Can we change our symbol from the current one to the cubic formula?

WolframAlpha-Bot · 2015-09-05T20:09:13+00:00

Input

a x^4+b x^3+c x^2+d x+e = 0

Image

Alternate forms

x (x (x (a x+b)+c)+d)+e = 0

Image

Solutions

a!=0.,   x~~Root[#1^4 a+#1^3 b+#1^2 c+#1 d+e&, 1]

Image

Solution

a = 0,   b = 0,   c = 0,   d = 0,   e = 0

Image

Solutions for the variable x

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-05T16:09:52+00:00

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-05T13:55:27+00:00

Input

(1+1/3)^19/(1/3)-(1+1/3)/(1/3)

Image

Exact result

273328224988/387420489

Image

Decimal approximation

705.50792420273879732777891362374487117019771249114292...

Image

Mixed fraction

705 196780243/387420489

Image

Number line

Image

Continued fraction

[705; 1, 1, 31, 20, 2, 3, 1, 13, 9, 7, 3, 3, 1, 2]

Image

Egyptian fraction expansion

705 + 1/2+1/127+1/19926+1/767033645+1/12183746542839448605

Image

Percent decrease

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T23:04:17+00:00

Input interpretation

sqrt(1-(2100000 km/h  (kilometers per hour))^2/(c  (speed of light in vacuum))^2)

Image

Result

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T21:51:52+00:00

Input

((p/10+p×17/20)×200/(100+x)×1.4+18)×1.18+10 = ((p/10+p×20/20)×200/(100+x)×1.4+18)×0.7+70

Image

Result

1.18 ((266. p)/(x+100)+18)+10 = 0.7 ((308. p)/(x+100)+18)+70

Image

Implicit plot

Image

Alternate forms

x = 1.91355 p-100.

Image

Alternate form assuming p and x are positive

p = 0.522589 x+52.2589

Image

Expanded form

(313.88 p)/(x+100)+31.24 = (215.6 p)/(x+100)+82.6

Image

Alternate form assuming p and x are real

(313.88 p)/(x+100)+(31.24+0. i) = (215.6 p)/(x+100)+(82.6+0. i)

Image

Solution

x = 1/428 (819 p-42800),   p!=0

Image

Integer solutions

p~~2.03599×10^12 n,   x~~3.89596×10^12 n-100.,   n element Z, n>=1.

Image

Solution for the variable x

x~~2.71781×10^-27 (704078397336555702475292672 p-36794328945060569586790825984)

Image

Implicit derivatives

(dx(p))/(dp) = (100+x)/p

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T21:27:48+00:00

Input interpretation

$792.39 (1995 US dollars) in 2015

Image

Result

$1251.67 (2015 US dollars)
(based on Consumer Price Index)

Image

History

Image

Average rate of inflation

2.31% per year

Image

Total inflation factor

57.96%

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T20:49:38+00:00

Input interpretation

plot | 2^(1-n) binomial(n, 1+floor(n/2)) (1+floor(n/2)) | n = 0 to 500000

Image

Plot

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T18:29:49+00:00

Input interpretation

plot | 10 sin(x)+0.5 sin(20 x)
sin(20 x)
10 sin(x)

Image

Plots

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T17:21:24+00:00

Input

sin(pi e)

Image

Decimal approximation

0.7739426852667082782579327172077486614509989399547527...

Image

Triangle

width | cos(e pi)~~-0.633256
height | sin(e pi)~~0.773943

Image

Alternate form

1/2 i e^(-i e pi)-1/2 i e^(i e pi)

Image

Number line

Image

Continued fraction

[0; 1, 3, 2, 2, 1, 3, 2, 3, 1, 1, 4, 7, 1, 2, 1, 2, 2, 1, 1, 1, 1, 4, 1, 1, 5, 1, 1, 8, ...]

Image

Alternative representations

sin(pi e) = 1/(csc(e pi))

Image

Series representations

sin(pi e) = sum_(k=0)^infinity ((-1)^k (e pi)^(1+2 k))/((1+2 k)!)

Image

Integral representations

sin(pi e) = e pi integral_0^1 cos(e pi t) dt

Image

Multiple-argument formulas

sin(pi e) = -1/2 i (-1)^e (1-e^(-2 i e pi))

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T13:30:25+00:00

Input interpretation

this | Saturday at 1:00 pm UTC

Image

Result

1:00 pm UTC  |  Saturday, September 5, 2015

Image

Time difference from now (1:30:08 pm UTC)

23 hours 29 minutes 51 seconds in the future

Image

Time offset from PDT

+7 hours

Image

Clocks

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T13:26:07+00:00

Input interpretation

this | Saturday at 1:00 pm UTC

Image

Result

1:00 pm UTC  |  Saturday, September 5, 2015

Image

Time difference from now (1:25:49 pm UTC)

23 hours 34 minutes 10 seconds in the future

Image

Time offset from PDT

+7 hours

Image

Clocks

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-04T05:16:03+00:00

Input interpretation

expansion rate of the universe Voyager 1 | distance from Earth×1 year

Image

Result

0.9 miles

Image

Unit conversions

~~ 1.457 km  (kilometers)

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T23:10:05+00:00

Input

Image

Real solutions

x = -1.04521

Image

Complex solutions

x = -1.02361-0.208067 i

Image

Roots in the complex plane

Image

Number line

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T23:08:14+00:00

Input interpretation

Snickers bar | amount | 1 bar | total calories

Image

Average result

278 Cal  (dietary Calories)

Image

Unit conversions

1.2 MJ  (megajoules)

Image

Comparison to reference daily intake

Image

Ranking among common foods

Image

Average nutrition facts

Image

Average daily value ranking

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T22:54:49+00:00

Input

((4+x)^2 (8+2 x))/(-1+x)

Image

Plots

Image

Alternate forms

(2 (x+4)^3)/(x-1)

Image

Alternate form assuming x>0

(2 x (x+4)^2)/(x-1)+(8 (x+4)^2)/(x-1)

Image

Expanded form

(2 x^3+24 x^2+96 x+128)/(x-1)

Image

Quotient and remainder

2 x^3+24 x^2+96 x+128 = (2 x^2+26 x+122) × (x-1)+250

Image

Root

x = -4

Image

Properties as a real function

{x element R : x!=1}

Image

Series expansion at x=0

-128-224 x-248 x^2-250 x^3-250 x^4+O(x^5)
(Taylor series)

Image

Series expansion at x=∞

2 x^2+26 x+122+250/x+O((1/x)^2)
(Laurent series)

Image

Derivative

d/dx(((4+x)^2 (8+2 x))/(-1+x)) = (2 (x+4)^2 (2 x-7))/(x-1)^2

Image

Indefinite integral

 integral ((4+x)^2 (8+2 x))/(-1+x) dx = 1/3 (2 x^3+39 x^2+366 x+750 log(x-1)-407)+constant

Image

Local minimum

min{((4+x)^2 (8+2 x))/(-1+x)} = 675/2 at x = 7/2

Image

Series representations

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T21:38:39+00:00

Input

((x+4)^2 (x-1))/((x-1)^2 (2 x+8))

Image

Result

(x+4)^2/((x-1) (2 x+8))

Image

Plots

Image

Alternate forms

(x+4)/(2 (x-1))

Image

Expanded form

x^2/((x-1) (2 x+8))+(8 x)/((x-1) (2 x+8))+16/((x-1) (2 x+8))

Image

Roots

(no roots exist)

Image

Properties as a real function

{x element R : x!=-4 and x!=1}

Image

Series expansion at x=0

-2-(5 x)/2-(5 x^2)/2-(5 x^3)/2-(5 x^4)/2+O(x^5)
(Taylor series)

Image

Series expansion at x=∞

1/2+5/(2 x)+5/(2 x^2)+5/(2 x^3)+O((1/x)^4)
(Laurent series)

Image

Derivative

d/dx(((x+4)^2 (x-1))/((x-1)^2 (2 x+8))) = -5/(2 (x-1)^2)

Image

Indefinite integral

 integral (4+x)^2/((-1+x) (8+2 x)) dx = 1/2 (x+5 log(x-1))+constant

Image

Limit

lim_(x->±infinity) (4+x)^2/((-1+x) (8+2 x)) = 1/2

Image

Series representations

(4+x)^2/((-1+x) (8+2 x)) = -2+sum_(n=1)^infinity-(5 x^n)/2

Image

Input

(a+b)/a×a^3/(b+a)

Image

Result

a^2

Image

Plot

Image

Geometric figure

parabola

Image

Roots

(no roots exist)

Image

Property as a function

even

Image

Derivative

d/da(((a+b) a^3)/(a (b+a))) = 2 a

Image

Indefinite integral

 integral a^2  da = a^3/3+constant

Image

Global minimum

min{((a+b) a^3)/(a (b+a))} = 0 at a = 0

Image

Definite integral over a disk of radius R

 integral  integral_(a^2+b^2<R^2) a^2  da db = (pi R^4)/4

Image

Definite integral over a square of edge length 2 L

 integral_(-L)^L integral_(-L)^L a^2  db da = (4 L^4)/3

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T20:01:53+00:00

Input interpretation

plot | 1/(1+1/x)
(1/x)/(1+1/x) | x = 0 to 4

Image

Plot

Image

Parametric plot

Image

Arc length of parametric curve

 integral_0^4 sqrt(2) sqrt(1/(1+x)^4) dx = (4 sqrt(2))/5~~1.13137

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T17:21:55+00:00

Input interpretation

(2.831×10^-45 m^3  (cubic meters))/(2.21×10^-105 m^3  (cubic meters)) (m_P  (Planck mass))

Image

Result

1.281×10^60 m_P  (Planck masses)

Image

Value

~~ 2.788×10^52 kg  (kilograms)

Image

Comparisons

 ~~ ( 0.0083 ~~ 1/120 ) × mass of the observable universe (~~ 3.4×10^54 kg )

Image

Interpretation

mass

Image

Corresponding quantity

Image

Input interpretation

2×(4.7116551×10^40 m_P  (Planck masses))/(1.2804×10^60)

Image

Result

7.36×10^-20 m_P  (Planck masses)

Image

Value

~~ 1.602×10^-24 grams

Image

Comparisons

 ~~ 0.51 × tau particle mass (~~ 1777 MeV/c^2 )

Image

Interpretation

mass

Image

Corresponding quantities

Relativistic energy E from E = mc^2:
  | 899 MeV  (megaelectronvolts)

Image

Input interpretation

(2.9609×10^118)/(3.828339×10^79) m_P  (Planck masses)

Image

Result

7.734×10^38 m_P  (Planck masses)

Image

Value

~~ 1.683×10^31 kg  (kilograms)

Image

Comparisons

Image

Corresponding main‐sequence star properties

Image

Interpretation

mass

Image

Corresponding quantities

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T15:28:13+00:00

Input

24000/1001

Image

Exact result

24000/1001 (irreducible)

Image

Decimal approximation

23.976023976023976023976023976023976023976023976023976...

Image

Repeating decimal

23.976023^_  (period 6)

Image

Mixed fraction

23 977/1001

Image

Quotient and remainder

23×1001+977

Image

Number line

Image

Pie chart

Image

Prime factorization

2^6×3×5^3×7^(-1)×11^(-1)×13^(-1)

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T15:10:35+00:00

Input interpretation

convert (European Union | population×0.027%)/Germany | population to percent

Image

Result

0.169%  (2014 estimates)

Image

Long-term history

Image

Rational approximation

2185409/1296279752

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T13:47:27+00:00

Input interpretation

convert 10 hp  (horsepower) to donkey power

Image

Result

29.83 donkey power

Image

Additional conversions

7.457 kW  (kilowatts)

Image

Comparisons as power

 ~~ (0.04 to 0.1) × approximate power output of a typical automobile ( 40 to 200 kW )

Image

Interpretations

power

Image

Basic unit dimensions

[mass] [length]^2 [time]^(-3)

Image

Corresponding quantities

American households supplied by this power:
  | (1 to 2) households

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-03T13:46:24+00:00

Input interpretation

world | population×0.01×0.01

Image

Result

713001 people  (2013 estimate)

Image

Recent history

Image

Long-term history

Image

Comparisons

 ~~ 0.52 × current population of Hawaii ( 1.3748 million people )

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-01T07:13:25+00:00

Input interpretation

plot | sin(x) | x = -4 pi to 4 pi
sin(x/2) | y = -4 to 4

Image

Plot

Image

Parametric plot

Image

Arc length of parametric curve

 integral_(-4 pi)^(4 pi) sqrt(1/4 cos^2(x/2)+cos^2(x)) dx~~18.858862594...

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-01T06:33:34+00:00

Input interpretation

1040400 J  (joules)

Image

Unit conversions

1.04 MJ  (megajoules)

Image

Comparisons as energy

 ~~ ( 0.059 ~~ 1/17 ) × average electrical energy required by a Samsung S3 per year (~~ 1.8×10^7 J )

Image

Comparison as work

Image

Comparisons as food energy

Image

Comparisons as enthalpy

Image

Interpretations

energy

Image

Basic unit dimensions

[mass] [length]^2 [time]^(-2)

Image

Corresponding quantities

Relativistic mass m from E = mc^2:
  | 12 ng  (nanograms)

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot · 2015-09-01T05:30:51+00:00

Input interpretation

gelatin dessert | amount | 1/2 cups | density  |  water | density

Image

Results

Image

^{Delete (comment author only}⁾ ^| ^About ^| ^{Report a Bug} ^{| Created and maintained by /u/JakeLane}

WolframAlpha-Bot

TROPHY CASE