Let the three coordinates be (A(x_1,y_1,z_1)), (B(x_2,y_2,z_2)), (C(x_3,y_3,z_3))
Form two direction vectors in the plane:
(vec{AB}=(x_2-x_1, y_2-y_1, z_2-z_1))
(vec{AC}=(x_3-x_1, y_3-y_1, z_3-z_1))
Compute the normal vector with the cross...
Identify the type of series
Determine whether it is arithmetic, geometric, telescoping, or another known form
Write the general term of the series
Use the appropriate summation...
Identify the number you want the square root of
Use a calculator and press the square root button
Use estimation by finding nearby perfect squares
For a...
List the multiples of the first number
List the multiples of the second number
Find the first multiple that appears in both lists
That common multiple is...
List the denominators
Find the least common multiple of the denominators
Use that least common multiple as the lowest common denominator
If the denominators are small, list...
List the denominators of the fractions
Find the least common multiple of the denominators
Use that least common multiple as the LCD
Rewrite each fraction with the...
List the factors of both numbers
Identify the factors they have in common
Choose the greatest common factor from the shared factors
Or find the prime factorization...
Subtract the two numbers
Divide the result by the original number
Multiply by 100
Use this formula: `((New Number - Original Number) / Original Number) × 100`
If...
Identify the two quantities being compared
Check whether one quantity changes in a constant ratio with the other
Write the relationship as a fraction or equation
Compare...
Divide the number by the smallest prime numbers starting from 2
If the number is divisible, record the prime divisor
Keep dividing the quotient by the...
Find the difference between the two numbers: subtract the smaller number from the larger number
Find the average of the two numbers: add them together...
Subtract the new value from the original value
Divide the result by the original value
Multiply by 100
Percentage decrease = ((Original value - New value) /...
Identify the shape, line segment, or object whose length you need
Determine the starting point and ending point
Use a ruler, tape measure, or measuring tool...
Write the prime factorization of both numbers
Identify all prime factors used in either number
Take the highest power of each prime factor
Multiply those highest powers...
Let the matrix be (A=begin{bmatrix}a&b&c d&e&f g&h&iend{bmatrix})
Compute the determinant:
(det(A)=a(ei-fh)-b(di-fg)+c(dh-eg))
If (det(A)=0), the inverse does not exist
Find the cofactor matrix:
(C=begin{bmatrix}
(ei-fh) & -(di-fg) & +(dh-eg)
(bi-ch) & +(ai-cg)...
Estimate between the nearest perfect squares
Identify the two perfect squares the number falls between
Decide which square it is closer to
Use repeated subtraction for perfect...
Convert the fraction to a decimal by dividing the numerator by the denominator
Multiply the decimal by 100
Add the percent sign
Example: 3/4 = 0.75 =...
Subtract the old number from the new number
Divide the result by the old number
Multiply by 100
The result is the percent change
Formula: ((new number -...
