Math

Refine Search

What is instantaneous velocity in calculus?

The average velocity for any object is determined by the change in distance divided by the change in time for two points on the graph of distance versus time. If the speed is either accelerating or decelerating, however, the average velocity does not fully describe the motion. The instantaneous velocity is obtained by taking the limit as the difference between two time points goes to zero. As the difference between the two points approaches zero, the average velocity approaches the instantaneous velocity. This is referred to in calculus as the derivative or the slope of the tangent line at tha..

Continue Reading

How tall is a story?

Some stories in a building may be taller than others. Ground-floor-level stories can be 25 feet or more in a commercial building or around 15 feet in a residential or hotel building. If the building is very tall it may contain mechanical floors which may be around 25 feet for commercial buildings and 15 feet for residential buildings.

Continue Reading

How are operations solved with decimals?

With problems that involve decimals, using addition or subtraction to solve equations is often easier than using multiplication or division as the problems are generally less complex. With other math problems, setting up equations to ensure values line up properly is important, and even more so when working with decimals. When using addition to solve decimal equations, the numbers should first be lined up in the column by keeping decimal points in line. Then, add each column separately, beginning with the right hand side. Move from right to left to solve the equation, carrying the remainder to..

Continue Reading

How do you simplify rational expressions?

As a simple example, take the rational expression (x^2 + 3x + 2)/(x +4). To factor this expression, bring it to its simplest terms by thinking, "What factors of 2 can add up to 3?" In this case, 1 and 2 are the factors, so break it down to [(x + 1)(x + 2)]/(x+ 4). Had the denominator been (x+1), it would have canceled out one of the terms in the numerator, leaving the expression as (x + 2).\nRational expressions and polynomials can also be factored by grouping. Arrange the terms from highest exponent to lowest, then set parentheses around groups of two terms. Bring out common factors, and add ..

Continue Reading

What does the mass of a substance divided by the unit volume equal?

At standard temperature and pressure, osmium and iridium are the densest elements. Hydrogen gas has the lowest density. Because the volume of a gas depends on temperature and pressure, the density of a gas also depends on temperature and pressure. Density is determined by mass, not weight; therefore, the density of a substance does not change with gravity. An object on the moon weighs less than on Earth, but it has the same density.

Continue Reading

What is the way to write out hundredths?

If a student has to convert a fraction like 3/100 to decimal form, then he multiples the 3 in the numerator by 0.01, which gives the result 0.03. To express this in word form, the student writes three hundredths. On a place value chart, the 100th place is the second position on the right side of the decimal point. The decimal 453.0875 has the digit 8 in the 100th place. The word form is also useful for writing out mixed fractions, such as 4 35/100. In word form, a students writes this out as four and thirty-five hundredths.

Continue Reading

What is function notation?

Writing functional notation as "y = f(x)" means that the value of variable y depends on the value of x. In the simple function "f(x) = x + 3", y intercepts the y-axis at point (0,3) on the graph, because x is 0 and y is 3. From there, the line is a one-to-one function, with y and x increasing at the same rate. There are also compound functions that are useful in problems requiring more than one set of data. For example, "g(f(x))" means the initial function f is taken, then treated as the original x-value with a new line created on the graph.\nDomain and range are two other concepts to understa..

Continue Reading

How do you write out one billion in numerals?

In scientific notation, a billion is any number to the power of nine: 1 x 109 \n\nA billion is equivalent to a thousand million, which explains the need for nine zeros. The value of a billion was once a subject of debate among the English and the French. The English believed a billion to be any number to the power of 12, while the French thought the power of 12 too impractical and based the billion on the power of nine. The power of nine has since become the most accepted form of the billion.

Continue Reading

What is the way to manually calculate percentages?

A percentage is used to describe how much of something there is compared to another amount. A common example is a piece of a pie. If someone takes a piece that is a quarter of the pie, that is equal to 25 percent of the pie. The total percentage of any one object or number cannot exceed 100 percent. For example, eating the whole pie would be eating 100 percent of the pie.

Continue Reading

How is simple variance calculated?

Calculate the meanPerform a simple average of all the numbers in the set.Subtract the mean and square the resultSubtract the mean from each number in the set and square each result.Add the resultsCalculate the sum of all of the squared results from the previous step.Divide the sum by one less than the number of data pointsDivide the sum from the previous step by one less than the number of data points in the original set. The resulting number is considered sample variance and is closely related to sample standard deviation, which is found by taking the square root of this final number.

Continue Reading
Showing 3761 to 3770 of 3956 (396 Pages)