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I do not understand what you have done Alan.    

If I graph  r=3sin(5Ɵ)     where r is the vertical axis and  theta is the horizontal axis i get an ordinary sine curve.

So what have you done?

Oh the period of this graph is 2pi/5    (in radians)  just like geno said.

2169/3 = 723

It is good getting practice on these Chris.  I did one the other day that was really hard.

Thanks for the question to Mellie.

r=6300. Volume=4/3πr³

So you want to know the volume of a sphere with r=6300. First, calculate r³ using the calculator and then times by π and then 1.33333333333...

Or this one!

(-4+x5)10+-5x

Our guest has answered this question.

(-4+x*5)*10+-5x

= 10(-4+5x)-5x

= -40 + 50x -5x

= 45x - 40

normally you would finish here  :)

I am not sure that this was your intended question.  

Maybe you meant

(-4+x^5)10+-5x     or sopmething else again

The ^ means  "to the power of"

so   3^4 means 3⁴

As follows:

.

Hmm!  What if n were 27 or 28 or ...?

-(1000000000000000000000000000000000000000000000101001010100100101001-17)

= -1000000000000000000000000000000000000000000000101001010100100100984

\(15\frac{6}{16}\div3 = (15\div3)+(\frac{6\div3}{16})= 5\frac{2}{16}= 5\frac{1}{8}\)

Ans- \(\frac{1}{2}=5\frac{1}{8}-\frac{1}{2}= 5\frac{1}{8}-\frac{4}{8}= \frac{41-4}{8}=\frac{37}{8}= 4\frac{5}{8}\)

I should have added this graph:

.

I am not very good at trig but I will try to solve it.

\((cos\space x-5sin\space x)^2=Acos\space 2x+Bsin\space 2x+C\)

\(cos^2\space x - 10sin\space x\space cos\space x + 25sin^2\space x= A(cos^2\space x - sin^2\space x)+B(2 sin\space x\space cos\space x)+C\)

The form of left hand side doesn't fit in the form of right hand side......

2x and 3x are like terms.

but 2x and 3y aren't

It means 'of the same variable' .

But note that 2x and 3xy aren't like terms too. The part without coefficient(for 2x the coefficient is 2, and for 3xy the coefficient is 3) should be EXACTLY the same.

\(cos30 = \dfrac{adjacent \space side}{20}\)

\(adjacent \space side = 20 cos30 = 10\sqrt3\)

\(opposite \space side=\sqrt{20^2-(10\sqrt3)^2}=\sqrt{100}=10\)

\(atan(\dfrac{10\sqrt3}{10})= atan(\sqrt3)=60 \space degrees\)

Wait, if that is for right-angled triangles why I don't just 90 - 30 ...... never mind, at least I got the answer XD

Sorry kid!. I think your problem is that you don't seem to understand written English. You completely misunderstand what we are saying. You better talk to your Math teacher, and he/she will explain it to you on the Blackboard or whatever, in detail.

The answer that CPhill calculated, which was: 1.04739 × 10^12  is EXACTLY the same as your answer!!!. Your answer for this: 4/3pi (6.3 * 10^3)^3  =comes from: evalute the product INSIDE the bracket, which comes to:6.3 x 1000 =6,300. Your raise this to the 3rd power: 6,300^3 =250,047,000,000=2.50047 x 10^11. Multiply this last number by 4/3 =333,396,000,000=3.33396 x 10^11. Finally you multiply this last number by Pi. So you get: 3.33396Pi x 10^11. BUT, this is exactly the same as CPhill's answer!!!!!!!!!!!. The reason you don't seem to understand is the fact that you use the word "Pi" in your answer, while CPhill uses the VALUE of Pi, which =3.1415926535........etc. Do you see the where the "problem" is?????

I'm sorry but the actual answer is 3.33pi * 10^11 so do you know how to get it?

It doesn't make any sense.. if you don't count the last two digits, then it will be 10^7, but it will NOT be 3.328, but instead, 332.8..

I still cannot understand your answer... I'm sorry but could you explain your answer again? in detail?

You didn't read the answer carefully. I said "to the last digit, which is 2" You don't count it, because the decimal point goes in front of it. Then you count EVERYTING to the right of the decimal point. So, 35,000,000 would look like this in scientific notation: 3.5 x 10^7.

OK

(4/3) pi  =  about 4.18879

Note that in the second part  we are "distributing" the exponent on the outside of the parentheses over both terms in the parentheses.....so

6.3^3  = about 250.047   and

(10^3 )^3  = 10^9    so....putting all this together, we have

4.18879 * 250.047 * 10^9  = about 1.047394373130  =  about  1.04739 x 10^12

Note : 77%  = 77/100 = .77   ....and since we can multuiply in any order, we have

3.2 * 10^7   * .77  =  

3.2 * .77 *10^7  =

2.464   * 10^7     

For the second problem......a 4% increase means that we can multiply the 2005 population by 1.04   and we have  

3.2 * 10^7 * 1.04    =   again, we can multiply in any order

3.2 * 1.04 * 10^7   =

3.328  * 10^7

Note that we didn't have to do anything to the 10^n  part of the scientific notation  !!!!

CPhill, could you please give answer in detail, I cannot understand your answer..

4/3pi (6.3 * 10^3)^3  =

(4/3) pi * 6.3^3  * 10^9    ≈   1.04739 × 10^12