# Math and Arithmetic

## Math is the study of abstractions. Math allows us to isolate one or a few features such as the number, shape or direction of some kind of object. Then we can study what can be learned about the behavior of those features while ignoring everything else about the object.

### What is a math dictionary? A math dictionary (or a mathematics dictionary) is usually a dictionary of the definitions of common mathematical terms, formulae and examples of common diagrams and pictures for the uninitiated or those learning math.

### Find the sum of the opposite of -18 and its additive inverse? the opposite of negative 18 is positive 18. It's just like absolute value. |-18| is 18 because 18 is 18 steps away from 0 so is -18 like how it is 18 away from 0 and not -18 away from 0. -18 away from 0 is not a thing. So therefore, the opposite of negative 18 is positive 18 because the opposite of negative is postitve.

### What is the percent error formula? Percent Error is the difference between the true value and the estimate divided by the true value and the result is multiplied by 100 to make it a percentage. The percent error obviously can be positive or negative; however, some prefer taking the absolute value of the difference. The formula is the absolute value of the experimental value (minus) the theoretical value divided by theoretical value times 100. % error = (|Your Result - Accepted Value| / Accepted Value) x 100

### How do you solve cosx - xsinx equals 0? To solve this, you need to find values of x where cos(x) = xsin(x). First of all, 0 is not a solution because cos(0) = 1, and sin(0) = 0. Since 0 is not a solution, divide both sides of the equation by sin(x) to get cot(x) = x (remember that cos divided by sin is the same as cot). The new question to answer is, when is cot(x) = x? Using Wolfram Alpha, the results are x ±9.52933440536196... x ±6.43729817917195... x ±3.42561845948173... x ±0.860333589019380... there will be an infinite number of solutions. If you'd like to do the calculation yourself (not asking WolframAlpha) then there's a trick which almost always works, even for equations which cant be done analytically. Starting with the basic equation, cos(x) = x*sin(x), transpose it to a form starting with "x =". In this case you could get: x = 1/tan(x), x = cot(x) or from tan(x) = 1/x you get x = Arctan(1/x). Because I like to do my calcs on an old calculator which only has Arctan and not Arccotan (Inverse cotangent(x)) I use the last above - x = Arctan(1/x) Starting with a value like 0.5, hit the 1/x key then shift tan keys. Just keep repeating those two operations and the display will converge on 0.860333. Too easy. This example of the method is not a good one as it takes about 25 iterations to converge to within 0.0000001 of the right answer. It is unusually slow. And finally, this method has only 50% chance of working first try. We were lucky picking x = Arctan(1/x). x = 1/tan(x) diverges ind the iterations do not converge on the answer. So if you try this method on another problem and it diverges, just transpose the equation again and have another go. Starting with x^2 + x - 3 = 0, and iterating x = 3-x^2, you find it diverges, so try x = sqr(3-x) which (with care and about 25 iterations) converges on 1.302775638.

### How do you write 60 million in number form? Something that is a million starts on the left of 6 digits before the decimal point. For instance, 1 million is 1,000,000.0. Then, 60 million in number form is: 60,000,000

### Water volume per foot of 2.5 inch pipe? Each one-foot section of 2.5-inch diameter pipe has a volume of 58.9 cubic inches or 0.255 gallons of liquid.

### What number comes next in the sequence 1 2 6 42 1806? Option 1 The sequence is found by multiplying each term by the number one greater than itself. First, 1 * 2 = 2. Then, 2 * 3 = 6. Then, 6 * 7 = 42, and so on. n*(n+1) = x (where n equals the previous x) 1*(1+1) = 2 2*(2+1) = 6 6*(6+1) = 42 42*(42+1) = 1806 1806*(1806 +1) = 3,263,442. Another way to consider it is that each term is being squared then added plus the original amount, so the second term will be equal to the first term squared, then add the first term. We find the equation (n^2) + n , where n is the previous term. So the next term is again 3,263,442. Option 2 For this option, we take each number and multiply it by the subsequent prime number, beginning in the same values and then diverging from the first choice. First we take 1 and multiply it by the smallest prime greater than itself - 2, and get 2. The next prime after 2 is 3 which gives us 2 * 3 = 6. Six times the next prime, 7, gives us 42. The number 42 times its nearest greater prime of 43 gives us 1806. Finally, 1806 times the next prime number (which is 1811) gives us 3,270,666. Option 3 The third approach to this series is a long process but seems logical too. Lets start. The original series is: 1, 2, 6, 42, 1806, ? The second digit can be derived by multiplying the first digit by 2. Then the third digit can be derived by multiplying the second digit by 3. Then the fourth digit is third digit times 7. The fifth is fourth digit multiplied by 43. So we had a second string of series of multipliers which consists: 2,3,7,43,? To get the fifth multiplier, a pattern can be seen from this series. The second digit is first digit is multiplied by 1 plus 1. The third digit is second digit multiplied by 2 plus 1. The fourth digit is third digit multiplied by 6 plus 1. This in turn has created the sequence 1, 2, 6 which in the sequential nature of these sequences seems to be created by multiplying by subsequent integers. So the next term would be 6 * 4 = 24. Going back to the multipliers we find that the fifth digit is 1033 (24 * 43). 2, 3, 7, 43, 1033 Again, the second digit is the first digit multiplied by 1 plus 1. The third digit is the second digit multiplied by 2 plus 1. The fourth digit is the third digit multiplied by 6 plus 1. The fifth digit is now the fourth digit multiplied by 24 plus 1. Now lets go back to the original series: 1, 2, 6, 42, 1806, ? Now we see the sixth digit is the fifth digit multiplied by 1033 which gives us 1,865,598. * * * * * Yet another possibility is to fit a polynomial to the given sequence. There are infinitely many polynomials of order 5 or above but consider T(n) = (1667n^4 - 16554n^3 + 57685n^2 - 82158n + 39384)/24. For n = 1, 2, 3, 4 and 5 it gives the required 5 numbers and T(6) = 8661. In reality, short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one. 3,263,442 10,650,056,950,806 etc The formula is X2 + X Simplest way is: n=n*(n+1). === === === === === === other way: 1 2 12*1/2=6 .... 1 2 6 126*2/6=42 ..... 1 2 6 42 12642*6/42=1806 .... 1 2 6 42 1806 12642186*42/1806=2940042 .... 1 2 6 42 1806 2940042 There are at least two possible answers: 1. You could fit the polynomial function: tn = (1667n4 - 16554n3 + 57685n2 - 82158n + 39384)/24 for n = 1, 2, 3, ... Following the logic, the 6th term is 8661. 2. One alternative is t1 = 1 and tn+1 = tn*(tn + 1) for n = 1, 2, 3, ... That definition gives the next term as 3,263,442. There are many other solutions. 1806*1807=3263442 3,263,442 comes after 1806. The series is formed by a number multiplying itself increased by 1. Here is the equation: X(X+1) Y 1(1+1) 2 2(2+1) 6 6(6+1) 42 42(42+1) 1806 1806(1806+1) 3,263,442 In simpler numbers, 1 X 2 2 2 X 3 6 6 X 7 42 42 X 43 1806 1806 X 1807 3,263,442 3263442. The progression is n(n+1). 1 2 6 42 1'806 3'263'442 10'650'056'960'806 1st is 1 2nd is 1st*(1st+1) -> 1*2 3rd is 2nd*(2nd+1) -> 2*3 4th is 3rd*(3rd+1) -> 6*7 5th is 4th*(4th+1) -> 42*43 ... and so on 3263442 3263442

### How many minutes are in 50 hours? Obviously there are 60 minutes in an hour, so 60 x 50 = 3000 minutes in 50 hours! Hope this helps! :)

### What is the width of a house in meters? This cannot be answered without more information. No it can't, and I'm amazed how many enquirers seem not to realise that. However, I suspect this enquirer really wanted to know how to convert the dimension from feet to metres. (That is the right spelling - it's a French invention and word.) If so, 1 metre = 3.280 feet or 1 foot = 0.305 metre.

### What is the word form for 0.000001? The term is written as "One millionth." As a prefix in SI measurements it is "micro". For example, 0.000001 grams is the same as 1 microgram. 0.000001 metres is called a micrometer but also has the special name "micron". Sometimes expressed as "zero point zero zero zero zero zero one"

### How many ounces make a gallon? In a US gallon... 128 ounces Both US gallons and "Imperial" (UK) gallons contain 8 pints - but the US pint is 16 fluid ounces while the Imperial pint is 20 fluid ounces. So if you're working in Imperial gallons the answer is 160 fluid ounces. It's quite a big difference so worth double-checking which units you're supposed to be using! To know the weight of a certain volume you need to know the specific gravity of the fluid. In other words: the weight of one US gallon of water is not the same as the weight of one US gallon of gasoline. 1 gallon [US, liquid] = 128 ounce [US, liquid] 1 Imperial gallon = 160 Imperial fluid ounces 128 fluid ounces = 1 gal I'm happy to help =D

### How do you find the radius if you have the circumference? Circumference divided by pi to find the diameter then divide that by 2 to give you answer!! Formula: R=c/pi/2 eg. circumference =60 so, 60 divided by pi = 19.098, then divide 19.098 by 2 to give you 9.549!!

### How much is 10 raise to power -15? 10 to the power of -15 is 1/10^15. (1/1,000,000,000,000,000 [15 zeroes]) It can also be written as 0.000000000000001 (There are 15 zeroes). OR -1,000,000,000,000,000 (15 zeroes).

### What is 20 percent of twelve thousand one hundred dollars? I never saw much point in giving the answer to a mathematical question if the person didn't explain how to get to that answer. With calculators today many mathematical equations are easy to figure, but I am a strong believer in the person understanding the formula and how it works, not just typing numbers into a calculator and magically getting an answer. The question is what is 20% of \$12,100. First we must change the percentage to a decimal, this is easily done by moving the decimal place to spaces to the left (the % represents the decimal). Therefore it gives us .20 Then simply multiply \$12,100 x .20 12,100 x .20 = 2,420 Since we know we are dealing in dollars the answer is \$2,420

### What is range? What you do is that you subtract the smallest number & the largest number. For example: The numbers 24, 47, 78, & 36. Okay so the largest is 78 and the smallest is 24. So 78-24=54. 54 will be your range.

### How much does 1 liter of beer weighs in Kg? depends on the type of beer, place of brewery and everything like that. There is no conversion from weight to capacity, without knowing density. Presuming that beer has a very similar (but slightly higher) density to water, then 1 litre should weigh a bit more than 1 kg.

### What numbers add up to make 666?  