Math

Refine Search

What number between 30 and 40 has only one and itself as factors?

Prime numbers are defined as numbers that have only one and themselves as factors. The vast majority of whole numbers are either prime or composite. Composite numbers are those that have more than two factors, or numbers by which they are divisible. The only exception to this rule is the number one, which is neither prime nor composite. The primary practical application of prime numbers is cryptography algorithms, hash tables and random number generators.

Continue Reading

How do you find the hypotenuse of an isosceles triangle, given two lengths?

Make certain the triangle is a right triangleThe Pythagorean theorem can only be used with isosceles triangles that are right triangles. This means one of the angles must be 90 degrees. If it's not, the theorem cannot be used.Write down the Pythagorean theoremThe Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the two shorter legs. It's often written as h squared equals a squared plus b squared.Insert the numbersReplace a and b in the equation with the lengths of the two sides. As an example, let a = 3 and b = 4.Square both of the le..

Continue Reading

How do you factor the difference of two squares?

Find the squares and square roots involvedConsider the example problem x^2 - 9. Break down x^2 and 9 into their square roots, which are x and either 3 or (-3). Remember that this only works for variables and constants that break down into perfect square roots, so numbers such as 8 and variable expressions such as 2x^5 do not factor this way.Write the factors in proper formRemember that for any expression a^2 - b^2, the proper way to present the factoring is as follows: (a + b) (a - b). Look at the example problem from Step 1, and write the factors in the proper way: (x + 3) (x - 3).Remember to..

Continue Reading

What are the factors of 45?

A positive integer greater than 1 that has only two factors is considered a prime number. Numbers that have more than two factors are considered composite numbers. Factors that are prime numbers are called prime factors. A number can also be expressed in terms of its prime factors, with few exceptions. For example, the number 60 can be expressed as the product of 2, 2, 3 and 5. Methods of factoring large whole numbers is a key part of cryptology, and Internet data security relies on them.\nMathematicians from Pythagoras' School between 500 and 300 B.C. were interested in mystical and nume..

Continue Reading

How do I make an octagon shape?

Designate a starting pointThe first step in constructing an octagon is drawing a straight line on the paper. This is the construction line.Find the anglesAn octagon is made up of eight equal angles. The total of all of the angles is 360 degrees. Therefore, each angle is 1/8 of 360 degrees, or 45 degrees.Draw the sidesBeginning with the construction line, draw the first of the vertices. Using the protractor, measure a 45-degree angle. Using the ruler, determine the length of the side. Repeat these steps until all eight sides are completed.

Continue Reading

What does 1*tan(2*x) equal?

The identity of a trigonometric function refers to properties of the function that are true regardless of the input values. Using the double-angle identity to evaluate tan(2x) gives the (sin[2x]/cos[2x])/cos^2(x), since the tangent function is equal to the ratio of the sine to the cosine. The sin(2x) = 2 * sin(x) * cos(x), while cos(2x) = cos^2(x) ? sin^2(A) = 2 * cos^2(x) -1 = 1 - 2 * sin^2(x).

Continue Reading

What are some geometry formulas for triangles?

The Pythagorean Theorem states that the side lengths of a right triangle follow the pattern a squared + b squared = c squared, where a and b represent the triangle’s two shorter sides and c represents the triangle’s hypotenuse.\nFrom this relationship, a set of trigonometric functions emerges to describe the geometric connections among the triangle's side lengths and interior angles. Commonly known as SOHCAHTOA, these relationships are: sine (angle) = opposite/hypotenuse; cosine (angle) = adjacent/hypotenuse; and tangent (angle) = opposite/adjacent.

Continue Reading

Where can you find a calculator for determining RRSP contributions?

As someone gets closer to retirement, he should begin to switch from high-risk to low-risk investments to ensure the money is available when he retires. However, while working, the investment risk should be higher to get a larger return when income is still available. Therefore, the annual rate of return used in the calculator needs to be averaged based on the change in investment risk.

Continue Reading

Why does "m" represent slope?

Another suggestion made by John Conway was that this letter symbol for slope may refer to "modulus of slope." Some mathematics historians believe that the use of this letter symbol in the straight-line equation occurred over time. For example, the first appearance in print of the letter "m" for slope was in 1844. Through subsequent years, different textbooks also used other letter symbols, such as Swedish textbooks representing slope by the letter "s."The straight line equation, also called the slope-intercept form, is given as y = mx + b, where b is the y-intercept.

Continue Reading

What is the greatest nine-digit number you can make using nine different digits?

To create the largest possible nine-digit number, the hundred-millions digit must be the biggest digit. In this case, that number should be nine because it is the largest possible digit. The ten-millions digit should be the second biggest number, or eight in this case. If the number used was seven, for example, the entire nine-digit number would be smaller by ten million. This trend continues, causing each of the different digits to be in descending order.

Continue Reading
Showing 1021 to 1030 of 3956 (396 Pages)