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lol y is juan

Please what is the least common denominator of: 2/7 5/12 4/13

The LCD=1092: 312/1092, 455/1092, 336/1092

Melody: Please look at this Wolfram/Alpha result and see if you can explain it. Thanks:

http://www.wolframalpha.com/input/?i=simplify++%28-125%29^%284%2F3%29

Thanks

The least common denominator of all of the fractions is 2288.

So if we rewrote all of the equivilent fractions then tthey would be 624/2288, 2145/2288, 528/2288

Well to find this we need to know what percent of 64 60 is.

So first we divide 60 by 64 and get .9375 or 93.75%

Then we multiply the total number of students by the decimal number we jsut got.

7505*.9375=7035.9375

This s how many students are taking a liberala arts major.

Well 1% of 90 is .9 because 90/100

So 10% of 90 would be 9 because 90/10

if we take this and multiply it by 6 we should get the answer of 54

Find the remainder when $1! + 2! + 3! + \dots + 100!$ is divided by 30.

I am still new to modular arithemtic but this is what I am thinking that this is the same as

the remainder when 1! is divided by 30 + the reminder when 2! is divided by 30 +...... the reminder when 100! is divided by 30.

And then after all these reminders are added together divide them by 30 and find the remainder of the original question.

1!=1  and    1mod30=1

2!=2   and    2mod30=2

3!=6   and    6mod30=6

4!=6*4 and     24mod30=24

5!=24*5=120          120/30= 4      so 5!=0 mod 30

6!=120*6                 120*6/30=4*6=24      so  6!=0 mod 30

all the others up to 100! will equal 0 mod 30 

so

(1! + 2! + 3! + \dots + 100!) mod30 = (1+2+6+24) mod30   =  33mod30  = 3

( - 125)^ 4 / 3 as a simplified fraction

I think our guest made a small error

\(( - 125)^ {4 / 3} \\ =( - 125)^ {1+1/3} \\ =( - 125)^ 1\times( - 125)^{1/3} \\ =\; - 125\times\;-5 \\ =625 \)

or alternatively

\(( - 125)^ {4 / 3} \\ =(( - 125)^ {1/3})^4 \\ =(-5)^4 \\ =625 \)

I should not have put that exclaimation mark there because  0!=1  and you can divide by 1.   

BUT YOU CAN NEVER DIVIDE BY 0

0/0 is undefined!

You can never divide by 0 !                        

solve( (x-a)^2=sqrt(x-a), a)

I don't know what the ",a" means in the question so I ignored it......

I have also assumed that x and a are real numbers.

\( (x-a)^2=\sqrt{x-a}\\ (x-a)^2=(x-a)^{0.5}\\ \mbox{Divide both sides by } (x-a)^{0.5}\\ (x-a)^{3/2}=1\\ (x-a)^3=1\\ \mbox{The only real solution is }x-a=1\\ \mbox{or }\quad a=x-1 \)

I guess you want to say a ''tan'' (tangent). In trignometry the tangent formula is only used in a right angle trianle. the sign 'O' with a dash in it is the angle(theta).

If you are not satisfied with this explanation, contact me. Here is my mail id : kunalinfrance@gmail.com

This was a really good question that promoted lots of great answers.

Thanks ElectrivPavlov, Will85237,  and guest/s       

Here are a whole lot more answers :)

1/32

Gee that is a tough one!  Maybe the answer is 1.        

Mmm   could be wrong but Red tells me he thinks the answer is1, and it is not sensible to argue with a dinosaur!

Just take away 70 one cent coins and add 2 ten cents and 2 twenty-five cents then.

3/8

check

\(\frac{150}{360}*2*\pi*24 \\= \frac{5}{12}*2*\pi*24 \\= \frac{5}{1}*2*\pi*2 \\=20\pi\;\; units\)

GREAT

ElectricPavlov's answer is spot on  :)

8x - 3y = 34        (5,y)      That is, find y when x=5

8*5 - 3y = 34

40  - 3y = 34

      -3y  = 34 - 40

      -3y =  -6

         y = 2

That is just 1 followed by 100 zeros :)

Find the Fourth term of (6x+5)^5

I always am confused with these because I never know which end I am supposed to start from.  

I guess there is some convention that I can never remember.

The coefficients for a power of 5 are     5C0, 5C1, 5C3, 5C4, 5C5 and these are    1,5, 10,   5,1

So, depending on which end you start from, the forth one is either

\(5*(6x)^4*5^1 = 5*6^4x^4*5=25*1296*x^4=32400x^4\\ or\\ 5*5^4*(6x)^1=5^5*6x=18750x\)