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That is a LOT of digits.

 I do not think that I can count that high!!

Geno's answer is good but I will add that 

arc tan and inverse tan are the same thing.

On the web2calc you use atan 

but on many calcs the button looks like this     \(tan^{-1}\)

Hallo guest

Hi Rom and guest,

I agree this is an interesting question but I would do it differently, Maybe my way is wrong.

Rom I don't think that you found the angle did you?

The staircase goes around the silo much like the label goes around a can of peas

If you take the label off the peas, it is a rectangle.  

The length will be the circumference of the can 2*pi*r

and the height will be the hieght of the can.

so

getting back to the silo, the stairs go from the bottom corner of the 'rectangle' to the diagonally opposite corner.

like this.

I wanted to draw the diagram but Geogebra has stopped working for me    

Anyway it is a rectangle.  and the stairs are the diagonal.

The rectangle is 37 foot hight and    2*pi*7 = 14pi       foot long

The incline angle is the angle between the base and the diagonal.

\(tan\theta = \frac{37}{14\pi}\\ \theta = atan\left( \frac{37}{14\pi} \right)\\ \theta = 40^04'\)

So the angle of incline is 40.072 degrees (3dp)

or 40 degrees and 4 minutes to the nearest minute

how do i factor 8x^3 -27x^2 -6x -8

\(8x^3-27x^2-6x-8\\ \)

This does not factorise nicely.  (Only oine of the roots is even real)

Perhaps you copied it wrongly?

Interesting problem.

We treat the staircase as a space curve.

\(r(t)=\{7 \cos(2 \pi t), 7 \sin(2 \pi t), 37 t\},~~~~0\leq t \leq 1\)

To find the length of the curve we integrate the norm of the time derivative of the curve.

\(L = \displaystyle{\int_0^1}\|\dot{r}\|~dt\)

\(\dot{r}=\{-14\pi \sin(2 \pi t), 14\pi \cos(2\pi t), 37\}\\ \|\dot{r}\| = \sqrt{(14\pi)^2+37^2} \\ L=\displaystyle{\int_0^1}\sqrt{(14\pi)^2+37^2}~dt = \sqrt{(14\pi)^2+37^2}\approx 57.48 ft\)

Rom is correct of course but it also discriminates between other tytpes of roots as well.

The symbol for the discriminant is a triangle.

so

\(if \;\;ax^2+bx+c=0\qquad then\qquad x=\frac{-b\pm\sqrt{b^2-4ac}}{2}\\ The \;discriminant \;is\;b^2-4ac\\ \triangle=b^2-4ac \)

IF the discriminant = zero there will be one real root.   (sometimes called a double root)

IF the discriminant > 0 then there will be 2 real roots.

If the discriminant < 0 there there will be no real roots.  If you have not done complex numbers yet then you would probably say that there were NO roots.  This is because you cannot take the square root of a negative number.

ROM already said all this.

BUT also

If the descriminant is a perfect square then the roots will be rational 

If the descriminant is NOT a perfect square then the roots will be irrational 

You have  ft/hr  if you divide it by ft/mile you will have your answer.....

ft/ hr = 607200            ft/mile = 5280

(ft/hr) / (ft/mile)  =  (ft/hr) x (mile/ft)  =  mile/hr    right?  (because 'ft' cancels out)

sooooo substitute some values in there:

(ft/hr) / (ft/mile)  =   607200 / 5280 = 115 mile/hr

If 6 and 20 are in the bottom of fractions, the lowest common denominator would be 60

I would add that it is the side of the angle that is NOT the hypoteneuse to that first answer.....

\(\mbox{If you have a quadratic polynomial }a x^2 + b x + c \mbox{ the roots of this are given by}\\ r_{1,2}=\dfrac{-b\pm\sqrt{b^2-4 a c}}{2a} \\ \mbox{The argument of the square root in this expression }(b^2 -4 a c) \mbox{ is called the discriminant.}\)

\(\mbox{It's called this because it's value discriminates between real and complex roots.}\\ \mbox{if it is non-negative then the roots of the quadratic will be real. If it is negative} \\ \mbox{they will be a complex conjugate pair.}\)

Go to this website and WATCH the video:https://www.khanacademy.org/test-prep/fr-twelveth-grade-math/Nombres-complexes/La-formule-des-racines-d'un-trin%C3%B4me/v/discriminant-of-quadratic-equations.

TOO BAD LAZY BONES!!!!!!!

If 17/90 is equal to 60/x what is the value if x

x=90/17 X 60=317.647, so: 17/90=60/317.647

It is the side that forms or touches the angle. The side opposite the angle is called just that "Opposite".

\((-5)\times \left(-\dfrac 2 3\right) = \dfrac{(-5)(-2)}{3}=\dfrac{10}{3} = 3\dfrac 1 3\)

\(7\% = \dfrac {7}{100} \mbox{ so} \\ 7\% \mbox{ of }40 = \dfrac{7}{100}\times 40 = 2.8\)

\(2x-1.5 = 31.83 \\ 2x = 33.33 \\ x = 16.665\)

\(v = a t \\ v = \left(9.8 \dfrac{m}{s^2}\right)(10s) = 98 m/s\)

what is the LCD OF 6 AND 20=1

38 followed by 22 zeros

supose that you had two rings that are the same size but one was 10K gold and the other was 18K gold which one would feel heavier?

I suppose it would depend on the density of the other elements in the two rings.

Gold is very dense so I would expect the 18K one to be heavier but if the other one contains lead  (which is heavier than gold)  then it would be heavier.

A go-kart's top speed is 607200 feet per hour. What is the speed in miles per hour?

=115 mph  (miles per hour)

18

FV=$250(1+6%)^4=$315.62