# 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.

###### Asked in Math and Arithmetic, Algebra

### 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.

###### Asked in Math and Arithmetic, Chemistry, Statistics, Percentages, Fractions, and Decimal Values

### 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

###### Asked in Math and Arithmetic, Trigonometry

### 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.

###### Asked in Math and Arithmetic

### 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

###### Asked in Math and Arithmetic, Geometry

### 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.

###### Asked in Math and Arithmetic, Units of Measure, Cooking Measurements

### 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

###### Asked in Math and Arithmetic, Mathematical Finance, Percentages, Fractions, and Decimal Values

### 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

###### Asked in Math and Arithmetic, Numbers

### What numbers add up to make 666?

666 is the sum of the first 36 numbers: 1+2+3+4... + 36 =
666.
In the book of Revelation, it was most likely intended as a
gematria reference; the sum of the numerals represented by hebrew
letters in a name. Various candidates have been suggested
throughout history.
For example, the hebrew letters of "Caesar Nero" would sum to
666. The roman numerals in "Ellen Gould White" add to 666
(interpreting W as VV and U as V). If you use the code A=101,
B=102, etc, then "Hitler" will add up to 666.
Actually, if you can make up the rules as you go along, it's not
hard to do with any name at all. Just pick a favorite bogeyman, say
"Bill Gates", and try various codes. Aha! the ASCII values in "BILL
GATES" (all caps) sum to 663, and then you can add 3 since he's
really Bill Gates III.
It's been done with Martin Luther, Muhammad, Ronald Reagan, etc.
If necessary, spell the name in Latin, or make up an
official-sounding title and add up its roman numerals, and then
find lots of subjective and cherry-picked evidence supporting why
your target is the Beast of Revelation. For example:
The Roman numerals in the blasphemous title of the pope who
claims to substitute for God, forgiving sins, etc., VICARIVS
FILII DEI, V=5, I=1, C=100, L=50, D=500; add up to 666:
5+1+100+1+5+1+50+1+1+500 +1 = 666.
The first beast of Revelations 13 is an empire which had seven
heads that persecuted God's people. First was Egypt where they were
slaves to the pharaohs, second Assyria captured the 10 tribes of
northern Israel, third Babylon captured the two remaining tribes of
Judah, fourth Medo-Persia, fifth Greece (five are fallen, in John's
time, and one is) sixth Rome destroyed the temple, seventh the
papacy with the pope ruling from the fall of Rome until the deadly
wound of 1798 when Napoleon captured the pope and confiscated all
the papal lands. Italy's Benito Mussolini healed the wound,
restoring the Vatican City by the Lateran Treaty in 1929. The
seventh, restored, became the eighth.
In 1776 a country rose to power on another continent, creating a
religious system derived from the Protestant daughters of the great
whore, keeping the traditions of man above the commandments of God,
trading Passover for Easter, Sabbath worship for "sun"day worship,
etc. These were sanctified by the pope, not by the apostles; they
are not mentioned in the Bible. Receive the mark of the beast by
obeying the pope's laws while disobeying God's laws.

###### Asked in Math and Arithmetic, Percentages, Fractions, and Decimal Values

### What is 25 percent of 80.00?

The easiest and simplest way to calculate a percentage of any
number is to remember that 10% of any number, is the number itself
with the decimal point one place to the left.
I.e 10% of 1478 is 147.8 (The decimal one place to the
left)
10% of 100,000,000 is 10,000,000.
That means that 10% of 80.00 is 8.000 (keeping the insignificant
digits). So 20% would be $16.00. But we need 5 percent more, so
we just split our 10% in half. Half of 8 is 4. So 25% of 80.00 is
16 + 4 which is 20.