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Here is one that uses radiuses

Cotan Q = tan 21° 25’ 21.02” . cos -7° 20’ 36” : sin 70° 33' 1.75” – sin -7° 20’ 36” . cotan 70° 33' 1.75”

What is te colon doing in the middle?

I am just playing - I do not even know what you are really wanting from this. I assume you want an exact (or approximate) value for Q?

But the colon makes no sense.

Let  A= 70° 33' 1.75”

Let B =  -7° 20’ 36”

Let C =  21° 25’ 21.02”

Cotan Q = tan C . cosB : sin A – sin B. cotan A

90+7+20/60+36/3600-70-33/60-1.75/3600 = 26.7928472222222222  that doesnt look helpful

Is the colon meant to be a division???

\(Cotan Q =( tan C . cosB ) \div ( sin A – sin B. cotan A)\\ Cotan Q =( tan C . cosB ) \div ( sin A – sin B* \frac{cosA}{sinA})\\ Cotan Q =( tan C . cosB ) \div (\frac{ sin ^2A – sin B* cosA}{sinA})\\ Cotan Q =( tan C . cosB ) \times (\frac{sinA}{ sin ^2A – sin B* cosA})\\ Cotan Q =\frac{tan C . cosB.sinA}{ sin ^2A – sin B* cosA}\\ tan Q =\frac{ sin ^2A – sin B* cosA}{tan C . cosB.sinA}\\\)

None of that looks very helpful.

The simple interest for 1 day would be:

$10 x [15/100] =$1.50

$10 / $1.50 =6.66667days =~7 days in which Mark will have her back at least $20.

[7 x $1.50] + $10 =$20.50 This is what Mark will pay Emily back in 7 days.

Just looked through a few on-line American dictionaries.  They all use radii for the plural of radius.

"What is the floor value of       -6.5                   [Or any number between -7 and -6]

I assume it is -7, is that correct ?"

Correct!

What is a radian and what is the plural form of radius cause I was watching khanacademy and he said radiuseseseses so I'm confused.

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For me the plural of radius is radii  BUT  my country (Australia) uses the same versoin of English as England does.

The USA has changed much of the spelling to make it easier. So maybe for them the plural of radius is radiuses.

A USA person will need to comment on this.

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The words radius and radian are closely related.

The circumference of a circle is  \(2\pi r\)

And there are  \(2\pi\)  radians in a revolution.

so                      \(\boxed{2\pi\;\;radians\;\;=\;\;360^\circ}\)

Rearranging this equations we get.

\(2\pi\;\;radians\;\;=\;\;360^\circ\\ 1\,radian=(\frac{180}{\pi})^\circ\\ or\\ 1^\circ=\frac{\pi}{180}\;radians\\ \)

Say a  number is       6.126543

Then 6 is the floor value

OR

6 is the number rounded down to the nearest integer. 

Just so you will know for next time

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A question for someone else.  Maybe Alan 

What is the floor value of       -6.5                   [Or any number between -7 and -6]

I assume it is -7, is that correct ?

Since you said, "base angle A", does that mean that triangle ABC is isosceles?

If so, the other base angle must be angle BCA (since angle ABC is already at least 60 degrees).

Sorry that it wasn't clear enough, I had to translate the question as best as I could from Chinese and naturally I'm not a native speaker of English! What I meant by the unit value was the number before the decimal point. 

"Given any positive even integer, x, the positive difference between the smallest odd number greater than 7x-2  and the largest odd number less than 3x+5 can be written in the form ax+b . What is a+b?"

If x is even then 7x - 2 is even, so the smallest odd number greater than 7x - 2 is 7x - 2 + 1 or 7x - 1

With x even then 3x + 5 is odd, so the largets odd number less than 3x + 5 is 3x + 5 - 2 or 3x + 3

Difference:  7x - 1 - (3x + 3) = 4x - 4  

ax + b = 4x - 4  so a = 4, b = -4

a + b = 0.

"Suppose f and g are polynomials, and that h(x)=f(g(x))+g(x). Find the degree of g(x) given that the degree of h(x) is 8 and the degree of f(x) is 4."

f(x) = a*x⁴ + b*x³ + ...

g(x) = c*xⁿ + d*x^n-1 + ...

h(x) = a*(c*xⁿ + d*x^n-1 + ...)⁴ + b*(c*xⁿ + d*x^n-1 + ...)³ + ... + c*xⁿ + d*x^n-1 + ...

h(x) = a*c⁴*x⁴ⁿ + ....

Must have 4n = 8  hence n = 2

Degree of g(x) is 2.

"what is the limit of the sequence (-1)^n over 2(n)-1?"

What does it look like?

.

"use the squeeze theorem to evaluate the following limits: an=sin(1/n) over n. an=cos(1/n)-1 / 2^n"

a_n = sin(1/n)       Try squeezing this between 1/n and 1/n²   (should get 0)

a_n = cos(1/n) - 1/2ⁿ      Try squeezing this between 1 - 1/n  and  1 - 1/2ⁿ    (should get 1)

.

Just put it in exacly as Alan has written it. Replace A with the Area you ahve been given.

Exactly what buttons to push depends on what calc you are using.

\(s=\sqrt{4\frac{A}{5}\tan{\frac{\pi}{5}}}\)

A= 387

sqrt(4*387/5*tan(pi/5)) = 14.9979187446241353 = 15

which is the same I got below. 

what is the perimeter of a regular pentagon whose area is 387cm2

\(Area \;of \;triangle=0.5abSinC\\ 77.4=0.5r^2Sin72\\ \frac{77.4}{0.5Sin72}=r^2\\ r=\sqrt{\frac{77.4}{0.5Sin72}}\)

r= sqr(77.4/(0.5*sin(72))) = 12.757991703716932

\(L^2=a^2+b^2-2abcosC\\ L^2=2r^2-2r^2*cos 72\\ L^2=a^2+b^2-2abcosC\\ L^2=2r^2-2r^2cos 72\\ L^2=2*12.757991703716932^2(1-cos(72))\)

sqrt(2*12.757991703716932^2(1-cos(72))) = 14.997918744628501

5*14.997918744628501 = 74.989593723142505

I get the perimeter to be 75cm long

Check the record here.  http://www.numberworld.org/y-cruncher/

To calculate the curcumference of the universe, you only need to use 39-40 digits of pi to have a very close estimate! (Inches off) also, you can calculate the curcumference of the earth with just 3.14, and be only 1 10 thousanth of an inch off!

As of October 7, 2017, pi has been calculated to 2.7 trillion digits. I'm not sure if the other answer was correct. 

Here you go:

John Napier: Spherical Trigonometry 

Maria Agnesi: Infinitesimal Calculus

Srinivasa Ramanujan: Hypergeometric Series 

When you kick a ball in the air, the parabola it travels in could be written out as a quadratic. 

You could have many different example when it comes to arch: kicking a penalty kick, throwing a free throw...

Euler is very famous for inventing new mathematical symbols and identities. 

Euler invented e, in the year 1736.

Euler also invented i, which was invented in 1777. 

Ch. Kramp invented !, in the year 1808. 

German mathematician invented the ± symbol, although it wasn't clear when. 

If you want to learn more about symbols, visit this website: https://www.encyclopediaofmath.org/index.php/Mathematical_symbols 

The greatest common factor (GCF) is 4

There are two methods to approach this problem. 

1. Listing

You list all the factors of 8 and all the factors of 12 and then you find the greatest common factpr.

8) 1 , 2 , 4 , 8

12) 1 , 2 , 3 , 4 , 6 , 12

2. Prime factorization 

First you factorize both numbers...

8) 2 * 2 * 2

12) 2 * 2 * 3

You take numbers that occur in both lists, which is 2 2's and you multiply them together. 2 * 2 is four. The answer is same both ways. The first method is easier in this case, but with bigger numbers, the second method will be eaiser. 

How to use calculator to solve this?

Computer scan:  Result:  Blarney Banker formula detected.

Initiate subroutine for mathematical correction.

_{Minimize overt BB criticism (this instance).}

Solve using table

\(\begin{array}{|rcll|} \hline \tiny \text { Time (Days) }| & \tiny \text {# of cells} \\ 0 |& 2 \\ 3 |& 4 \\ 6 |& 8 \\ 9 |& 16 \\ 12 |& 32 \\ 15 |& 64 \\ \hline \end{array}\\ \)

Generalized formula for doubling per unit time.

\(\Large N = Z*2^{(t/d)}\)

Where (N) is the number of (cells) after time (t), (Z) is the starting number of (cells) at time zero (0), and (d) is the time required to double (cell) count.

\(\Large (2)*2^{(15/3)} = 64\)

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Update Statistical counters:

Increment BB error count by 1: BB=(6.0244834478561245 E21) + 1

End subroutine.

Resume normal operation.

The radius of the cylinder = 30mm

And its length = 240 mm

So....the lateral surface area is    2pi * radius  * length  = 

2pi * 30 * 240  =  14400 pi mm^2

And the surface area of the two ends is   pi * 30^2  = 900pi mm^2

So the total surface area of the cylinder  is  [ 14400+ 900 ]pi mm^2  =  15300 pi mm^2  ≈ 

48,066 mm^2

The total surface area of the box is

[2* 120^2 + 4*120*60 ]  =  57,600 mm^2  

So the cylinder has the smaller surface area