to hide what I’m doing. I think I fooled everyone. Hehehe.
Just so you know, Artsyleilani, you’ve not fooled anyone, except yourself. If you continue to do this, you may find your account banned; then you will be up bullshitcreek without a paddle or help.
There are several ways of doing it:
2^-6 =1 / 64
4^-3 =1 / 64
8^-2=1 / 64
64^ -1=1 / 64
Also:
16^ -3/2 = 1/64
32^ -6/5= 1/64. But the exponents here are not "integers".
It’s 6
I think it's 4 groups.
do some pythagorean theorem... but draw it out first.
DEM is half of DFE.
So 18 / 2 = 9.
And since G is 2/3 its way on the median.
That means GEM is 1/3 of DEM.
So.... 3????????????????????????????????????????????????????
Approximate the value using a calculator. Express answer rounded to three decimal places. 51.1
Hi Coolstuff,
As a teaching suggestion you could have just factorised the top and let the asker copy your method to factorise the bottom by themselves.
It seems someone else snuck in candy as well...!!