All Answers 354493 Answers

Logic Melody? What logic. This has been around since L. Euler!!.

Start at the bottom with 2. Take its reciprocal =1/2 + 1 to the left=1 1/2. Multiply by the same 2 at the bottom =3. Take the last mixed fraction we just got, i.e., 1 1/2. Take the reciprocal of this =2/3 + 2 to its left=2 2/3. Multiply this by the last whole integer we got, which was a 3, and you get=8. Since this is 2nd to the last fraction, then 8 is the numerator. Finally, take the last mixed fraction we got, or 2 2/3 and take its reciprocal =.375 + 1 to its left=1 3/8 x last whole integer we got,8, which was the numerator and you get: 1/ 3/8 x 8 =11 which is your denominator. Therefore this "continued fraction" =8/11. Fair?.

You need to show your logic guest. 

Thank you!

I take your problem to mean:

1/(5^x), if so, then:

Solve for x:
5^(-x) = 2

Take reciporicals of both sides:
5^x = 1/2

Take the logarithm base 5 of both sides:
Answer: |x = -(log(2))/(log(5))

3! means 3*2*1 = 6

8! means  8*7*6*5*4*3*2*1

etc

3! is 3 said as  factorial    

Hi Rauhan

Given that the total distance travelled is 1.4 km, and the acceleration is 4m/s^2 for the the first T second, find:

(a) the value of V

(b) the value of T

I will assume that the object is originally at rest at the origin. From time 0 the acceleration is a constant 4m/s^2  

And that after T seconds it has traveled 1.4 km.

There are a lot of assumptions here

\(\ddot x=4\\ \dot x=4t+k \qquad but\;\;k=0\\ \dot x=4t\\~\\ x=(4/2)t^2+c \qquad c=0\\ x=2t^2\\ \text{When t=T, x=1.4}\\ 1.4=2T^2\\ T^2=1.4/2 = 0.7\\ T=\sqrt{7}\approx 2.646\;seconds \)

THERE IS A "BUG" IN THE SYSTEM.

what is 20 percent of 10

20/100 x 10 = 2

x=75

what is the 8th term of 1,5,33,229,1601........

The 8th term=549,029 and is given by:a(n) = 1/21 (7^n * 2 + 7)

21. 

<-- This is Billy. Say Hi to Billy.

0 seriously, you had to ask that one?

This is simply "continued fraction" of: 8/11, which is your answer.

(f*g)(x)   literally means that we are multiplying the functions f and g together...so we have

1 / x + 1  *   - 1 /x  =    -1/x^2  -  1/x

If "f" is supposed to be 1 / [x + 1]......then we have

1 / [x + 1]  * -1/x  =     -1/ [ x (x + 1) ]  = -1/ [x^2 + x ]

The height after the  3rd bounce is given  by  :

8 (2/3)^3  = 64/27 ft ≈  2.37 ft

Solve for n over the integers:
8.5293404291712×10^9076 (1+3/5 (1-(4/9)^n)) = 1.70586808583424×10^9076 (8-3^(1-2 n) 4^n)

Subtract 1.36469446866739×10^9077-1.70586808583424×10^9076 3^(1-2 n) 4^n from both sides and collect in terms of 3^(1-2 n) 4^n:
0 = 0

0 = 0 is trivially true:
Answer: |True

Possible derivation:
d/dx(-3 x+4 x^2)
Differentiate the sum term by term and factor out constants:
 = -3 (d/dx(x))+4 (d/dx(x^2))
The derivative of x is 1:
 = 4 (d/dx(x^2))-1 3
Use the power rule, d/dx(x^n) = n x^(n-1), where n = 2: d/dx(x^2) = 2 x:
 = -3+4 2 x
Simplify the expression:
Answer: |= -3 + 8x

Solve for x:
3 (x-2)^2 = x (x-2)

Expand out terms of the right hand side:
3 (x-2)^2 = x^2-2 x

Subtract x^2-2 x from both sides:
3 (x-2)^2+2 x-x^2 = 0

Expand out terms of the left hand side:
2 x^2-10 x+12 = 0

The left hand side factors into a product with three terms:
2 (x-3) (x-2) = 0

Divide both sides by 2:
(x-3) (x-2) = 0

Split into two equations:
x-3 = 0 or x-2 = 0

Add 3 to both sides:
x = 3 or x-2 = 0

Add 2 to both sides:
Answer: |x = 3          or           x = 2

LMFAO! This is GREAT!!!

In this corner weighing in at 7.8st, and wearing a red hat, GingerAle, the spunky, genetically enhanced chimp. In the other corner, weighing in like a fat cat (about 25st), and wearing a suit without pockets, the guest fat cat banker.

In the first round, the fat cat banker baited the audience to kick a can containing a formula from the river Lethe. There were no takers.  GingerAle, the chimp waited patiently, biding her time playing Monopoly with her dog and cheating cat.

In round two, the fat cat banker finished his magic in-can-tation so his mystical computer would bring forth a rendering of numinous understanding.  His presentation is as mystical as his formula. It’s so advanced only one banker in the world can understand it –the fat cat banker himself. It’s like understanding our own poetry and thinking it’s great no matter how awful it is. (I sent this link to my banker for his opinion).

In round three, Ginger comes out with subtle finesse, jabs the fat cat banker in the solar plexus, and then skillfully enlarges a certain orifice that’s causing her opponent to retain large quantities of BS (banker stuff).   She also presents a logical and easy to understand solution to the question. 

In round four, the fat cat banker comes out like a snarling Tasmanian devil.  The orifice enlargement worked well, because he sure laid a pile on GingerAle.  He forgets though, that chimps are very skilled at throwing excrement at deserving targets –he may be sorry.  He also might be faulted for a technical foul, for saying, “you don't seem to know your head from your tail!”  Most advanced humans should know that chimps don’t have tails.”  His latest comment, “Behave yourself like a lady,” has some audience members murmuring that LancelotLink may have gone transgender.  She definitely has the trolling skills, but her style is very different. 

Well, there you have a folks! Stay tuned for round five, where the barbs and poo throwing may get better. For those not in the know, this isn’t the first match for these two –it’s not the second either. 

 I don't believe so, but average is simple. Just add up all the numbers that were given and divide by how many numbers there are. For example, lets say the numbers are 5, 4, 4 ,5, 6, and 1. 5+4=9+4=13+5=18+6=24+1=25. The numbers added up is 25 and there were 6 numbers given. 25 divided by 6 is 4.1666666666666667 so the average is roughly 4. Most average problems don't have an infinite decimal like that, since I chose a bad set of numbers, but it still works the same.

19. Also that meme is years old now, get with the times.

If he buys balloons for $3.99 and sells them for $0.50, he will never make a profit.

Does he buy a box of balloons (perhaps 50 or 100 in a box) and then sell them for $0.50 each?

Solve for x:                                               0.33ax  =  bu

Divide both sides by 0.33a:    0.33ax / (0.33a)  =  bu / (0.33a)

                                                                            x  =  bu / (0.33a)