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What is the antiderivative of tan(x)?

Both solutions for the antiderivative of tan(x) can be found by using an integration technique called substitution. In integration, the substitution technique works in the reverse manner of the chain rule for differentiation. Using substitution, the variable u is used to replace one of the terms in the integral and the derivative of u replaces the term dx in the function. After solving in terms of u, the terms from the original function are substituted back in place of u and du.

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How do you calculate your average monthly water bill?

A water bill is generated monthly by a municipal water department and provides the customer the quantity of water used the previous month and the amount of money owed to the water department for that water. Water bills increase as more water is used and decrease as less water is used. Averaging water bills gives the consumer a better idea of water use and its associated cost than can be determined by viewing individual monthly bills. For example, a $200 bill one month and $20 bill the next yields an average of $110 per month. While the bills taken individually provide a distorted view, the ave..

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How do you convert numbers to words?

If a number contains more than three digits, commas are generally placed at three-digit intervals. Within each set of three, the first digit represents hundreds, the second digit represents tens, and the third digit represents ones. The three digits on the right do not have any additional word added (if there is no decimal point). The next three digits to the left have the word "thousand." After that comes "million," "billion" and "trillion." The highest group of numbers must be written first because the number is read from left to right.\nIf there is a zero, skip that place value and go to th..

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What are some free programs for solving algebra problems?

The Free Universal Algebra Equation Solver is designed to explain algebraic equations in addition to solving them, helping users learn why they reached the correct answer. Users can input equations based on rational, irrational, exponential and logarithmic algebra problems. Users can also set up absolute value systems and define parameters, and the system is designed to cover all types of Algebra classes, including up to college algebra. Users can also supplement their learning by the written and verbal commentaries available with the software, though users need an Internet connection for the ..

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What is the standard form of 8 million 12 hundred thousand 110 thousand 9 thousand?

Eight and one are in the millions place. Two and one go in the hundred thousands. One is in the ten thousands, nine is in the thousands, and zeros go in the hundreds, tens and ones places. Add the two numbers in the millions and then the two numbers in the hundred thousands. The eight and the one in the millions place equal nine, and the two and the one in the hundred thousands place equal three. The numbers in the other places stay the same because there is only one number in each of the places.

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What is the end behavior of polynomial functions?

Even-degree polynomials behave like quadratics, while odd-degree polynomials behave like cubic graphs. If an even-degree polynomial has a positive leading coefficient, the two ends of the graph point upward. If an even-degree polynomial has a negative leading coefficient, the two ends of the graph point downward. If an odd-degree polynomial is positive, the left end points down and the right end points up. If an odd-degree polynomial has a positive leading coefficient, the left end points up and the right end points down.

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What are the multiples of 18?

A multiple is a number that is the result of multiplying a number by any integer. A number is identified as a multiple of another number if the first is divisible by the second without any remainder. For example, 90 is a multiple of 18. When 90 is divided by 18, the answer is 5. When 92 is divided by 18, the answer is 5 with a remainder of 2. That means 92 is not a multiple of 18.\n\nThe concept of multiples is generally taught in elementary math during and following lessons about multiplication. Understanding multiples becomes important in later elementary math lessons, and multiples are used..

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What fraction of an hour is 40 minutes?

In this instance, the whole is one hour, which is equivalent to 60 minutes; therefore, the fraction is 40/60. To make the answer more useful, it should be simplified. To do this, find the largest number that is a factor of both the numerator and the denominator. The number 20 divides evenly into both 40 and 60, leaving the fraction 2/3.

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What is the LCM of eight and 12?

In this example, 8 can be multiplied by 3 to give 24, and 12 can be multiplied by 2 to also give 24. In some cases, the least common multiple between two numbers is the product of the two numbers in question. For example, the least common multiple of 11 and 12 is the product of 11 and 12, or 132.\nA least common multiple can be found for more than two numbers at a time; the same rules still apply.

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How do I type roman numerals?

Roman numerals use a combination of letters to denote specific values. Each of the seven letters corresponds to a numerical value: I for one, V for five, X for ten, L for fifty, C for 100 and M for 1,000. Zero has no Roman numeral representation.\nCombine and arrange the letters in particular order to symbolize numbers. Roman numerals written in groups are added together, therefore, II is equivalent to two because I + I = 1 + 1 = 2. A letter can only be repeated three times; thus, III represents three but, IIII cannot represent four. Four is characterized by IV because Romans made the rule t..

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