Alpha Examples: Step-by-Step Solutions - Wolfram|Alpha

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Step-by-Step Solutions

Solutions for over 200 topics within math, chemistry and physics problems across all levels of education, from elementary school to college.

Arithmetic ›

See how to show your work for arithmetic problems.

See step-by-step solutions for doing basic multiplication or division problems:

3 × 560431 / 89

See the steps for applying the order of operations for arithmetic:

9 (3+1) + 17 / (6-12)

Follow the steps to convert an improper fraction to a mixed number:

87/5 as a mixed numberMore examplesStatistics ›

See the steps for analyzing data and applying statistical methods.

Perform basic statistical analysis on a set of data, seeing the steps along the way:

average of {1, 2, 3, 4, 5, 6, 7}mode of {1, 5, 4, 2, 3, 4, 5, 11, 4, 11, 20}variance 4, 6, 7, 9, 10, 11quartile of {1, 2, 3, 4, 5, 6}More examplesDifferential Equations ›

Explore step-by-step solutions for solving equations involving derivatives.

See how ordinary differential equations are solved:

solve y' = y^2 xy'(t) - 2y(t) = 3 e^(2t)t y(t) (1 + t y(t)^2) y'(t) = 1y''+ y = sin(2x)More examplesProofs ›

Get step-by-step results for proving mathematical statements.

See the steps toward proving a trigonometric identity:

(1 + tan(x))/(1 - tan(x)) = (cos(x) + sin(x))/(cos(x) - sin(x))

Prove a sum identity by induction:

prove by induction sum of j from 1 to n = n(n+1)/2 for n>0

Prove an inequality by induction:

prove by induction (3n)! > 3^n (n!)^3 for n>0

Investigate the convergence or divergence of an infinite sum step by step:

Does the sum of 5*3^(1 - n) converge?More examplesAlgebra ›

Learn how to manipulate and solve expressions with variables step by step.

Solve equations one step at a time:

find t for t^2 + 3t + 2 = 0

Factor polynomials step by step:

factor x^3+2x^2+x+2

Expand polynomials using the distributive law, the binomial theorem and other procedures:

expanded form of (x + 3)^2

Learn to rewrite a rational expression using partial fraction decomposition:

partial fraction decomposition 1/(x^2 + 4x + 3)More examplesTrigonometry ›

Learn the steps for evaluating or manipulating trigonometric expressions.

Show your work for solving the unknown measurements of a triangle:

right triangle with hypotenuse 2, A = 60 degrees

See the steps for how to find the values of a trigonometric function:

sin(2pi/3)

Get step-by-step solutions for applying the sum and difference formulas:

simplify sin(x-y) + sin(x+y)More examplesDiscrete Mathematics ›

See the steps involved for determining different properties of numbers.

Find step-by-step solutions for prime factorization, primality testing, GCD and more:

is 73 prime?lcm(90, 342)are 12 and 21 coprime?

Follow the steps to convert between bases:

convert 33ab3653 base 12 to base 10More examplesChemistry ›

Explore a wide array of chemistry topics with step-by-step solutions.

Get a step-by-step procedure to draw the Lewis structures of molecules:

What is the Lewis structure of NO2

Follow the steps for unit conversion:

convert 5mL benzene to moles

Learn how to balance a chemical reaction:

glucose + oxygen -> water + carbon dioxide

Compute oxidation states of chemicals:

oxidation states of chromium(III) chlorideMore examplesGeometry ›

Explore two- and three-dimensional shapes and their properties.

Compute properties of geometric objects step by step:

area of a circle with radius 2find the surface area of a sphere with radius = 8

Learn how to compute different properties for graphical objects:

(2, -4, 7) to (-4, 6, 1) distanceexpress x^2+y^2=3 in polar coordinates

Determine the equation of a line with certain properties using a selected form:

equation of line through (2, 5), (4, 1)More examplesCalculus ›

Get step-by-step solutions for common calculus problems, like computing limits, derivatives and integrals.

Find the derivative using the product rule, chain rule and other methods:

compute the derivative of x*sin[x]

Calculate an indefinite integral by substitution, integration by parts and other methods:

integrate sin(x)cos(x)^2

Learn how to take a limit:

limit of (x - 3) / (x^2 - 2x - 3) as x approaches 3

Explore step by step a variety of tests to discover local and global extrema:

find the extrema of 3x^4 - 4x^3 - 12x^2 + 1More examplesLinear Algebra ›

Solve problems involving vectors and matrices step by step.

Compute properties of a matrix step by step:

{{2, 2^2, 8/4}, {1, - 4, 7 - 4}}

Find the determinant step by step with various methods:

determinant of {{1,2,1}, {1,1,0}, {0,1,1}}

Compute eigenvalues and eigenvectors step by step:

eigenvalues {{3,-1},{0,2}}

Compute a cross product step by step:

(1,2,3)x(3,4,5)More examplesPhysics ›

See how to solve physics problems step by step.

Do physics calculations step by step:

Doppler shift for sound at source frequency 100 kHz for 70 mphcoulomb's law for 0.1 C and 0.2 C at 2 meters distancelength contraction for a proper length of 1 yard at 0.93cphoton energy 435nmwater flow through a pipe 2" diameter, 10' length of pipe with 2 kPa pressure differenceMore examplesGoProNowLearn more about Wolfram|Alpha Pro »