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I don't really understand this at the moment and haven't got the time to get my head into it so I'll have to come back to it and the other factorising questions you set on the other post in a few days. I'll message you when I've done them rather than you having to check. Thanks for the challenges.

9-3a/4+20y if x=8 and y=2.....I'm assuming that we have

(9-3a)/(4+20y) if x=8 and y=2.....if so, we have

[9-3(8)]/[4+20(2)] =

[-15 ] / [ 44] =

( -15 / 44)

The taper angle is given by

tanΘ = 6 / 650

And using the tangent inverse to find Θ, we have

tan^-1(6/650) = about  .529°

Here's a pic.....(1/100th scale).....the taper angle is GDB....

3.141592653597932384626 just off the top of my head

When multiplying decimals, such as .5*.03 there is a simple trick. count how mank decimal places there are, and tht is how mank your answer will be, in example,      

.5*.03 there are 3 decimal places. 0.5 0.03. So your answer will have 3 decimal places. You multiply 5*3= 15 with 3 decimal places it is .015

.5 x .03  .....just forget the decimals and multiply 5 x 3  .... so we have

5 x 3 = 15

Now.... this is really...

15.

But, we moved the decimal point one place to the right in multiplying the ".5" and two places to the right in multiplying the ".03"....so that's a total of three places to the right....so....we must "correct" this in the answer of "15" by moving the decimal point back to the left three places....so we have...

.015  ..  and that's it...!!!

21

Tha awnser is negative infinity 

Just type them on your keybord for example:

2x+3=5

then it will say 

x=1

-Magnus

(x/y) - (y/x) + (3/xy)  ..  I assume you want to simplify this???.....assuming that the "y" in the last term is in the denominator, we have

[ x^2 - y^2 ] / xy + 3/(xy) =

[ x^2 - y^2 + 3 ] / (xy)

its obvio

us TWENY WEN

Using the Pythagorean Theorem, we have

15^2 +(3x)^2  = (3x + 3)^2    expand

225 + 9x^2 = 9x^2 + 18x + 9   rearrange and simplify

18x - 216 = 0

18x = 216

x = 12

It's probably better to give to much info than too little......"labeling" your answers is always a good thing....

It's an intresting question, though. 

Simplifying rational numbers w/ several digits in both the numerator and denominator, by hand, is certainly not somthing every adult know how to do. And one can learn A LOT from such problems: the times table, divisibility rules, prime numbers, coprimes, and so forth. But, indeed, many calculators solve this instantly.

Questions involving simplifying rational numbers occur pretty often, so parhaps it should be included in "Great Answers to Learn From" or sth. I haven't looked into the matter yet...

 5 + (7-1)2/6

=5 +6*2/6

=5 + 2

=7//

that is the answer

Since sine and cosine are co-functions, cos x = sin(90-x)

Therefore, cos x = 1/3

And using the cosine inverse, we have

cos^-1 (1/3)  = about 70.53°

And the sin (90 - 70.53) = 1//3   !!!!

I'll probably refer to Wolfram Alpha for any related questions in future posts.

Well, both the denominator (bottom) and numerator (top) is even numbers (divisible by 2), so you can divide them by 2. You'll get:

39/137

Since the digit sum of the numerator is divisible by 3, the whole number must be divisible by 3. What about the denominator? Nah, it's digit sum is 11, so the whole number isn't divisible by three. 

But, we have nontheless gotten further in our solving. Since 39 is divisible by 3, we can much easier factorize it:

39/ 3 = 13       =>     3*13 = 39

Now all we have to do is to check if 137 is divisible by 11. (We have already checked for 3). 

No. 137 isn't divisible by 11. 

Since 39 and 137 doesn't have any factors in common, the simplest version of the original fraction is:

39/137

You can evaluate this using the on-site calculator.

The formula for the area of a circle is:

A = pi * r²

And to get the volume of a cylinder, simply multiply by the heigth:

V = pi * r²h

Thus:

V ≈ 3.14 * 10 cm * 10 cm * 6.5 cm = <your answer> cm³

*** Thx ***

3.14159heilhitler81568532455...

Very nice, Tetration.

Thanks, heureka.

Order of operations:

1. Solve the paranthesis

2. Multiply(*) / divide (:)

3. Add (+) / subtract (-)

3x - 2(x - 3) = 5x + 4(x + 5)       Solve the paranthesis. I'll use this formula: a - b = -(b - a), It'll make easier

                                                  to avoid careless mistakes based on multiple minuses.

3x + 2(3 - x) = 5x + 4x + 20       Combine like terms, solve the last parantesis

3x + 6 - 2x = 9x + 20                 Combine like terms once again. Move the six over to the right,

                                                 Remember: You wanna end up w/ the variables on the left, and numbers on

                                                 the right

x = 9x + 14                               Move the 9x over

-8x = 14                                   Divide by -8

x = - 7/4