Jeffes02

Good work of yours! It is really easily for people to confuse others with inappropiate use of brackets.

Input: 121^-1/2 as a surd

Intepretation: Express the number \(121^{-\frac{1}{2}}\)

We apply the rule of exponentials:

\(a^\frac{n}{m}\)=\(\sqrt[m]{a^n}\)

And:

\(a^{-b}=\frac{1}{a^b}\)

Merge the two rules and we get:
\(a^{-\frac{n}{m}}=\frac{1}{\sqrt[m]{a^n}}\)

Now plug \(a=121,m=2,n=1\) into the equation above:

\(121^{-\frac{1}{2}}=\frac{1}{\sqrt[2]{121^1}}\)

Simplify:

\(=\frac{1}{\sqrt{121}}\)

\(=\frac{1}{11}\)

Done :D

Intepretation: Approx for \(x\) in the function \(C(x)=\frac{8000}{x-50}\) when \(C(x)=1250\)

 Solution:

Solve for \(x\) when \(\frac{8000}{x-50}=1250\)

Multiple both sides by a factor of \(x-50\):

\(1250(x-50)=8000\)

Expand:

\(1250x-62500=8000\)

Move the numerical term to the right:

\(1250x=70500\)

Divide both sides by the greatest common divisor of \(1250\) and \(70500\) (Which is equal to \(250\))

\(5x=282\)

Divide both sides by \(5\):

\(x =\frac{282}{5}\)

\(=56.4 \approx 56\)

Done :D

(You accidently posted the formula for \(C(x)\) in your question two times, be careful.)

Input: Solve for X. a/b(2x - 12) = c/d

Intepretation: Solve for \(x\) in \(\frac{a}{b}(2x-12)=\frac{c}{d}\)

Solution:

Multiple both sides by \(bd\):

\(ad(2x-12)=bc\)

Expand:

\(2adx-12ad=bc\)

Move the numerical term to the right:

\(2adx=12ad+bc\)

Divide both sides by \(2\)
\(adx=6ad+\frac{bc}{2}\)

Finally, divide both sides by a factor of \(ad\):

\(x=6+\frac{bc}{2ad}\)

Done :)

Input: 3ax/5 - 4c = ax/5

Intepretation: \(\frac{3ax}{5}-4c=\frac{ax}{5}\)

Multiply by \(5\) on both sides:

\(3ax-20c=ax\)

Move the \(x\) term to the left, numeric ones to the right:

\(3ax-ax=20c\)

Simplify:

\(2ax=20c\)

Divide by \(2\) on both sides:

\(ax=10c\)

Finally, divide \(a\) on both sides:

\(x=\frac{10c}{a}\)

Done.

Input : a - c/x - a = m

Intepretation: \(a-\frac{c}{x}-a=m\)

Cancel the \(a\) out on the left side:

\(-\frac{c}{x}=m\)

Multiply both sides by \(x\):

\(-c=mx\)

Divide both sides by \(m\):

\(x=-\frac{c}{m}\)

Done :)

Just like all other calculators written in C++, such as this one, the maximum input/output number that such a script can handle is around \(10^{308}\), the limit of C++ integer values, if exceeded, digit overflowing occurs and the calculator will represent the number as infinity (i.e. the flipped \(8\) symbol).

Make sure your numerator & denominator is both less than \(308\) digits long in base-\(10\), if one of them is over this limit in your fraction, that one will appear as infinity, while the other number will be fine. If both of them are over the limit, it will simply show infinity/infinity. Be careful not to exceed the calculators limits!

Your help:

Intepretation: \((a-1)\cdot x^2+(a-3)\cdot x-2>0\)

Solution:

\(1.a=0, x<-1 \)

\(2.a>0, x>\frac{2}{a-1}\)

\(3.a>1, x<-1\)

\(4.-1

\(5.a<-1,\space-1

(Source: http://www.wolframalpha.com/input/?i=(a-1)*x%5E2%2B(a-3)*x-2%3E0)

Input: b(5px-3c) = a(qx-4)

Intepretation: Solve for \(x\) in \(\)\(b(5px+3c) = a(qx-4)\)

Expand:

\(5bpx-3bc=aqx-4a\)

Move the \(x\) terms to the right, integer ones to the left:

\(5bpx-aqx=3bc-4a\)

Pull the x out from the left term:

\((5bp-aq)x=3bc-4a\)

Divide both sides by \(5bp-aq\):

\(x=\frac{3bc-4a}{5bp-aq}\)

Done :D

This is called a \("Repeating\space Decimal"\), just like how the results are in fractional loops, the cause of it is because the remainder always cease to disappear in divisions, like how grass never go away no matter how many times you cut it.

In your case, \(\frac{191}{7}=27.285714285714...\)

The number \(\frac{191}{7}\) can also be written as \(27+\frac{2}{7}\)

Since we know that \(\frac{1}{7}=0.142857142857...\)

The number  \(\frac{2}{7}=2\cdot\frac{1}{7}=0.285714285714...\)

Adding the previously deattached \(27\)

\(\frac{191}{7}\) can be written in decimal form as: \(27.285714285714...\)

(Source: https://en.wikipedia.org/wiki/Repeating_decimal)

Hope this helps :)