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Almost asinus.   You are right with cos and tan, but sin(150°) = sin(30°)   (sin is positive in the second quadrant).

Yes.   sinh(x) = (e^x - e^-x)/2  so  sinh(-x) = - sinh(x)

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This is undefined in mathematics.  

Thanks for the trip down memory lane Nauseated  :)

But

I think i have seen new people with negative points.  ://

Hello guest!

Express the following in terms of the sine, cosine or tangent of an acute angle.

sin150°

cos220°

tan325 °

sin150°   = sin (- 30°)

cos220°  = - cos 40°

tan325 °  = tan (- 35°)

Greeting asinus :- )

 !

You don't supply the pie chart, but it might look something like this:

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Divide by 100:   8% → 0.08

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On third thoughts, Melody is correct!   Easiest way to see this is to consider only four people, two men, two women around a table in four chairs.  There are clearly only two distinct arrangements if rotations are ignored.  Melody's method gives 1!*2! = 2.  

yes he mean that

Hello Guest!

10 plus 2.5 divided by 3.6?

(10 + 5/2) / (18/5)

= (25/2) * (5/18)

= 125/36

= 3  17/36

= 3.47222...

= 5³ / (2² * 3²)

While translating the ancient Babylonian, I was in a “causality loop.” This isn’t as bad as an infinite loop, but you could be in it for eons, and never know until you escaped.

Sisyphus is definitely fixated on his bolder -- well more than LancelotLink is on his banana daiquiris.  I have wondered if his obsession would change if he knew the contents. The roman Zero is valuable –Archimedes probably though it one of the “holy grails” in his world. 

You description of Sisyphus is very close to some of the engineering techs I work with: useless rock-heads, with zero on their minds –but very focused on it. 

A Down vote was an available option on the forum’s previous operating system. Posts with negative points are a carryover from there.  

Some of my great troll posts have negative points. We trolls consider them points for excellent work. The best ones Melody made into Scooby snacks

‘tis a pity it’s not an option anymore.  Those were the days . . . .  . ..

Nice work, Nauseated......I looked at this one...but...I found myself, here, only after a short few minutes :

I also asked for some help from that damned Sisyphus.....

But.....these days....it's useless......he has "zero" on his mind and is a complete rockhead......

Nice work, Melody.....I have a little different approc\ach......but...it should still work out the same

The total area can be found by the trig "formula"

500  = 8*(1/2)(radius)^2 *sin (45)

500 = 4 * (radius)^2 * [1 / √2]

500 = (4/√2) * (radius)^2

125√2  = (radius)^2   take the square root of both sides

√ [125√2]  = r ≈  13.2957  ft   ≈  13.3 ft [rounded]

And using the Law of Sines, (1/2) the side length, s, is given by

(1/2)s / sin (22.5)  = √ [125√2] / sin(90)

s = 2*sin(22.5) *√ [125√2]   ≈    10.176 ft  ≈ 10.18  ft [rounded]

And using the Law of Sines, again, we can find the apothem, a, as :

a / sin(67.5)  =  √ [125√2] / sin(90)

a = sin(67.5)* √ [125√2]  ≈ 12.28 ft

\(cos(30°)\)

\(\sqrt3/2\)

Solution to #11

To calculate the normalized strain for isotropic, homogenized compounds, exhibiting linear elastic properties, in cubical form, where the stresses are orthogonal in three dimensions, use the generalized Hooke’s law formula

\(\varepsilon_x=\dfrac{\sigma_x-\nu(\sigma_y-\sigma_z)}{E}\\\\ \dfrac{-15 -0.49(-15-15)}{1000} = -0.0003 in/in\)

\(\varepsilon_x=\varepsilon_y=\varepsilon_z=-0.0003 in/in\\ \Delta_x =\Delta_y=\Delta_z =(-0.0003in/in) *4in =-0.0012in \)

\({Final~ side~ length~ } 4-0.0012= 3.9988\\ {Final~ volume =} 3.9988^3\\ \Delta Volume ~4^3-3.9988^3=0.057583 \)

Source:

Formulae Esoterica

Processus algorythmic

Twelfth edition -Volume II

Morgan le Fay

Translated from ancient Babylonian

Hi  Gibsonj338

If the area of a regular octagon is equal to 500 feet, what is the length of all the sides,  the radius, and the apothem.  Please show how you got your answers and round your answers to the nearest hundreths

I assume that you mean the area is 500 feet^2    :)

Let the length of the apothem be 'h'  and the length of half a side be 'b'

\(500=16*0.5*bh\\ 500=8bh\\~\\ \mbox{Now I need to find the angle (theta) between the apothem and the side }\\ \theta=180(8-2)\div 8\div2\\ \theta=\frac{6*180}{16} \\ \theta=67.5 degrees \\\)

\(tan 67.5 = \frac{h}{b}\\ b = \frac{h}{tan 67.5}\\\)

Now solve the 2 equations simultaneously to get your solution.

\(500=\frac{8h^2}{tan67.5}\\ \frac{500\;tan\;67.5}{8}=h^2\\ h=\sqrt{\frac{500\;tan\;67.5}{8}}\\\)

sqrt(500*tan(67.5*pi/180)/8 = 12.2836618175653346

5.0880593204403051371 = 5.088059320440305(12.2836618175653346/tan((67.5*pi/180))*2 = 10.17611864088061027431371e0

the apothem is  12.28366 feet and the   side is 10.176118 feet

the apothem is  12.28 feet and the   side is 10.18 feet       to the nearest hundreth foot

check

8*(0.5*12.28*10.18) should equal 500

8*(0.5*12.28*10.18) = 500.0416    good

so that seems ok I think.

SEE MY ANSWER ON YOUR FIRST POST!!.

500=L((0.0239/12)/(1-(1+(0.239/12)^-60

First, this is the formula for finding the amount of a loan with a monthly payments of $500 @ 2.39% compounded monthly over a period of 5 years, or 60 months.

500=L*(0.00199167) / (1 - (1.00199167)^-60)

500=L*(0.00199167) / (1 - 0.8874695)

500=L*(0.00199167) / (0.1125305)

500=L* 0.01769893) Divide both sides by .01769893

L=$28,250.30. The accurate amount is $28,250.34 when calculations carried to 15 decimal places.

Thank you sooooooooooooooooooooooooooooooooooooo much. You are a life saver!!

-3x+3y=-3     divide everything by -3   →  x -  y   = 1   add y to both sides →  x = 1 + y      (1)

9x-12y=-18    (2)

Subbing (1)  into (2), we have

9(1 + y) - 12y  = - 18    simplify

9 + 9y  - 12y   = -18

9 - 3y   = -18       subtract 9 from both sides

-3y    = -27        divide both sides by -3

y = 9

And using (1)  .....  x = 1 + y   =  1 + 9   = 10

500=L((0.0239/12)/(1-(1+(0.239/12)^-60

Multiply both sides by (1-(1+(0.239/12)^-60

500 (1-(1+(0.239/12)^-60  =  L((0.0239/12)

Divide both sides by ((0.0239/12)

500 (1-(1+(0.239/12)^-60 / ((0.0239/12)  = L

P.S. -  you have mis-matched parentheses, so it's hard to tell exactly what "L" might be