Jeffes02

(If you wanted us to do four questions, please put them all in one question rather than serving all of them in quick succession.)

Input:( 2 xy 2 ) 3 ÷ 3 x 2 y 3 × 9 x 3 y 2

Intepretation: \(\frac{\left(2xy^2\right)^3}{3x^2y^3}\cdot 9x^3y^2\)

Simplification:

\(=\frac{\left(2xy^2\right)^3}{y}\cdot 3x\)

Extract 2 out of the parenthese:

\(=\frac{8\left(xy^2\right)^3}{y}\cdot 3x\)

Continue Simplification:

\(=\frac{8(x^3y^6)}{y}\cdot 3x\)

\(=8x^3y^5\cdot 3x\)

\(=24x^4y^5\)

Q.E.D.

Interesting enough... No wonder it burnt your brain, here we go:

Illustration (Made om quick session in 3 mins)

We know the height of the building is 33 meters, therefore we obtain the following equation:

Set the distance from the foundation of the building to the church's foundation \(A\).\

Apply trigonometric identity.

The angle of  depression is 25 degrees, therefore:

\(A=tan(25°)*33\)

\(A≈ 0.4663*25\)

\(A≈ 11.6575\)

That means the distance from the church's top to the same height of the building is also \(A=11.6575\)

Applying trigonometric identites for the second time

Church height=\(11.6575*sec(18°)\)

\(≈11.6575*1.0515\)

\(=12.258\)=Church's Height

Q.E.D.

(Don't even ask me about how tensed I am to win over Heureka over the speed of solving this question)

For you to calculate the answer via this calculator, type in the following code:

(-6)/(-2)

The fraction symbol is /.

The answer would be:

\(\frac{\left(-6\right)}{\left(-2\right)}=3\)

Q.E.D.

If you want to know how much is 3 months of salary for you:

Ans: \(3*2850\)

\(=8550\) (Some Units)

Assuming your "5 years 21 days basic and 3 years 30 days basic" means 8 years + one month + 21 days:

Total basic of the time duration above:

\(1425\cdot \left(8\cdot 12+1+\frac{21}{30}\right)\)

\(=139222.5\) (Some Units)

You missed something in your question:
1.The unit of your salary.

2.Define "5 year 21 days basic and 3 years 30 days basic"

3.Less grammatical errors for correct intepretation.

4.Spelling.

5.Capitalization.

6.Punctuation.

Your input: 3/4-2/5*7/12

Intepretation: \(\frac{3}{4}-\frac{2}{5}\cdot \frac{7}{12}\)

Expand the fractions:

\(=\frac{3}{4}-\frac{14}{60}\)

Reduce the fractions' denominator:

\(=\frac{45}{60}-\frac{14}{60}\)

Subtract:

\(=\frac{31}{60}\)

\(=0.516666...\)

Q.E.D.

Share it on social media (i.e. By the "Share" and "Tweet" buttons under your questions.)

(Weird my previous answer seems to have disappeared.)

Your input: 512^(1/9)*10-2*8v

Intepretation: \(512^{\frac{1}{9}}\cdot 10-2\cdot 8v\)

We know that \(2^9=512\), therefore \(512^{\frac{1}{9}}=2\)

Ans: \(2*10-2*8v\)

\(=20-16v\)

\(=4(5-4v)\)

Q.E.D.

A.(-2.5)^3/(-2.5)^-2

Intepretation: \(\frac{\left(-2.5\right)^3}{\left(-2.5\right)^{-2}}\)

The negative second power will be positive, for the third power it is negative.

Rewrite as:\(-\frac{\left(2.5\right)^3}{\left(2.5\right)^{-2}}\)

\(=-\left(2.5\right)^5\)

\(=-97.65625\)

B.(3^3)(3^-6)

Intepretation: \(\frac{3^3}{3^{-6}}\)

\(=3^9\)

\(=19,683\)

C.s^2 t^-1/(s^4 t^4)^1/2

Intepretation: \(\frac{s^2t^{-1}}{\left(s^4t^4\right)^{\frac{1}{2}}}\)

\(=\frac{s^2t^{-1}}{s^2t^2}\)

The \(s^2\) cancels each other out:

\(=\frac{t^{-1}}{t^2}\)

\(=t^{-3}\)

Q.E.D.

I didn't manage to write the answer of this question by any mathematical ways, nor by using my hand, but the function gets closer and closer to \(≈ 1.41421356237\) as more layers are added, which equals to \(\sqrt2\).

This is also the reason that \(\sqrt2\) is an irrational number instead of a rational one, since it needs infinite fractions to express it.

Program: http://www.wolframalpha.com/input/?i=1%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1%2F(2%2B1)))))))))

That is correct, but I would have to assume so since he didn't mention about it by anyway in his question. :P