Here's (b)

x^2 + xy - y^2  = 1    using implicit differentiation, we have

2x + y + xy' - 2yy'  = 0

xy' - 2yy'  = -2x - y       multiply through by - 1 on both sides

2yy' - xy'  = 2x + y

y'(2y - x) = 2x + y

y' =  [2x + y ] /  [2y - x ]      and the slope of the tangent line at (2.3) is given by

y' = [2(2) + 3] / [2(3) - 2 ]   =   [7] / [ 6 - 2]  =  7 / 4  

Idk what that means but I will take your advice, I am trying to become better at math and practice :P

∫√(4 - x^2) dx       

Let x = 2sinΘ       dx = 2cosΘ dΘ  .....    when x =0, Θ = 0  and when x = 2, Θ = pi/2 ... so we have

∫√(4 - 4sin^2 Θ) 2cosΘ dΘ =

2∫√[(4(1 - sin^2  Θ) ] cos Θ  dΘ =

2 ∫2 √[ 1 - sin^2  Θ) ] cos Θ  dΘ =

4 ∫ cos Θ * cos Θ  dΘ =

4 ∫ cos ^2 Θ  dΘ          and using  cos^2 Θ = (1/2)(1 + cos2 Θ)  , we have

2 ∫ [1 + cos2 Θ]  dΘ  =

2Θ   + sin 2Θ  ....and substituting in the limits of integration, we have

2 [ pi/2 - 0 ] + [sin 2 (pi/2) - sin 2(0)] =

pi + [ sin (pi) - sin(0)] =

[pi ] +  [0]  =

pi =  about 3.1416

Assuming that the problem is:  3^{n + 2} + 3^{n + 3} - 3^{n + 1}  =  3ⁿ·3² + 3ⁿ·3³ + 3ⁿ·3  =  9· 3ⁿ + 27· 3ⁿ + 3· 3ⁿ

   =  (9 + 27 + 3)· 3ⁿ   =  39· 3ⁿ 

A rational number is a number that can be written as an integer divided by an integer (but, it can't be divided by zero).

Integers are numbers from this set:  { ..., -4, -3, -2, -1, 0, 1, 2, 3, 4, ... }

Since both 11 and 29 are integers, the fraction 11/29 is a rational number, not an irrational number.

8766000 is what she is trying to say I think

21 :>:>:>:>

All I know is that this: 0.3793103448275862, is the answer.

To be a perpendicular bisector it must be both perpendicular and a bisector.

To be a bisector, it must pass through the midpoint of the line segment AB.

A formula for finding the midpoint of A(x₁, y₁) and B(x₂, y₂) is  Midpoint  =  ( (x₁ + x₂)/2, (y₁ + y₂)/2 ).

--->   Midpoint  =  ( (2 + 8)/2, (-1 + 3)/2 )  =  (5, 1)

To be perpendicular, the slope of the line must be the negative reciprocal of the original line.

A formula for slope is:  m  =  (y₂ - y₁) / (x₂ - x₁)

--->   Slope  =  (3 - -1) / (8 - 2)  =  4/6  =  2/3

--->  Negative reciprocal of that slope:  m  =  -3/2

Point-slope equation of a line:  y - y₁  =  m(x - x₁)

--->   Point  =  (5, 1)         Slope  =  -3/2

--->   y - 1  =  -3/2(x - 5)

--->   2y - 2  =  -3(x - 5)

--->   2y - 2  =  -3x + 15

--->   2y  =  -3x + 17

--->   3x + 2y  =  17

I have no idea what a "soda clip" is; I'm not even certain what you're asking ... but never let it be said that my ignorance prevents me from attempting an answer ...

If 10 soda clips is 2,8 g then 1 soda clip is 0,28 g.

3.620 kg will be 3.620 kg x 1000 g / kg = 3620 g

3620 g ÷ 0,28 g = 12.929 (approximately)

(I'm also assuming that you write twelve thousand as 12.000 and three hundredths as 0,03.)

Happy New Years Eve  

I wish you all a wonderful 2015

Even today our enthusiastic answerers were helping and encourageing the budding mathematicians of the world!

these wonderful people were geno3141m CPhill, Tetration, Jillybean and NotTheBestMathMaster.  Thanks

^^^^^^^^^^^^^^^^^^^

You know for a long time I have thought that Santas red and white outfit was the direct result of coca cola advertising in the early 1950s but according to this artical that is not true.  

Is there a question here?

I don't know I was going to try and convert to metric maxims.   

Imperial minims sound even worse!     

I was working on this same problem, but my answer needs to be in imperial minims.

Can you convert it to that? 

It is still k%

k% of  28,000

= $${\frac{{\mathtt{k}}}{{\mathtt{100}}}}{\mathtt{\,\times\,}}{\mathtt{28\,000}}$$

= $${\mathtt{k}}{\mathtt{\,\times\,}}{\mathtt{280}}$$

= $$280k$$      dollars

$$\begin{array}{rll}
V&=&A\times h\\\\
12x^3&=&A\times 3x\\\\
\frac{12x^3}{3x}&=&A\\\\
A&=&\frac{12x^3}{3x}\\\\
A&=&4x^2\\\\

\end{array}$$

PEDMAS, which is        (PEMDAS would be the same thing)

parentheses,

then exponents,

(multiplication, division),   equally important - do from left to right

(addition, subtraction )      equally important - do from left to right

--------------------

In Australia we call it    BODMAS

Brackets

order of  (power of)

the rest is the same.

No I did not know that.  How could I know that when you did not say that?

Anyway.

Here is the same equation in degrees

PEMDAS, which is parantheses, then exponents, multiplication, division, addition, subtraction

tx for the information but i wanted theta in degrees. do u know that?

what value of theta satisfies the equation sin(3theta+5)=cos(4theta+1)?

I have assueed that theta is in radians.

You can see the graph that I have drawn.  Each root - where it crosses the x (theta) axis - is a soution to this equation,

so for any interval of 2pi there will be 8 different answers   

That is   for any interval   $$a\le \theta \le a+2\pi$$     there will be 8 solutions to this equation.

1000*24*365.25   times

I don't know how good and estimation that you need.  Lets see.....

$$\\1000*24*365.25\\
\approx 1000*25*400\\
=1000*\frac{100}{4}*400\\
=1000*100*100\\
=10^3*10^2*10^2\\
=10^{3+2+2}\\
=10^7$$

I will assume this is in degrees.

Cot (65) is a value - it is not a function because there is no variable.  

cot (65) = tan (90-65) = tan (25)

Tan(25) is not a function either.      

This is what I think anyway - one of the other mathematicians might contradict me.    

$$\\66,000,000=6.6\times10^7\\\\
60,000=6\times10^4\\\\
66000000\div60000\\
=(6.6\times10^7)\div (6\times 10^4)\\
=(6.6\div 6)\times(10^7\div 10^4)\\
=1.1\times 10^{7-4}\\
=1.1\times 10^{3}\\$$

Geno, it could be 

[ (8 - 9) / (5 - 6) ]^{(2 - 3)}