Great answers to learn from

$$Introduction:$$

Hello! You have reached the "Great answers to learn from" page. This page is meant to be a collection of great answers that people could look back upon and learn from. Hopefully if you have a certain topic you want to learn about, you can some posts on that topic here!

For the most part, this thread is organized into "grade levels" of mathematics to make it easier to find what you want to learn about.

Finally, if you have anything you want to add to this post, go ahead and reply to it with what you want added, or you can message me and I'll add it to the proper section.

Roots and exponents:

• Simplifying.

http://web2.0calc.com/questions/3-sup3-radic-24-sup3-radic-375

http://web2.0calc.com/questions/can-anyone-do-square-roots

• Finding a root of a negative number

http://web2.0calc.com/questions/can-i-calculate-a-negative-number-to-the-power-of-a-fraction-ie-1-42-1-7

• Rationalising a denominator:

http://web2.0calc.com/questions/in-question-21-nbsp

• Exponets with negative bases:

http://web2.0calc.com/questions/if-a-negative-number-is-in-parenthesis-and-has-a-positive-exponent-how-does-it-get-a-positive-number-outcome-while-a-negative-number-withou

Fractions:

• Dividing two fractions:

http://web2.0calc.com/questions/3-4-5-8

• Find the Least Common Denominator (LCD):

http://web2.0calc.com/questions/what-is-the-lcd-for-5-9-and-2-3

Dealing with time in math, on a handheld calculator!

http://web2.0calc.com/questions/what-is-21hours-and-58-minutes-subtracted-by-4-36-p-m-equal

Directed numbers and plotting on a number line

http://web2.0calc.com/questions/the-answer-to-the-expression-3-6-located-on-a-horizontal-number-line

Is zero even or odd?

http://web2.0calc.com/questions/0-is-a-nbsp-odd-number-or-even-number-why-please-explain

Speed and rates:

• Migrating elephants!

http://web2.0calc.com/questions/a-migrating-elephant-herd-started-moving-at-a-rate-of-6-miles-per-hour-one-elephant-stood-still-and-was-left-behind-then-this-stray-elepha

• Speed of a current

http://web2.0calc.com/questions/a-boat-on-a-river-travels-20-miles-downstream-in-only-2-hours-it-takes-the-same-boat-6-hours-to-travel-12-miles-upstream-what-are-the-spee

Comparing numbers; the apparent brightness of stars!

http://web2.0calc.com/questions/science-link-math-question

Percentages:

• Find a total when given a part

http://web2.0calc.com/questions/435-is-15-of-what-number

Variant of Average:

http://web2.0calc.com/questions/the-average-of-six-numbers-is-6-if-3-is-subtracted-from-each-of-four-of-the-numbers-what-is-the-new-average#r1

Adding up all the numbers between two specific numbers:

http://web2.0calc.com/questions/what-is-all-the-numbers-from-1-to-100-added-up

Forever repeating decimal!

http://web2.0calc.com/questions/0-99999

Order of operations - multiplication before addition:

http://web2.0calc.com/questions/3x60-5x9-2x2

The basics of algebra:

• What does "x" mean?

http://web2.0calc.com/questions/5x-21-2x-what-does-x-mean

• Solving for x by "balancing" out two sides of an equation:

http://web2.0calc.com/questions/solve-for-x-7 

• Why would I use x²?

http://web2.0calc.com/questions/what-does-x-squared-equal

Algebra word problem examples:

• Simultaneous equations:

http://web2.0calc.com/questions/a-shopkeeper-paid-9-380-for-some-shirts-and-jeans-he-bought-4-times-as-many-shirts-as-jeans-each-pair-of-jeans-cost-40-more-than-a-shirt-h

http://web2.0calc.com/questions/how-old-they-are

• Set it up algebraicly, and solve!

http://web2.0calc.com/questions/i-know-the-answer-but-do-not-know-how-to-do-the-work

http://web2.0calc.com/questions/you-want-to-place-a-towel-bar-that-is-8-1-4-inches-long-in-the-center-of-a-door-that-is-26-1-3-inches-long-how-far-should-you-place-the-bar

http://web2.0calc.com/questions/mr-lee-baked-185-more-chicken-pies-than-tuna-pines-after-selling-3-5-of-the-chicken-pies-and-half-of-the-tuna-pies-he-had-146-pies-left-how

Fractions and solving for x:

http://web2.0calc.com/questions/if-then

http://web2.0calc.com/questions/solve-for-x-3-over-4-x-5-over-8-4x

Three different techniques to this answer dealing with polynomials:

http://web2.0calc.com/questions/5a-5-5a-5

Imaginary numbers:

• Introduction to imaginary numbers

http://web2.0calc.com/questions/help-me-with-solving-this-equation-please

• Finding Complex Roots with imaginary numbers (Difficult)   

http://web2.0calc.com/questions/how-do-i-solve-the-sqrt4-16-complex-numbers-4-different-roots

• Complex number proof that iⁱ is a real number:

http://web2.0calc.com/questions/puzzle-question-i-i

Difficult inequality solution

http://web2.0calc.com/questions/how-can-i-solve-the-first-question-nbsp

Solveing a nonlinear inequality. This one looks like a parabola!

http://web2.0calc.com/questions/solve-the-nonlinear-inequality

Well explained by heureka:

http://web2.0calc.com/questions/5x-8-3x-3-whats-the-x

Heureka just being awesome:

http://web2.0calc.com/questions/solve-the-equation_1

An example of scientific notation:

http://web2.0calc.com/questions/if-i-have-1-5-trillion-us-dollars-and-wanted-to-divide-it-up-between-7-billion-people-the-world-s-population-how-much-would-each-person-g

A more complicated algebra question answered by Alan

http://web2.0calc.com/questions/x-2-xy-y-2-28-y-2-x-how-do-you-get-x-and-y

Horizontal and slant Asymtotes (Advanced)

http://web2.0calc.com/questions/horizontal-asymptote-of-y-x-2-6x-3-x-3

Quadratic equations:

• Complicated one:

http://web2.0calc.com/questions/please-help_40

• Solving with the quadratic formula:

http://web2.0calc.com/questions/help-me-with-solving-this-equation-please

• A little different than the usual quadratic questions:

http://web2.0calc.com/questions/x-7sqrt-x-10-0

Finding the equation of a polynomial when you are given the roots:

http://web2.0calc.com/questions/find-the-family-of-quadratic-functions-in-simplest-form-with-roots-at-2-plus-minus-3-root-5

Linear Representation (graphing the equation of a line) of a worded problem:

http://web2.0calc.com/questions/gregory-planted-a-lemon-tree-in-hid-back-yard-when-he-planted-the-tree-it-was-2-feet-tall-he-noticed-that-it-has-been-growing-3-inches-ev 

What is a logarithm? (thanks to anonymous)

http://www.mathsisfun.com/algebra/logarithms.html

Half life problem:

http://web2.0calc.com/questions/the-half-life-of-carbon-14-is-around-5700-years-find-the-of-the-original-carbon-14-that-remains-in-a-sample-after-1835-years-have-passed

Solving for x when x is raised to a power:

http://web2.0calc.com/questions/can-t-seem-to-get-this-equation-solved

Finding why an equation with logs equals zero - two different approaches:

http://web2.0calc.com/questions/why-does-log-2ab-log-5-a-log10b-0

Radioactive decay!

http://web2.0calc.com/questions/a-15-g-sample-of-radioactive-iodine-decays-in-such-a-way-that-the-mass-remaining-after-nbsp-t-nbsp-days-is-given-by-nbsp

This certainly looks like a more difficult logarithmic equation to me!

http://web2.0calc.com/questions/difficult-logarithmic-equation-without-a-calculator

Harder logarithm problem. Three people got the same answer, so it should be right!

http://web2.0calc.com/questions/log-3-6-log-9-6-log-4-6-log-18-6

Triangles! Great picture and explanation by CPhill

http://web2.0calc.com/questions/so-i-have-two-triangles-here-but-are-they-overlapping-i-can-t-draw-i-diagram-that-fits-the-discription-p-nbsp-does-anyone-have-a-suges

Finding the circumference from the diameter:

http://web2.0calc.com/questions/circumference-of-pipe-diameter-3090mm

Height of a triangle, the Pythagorean theorem!

http://web2.0calc.com/questions/how-do-i-figure-out-the-right-of-a-triangle-when-ab-equals-13-and-cb-equals-12

Heron's formula to find the area of a triangle:

http://web2.0calc.com/questions/triangle-s-sides-are-a-5-b-12-and-c-9-what-is-the-area-of-the-triangle

Volume of a sphere:

http://web2.0calc.com/questions/a-spherical-ball-hss-a-diameter-of-45cm-workout-the-volume-of-the-ball

Word problems:

• Hay bales (cylinder):

http://web2.0calc.com/questions/i-have-a-bale-of-hay-that-is-5-in-diameter-and-4-wide-if-i-store-the-bale-outside-the-outer-8-inches-gets-damaged-by-sun-and-rain-what

• Wagon wheels (circumference of a circle):

http://web2.0calc.com/questions/neeeed-help-on-this

$$Statistics\;and\;Probability$$

Z scores:

http://web2.0calc.com/questions/how-do-i-find-the-area-under-the-standard-normal-curve-over-the-interval-specified-below-between-z-44-and-z-44

Permutations where some objects are not unique:

http://web2.0calc.com/questions/permutations_2

$$Set\;Theory:$$

Introductory set theory:

http://web2.0calc.com/questions/represent-the-following-number-as-being-members-of-set-k-2-4-2-0-6-0-10-8

Verifying the identity

http://web2.0calc.com/questions/verify-the-identity-cot-theta-sec-theta-csc-theta

Why is Sinθ approximately equal to θ for very small values of θ 

http://web2.0calc.com/questions/why-is-sin-of-theta-appromately-equal-to-theta

How do you choose the correct trigonometric ratio (sin, cos or tan) to use?

http://web2.0calc.com/questions/how-do-i-know-when-to-use-tan-instead-of-sin-or-cos-when-i-think-i-ve-got-it-right-by-using-sin-or-cos-i-ve-really-got-it-wrong-because-i

Finding an angle on a right sided triangle:

http://web2.0calc.com/questions/i-need-help-finding-the-angle-of-a-right-sided-triangle#rr2

Unusual trig. equation (solve for θ)

http://web2.0calc.com/questions/sin-3-cos-26-solve-for

Changing radians to degrees:

http://web2.0calc.com/questions/how-do-turn-radians-to-degrees

Bearings and vectors:

http://web2.0calc.com/questions/an-aeroplan-heads-in-a-direction-of-s30-w-at-a-speed-of-300km-h-the-wind-b**w-at-a-speed-of-50km-h-in-the-direction-of-s20-e-what-is-the

Velocities - Looks like a great answer from Alan:

http://web2.0calc.com/questions/urgent-solve-in-key-steps-please-v2sin-30-v1cos-30-cos-45-cos45-17#r6

Light rays!

http://web2.0calc.com/questions/if-a-light-ray-is-incident-of-the-glass-surface-with-index-of-refraction-n-1-50-at-0-degree-anglee-what-would-be-the-angle-of-refraction-if#r2

Some more trig. questions:

http://web2.0calc.com/questions/8-sec2-x-4-tan2-x-12-0

http://web2.0calc.com/questions/3cosx-4sinx-1

High level Trig:

http://web2.0calc.com/questions/how-can-i-show-that-the-bound-between-sin-v-2-cos-v-2-1-is-true-for-all-degrees-in-the-intervall-0-v-180

University level Trigonometry:

http://web2.0calc.com/questions/how-to-know-when-the-function-is-continuous

 $$Commercial\;Mathematics$$

Difficult:

• Compare Renting to Buying - Annuities

 http://web2.0calc.com/questions/need-done-if-possible

Forces explained by Alan

http://web2.0calc.com/questions/finding-friction-coefficient-from-kinetic-energy

http://web2.0calc.com/questions/2d-forces-equation#r0

Vectors:

• Vector forces:

http://web2.0calc.com/questions/collinear-resolving-angles-of-a-parallelogram

• Converting to vector units:

http://web2.0calc.com/questions/how-to-turn-into-vector-units

• Magnitude of vector forces:

http://web2.0calc.com/questions/u-6i-j-and-v-10i-j-find-the-manitude-of-u-v

• Another vector problem:

http://web2.0calc.com/questions/the-acute-angle-in-degrees-that-makes-a-with-c-when-a-4i-0j-k-c-i-j-3k

Distance/displacement:

http://web2.0calc.com/questions/total-distance

Misc. physics problems:

http://web2.0calc.com/questions/nbsp_3

$$Puzzles:$$

Some thinking puzzle problems:

http://web2.0calc.com/questions/prove-that-in-a-gathering-of-n-persons-there-is-always-2-persones-of-them-that-have-same-amount-of-friends-among-these-persones

http://web2.0calc.com/questions/a-drinking-problem