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How come a fish is an animal and a person is an animal but a fish is not a person?

MWizzard,

I have been playing with it in Desmos and with Wolfram Alpha.

In Desmos for some strange reason, the left hand side th angle is taken to be in degrees and the answer is is given in radians, I do not understand why it has done this.

Generally speaking,    

\(\displaystyle \lim_{x \rightarrow \infty} \;xsin(\frac{a}{x})=a\)

If you know calculus I think this can be shown with L'Hopital's rule.  

I have no intuitive understanding of why this is so but if you know L'Hopital's rule I can show your that it is true.

\(\displaystyle \lim_{x \rightarrow \infty} \;xsin(\frac{a}{x})=a\\ =\displaystyle \lim_{x \rightarrow \infty} \;\frac{sin(\frac{a}{x})}{\frac{1}{x}}=\frac{0}{0}\\ \mbox{This is indeterminant and we can use L'Hopital's rule to find the answer}\\ =\displaystyle \lim_{x \rightarrow \infty} \;\frac{\frac{d}{dx}sin(\frac{a}{x})}{\frac{d}{dx}\frac{1}{x}}\\ =\displaystyle \lim_{x \rightarrow \infty} \;\frac{\frac{d}{dx}sin(ax^{-1})}{\frac{d}{dx}x^{-1}}\\ =\displaystyle \lim_{x \rightarrow \infty} \;\frac{(-ax^{-2}cos(ax^{-1}))}{-1x^{-2}}\\ =\displaystyle \lim_{x \rightarrow \infty} \;\;+acos(ax^{-1})\\ =+acos(0)\\ =\;a \)

12 is how many you should give her

Oops, wrong interpretation for question 2.

I meant:

12P7 = 3991680 ways

\(1 \, million \, \times \, 500 \, trillion = (1 \times 10^6) \times (500 \times 10^{12}) \\ = (1 \times 10^6) \times (5 \times 10^{14}) = (5 \times 10^{20})\)

(scientific notation) 

\(V = πr^2h \\ 100 = πr^2h \\ 100 = π \, \times \, (r)^2 \, \times h \quad |\; \times 4^2 \\ 1\,600 = π \, \times \, (4r)^2 \, \times \, h \quad | \; \times 12 \\ 19\,200 = π \,\times\,(4r)^2\,\times\,12h\)

\(\therefore \tt Container \, B \, can \, hold \, 19 \,200 \, ounces \, of \, water.\)    

from

MWizard2k04 AKA MathW0122

Jan 22, 2004 is not my birthday!

خوب اگر شما به من بگویید چه شده است شما سوال، من ممکن است قادر به پاسخ      

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

You took the photo... Backwards! I do not want to waste my time.

\(h = \frac{10000}{(\pi)(16^2)}\)

which is about 12.434

Using a calculator, you get

\({\pi}^{2}=9.8696044010893586.......\)

Trig means trigonometry which involves a few trigonometric functions when you calculate.(sin(x), cos(x), tan(x), cot(x), csc(x), sec(x)).

10(x+2y)

Using the Sine Rule,

\(\frac{16}{sin(54)}=\frac{12}{sin C}\)

\(12sin(54)=16sinC\)

\(sinC=\frac{3sin54}{4}\)

\(C = sin{}^{-1}(\frac{3sin54}{4})\)which is about 37.35579 degrees

54 + 37.35579...... + A = 180  (angle sum of triangle)

                                 A = 88.6442......

Applying the Sine Rule again,

\(\frac{a}{sin A}=\frac{16}{sin54}\)

\(a = \frac{16sin88.6442......}{sin54}=19.77155\)

500 Quintillion

It is impossible because it will make everything doesn't taste like everything XD

0.1478(x-45)=(623.15/x)^3.029

Much easier, angle BOC is is double the angle BAC.

Use the equation:

V= (πr^2) (h)

Plug in the values you have...

2= (πr^2) (10)

Divide each side by ten...

.2 = πr^2

Square root both sIdes

πr= 0.4472135954999579

Αnd the estimated answer is that above.

If arthmetic then the equation is:

Term n = First Term + Common Difference( Term - 1)

400-300=100