Melody

ok, 

All of that is really good.  You are really starting to get the hang of it.

You do need to know automatically that if

y=asinx  +b

then 

y intercept of b

midline y=b

Amplitude 2pi

And it will go up first if 'a' is positive and down if 'a' is negative.     (from the x axis)

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

Answer the questions for the 2 graphs below.  AFTER you determine the equation, check it using Desmos.

Q1)

a) midline

b) y intercept

c) wavelength

d) amplitude

e)  Does it start going up or down?

f) SO what is the equation

Question 2)

a) midline

b) y intercept

c) wavelength

d) amplitude

e)  Does it start going up or down?

f) SO what is the equation

Thanks guest and thanks to Max.

Max's answer required very good visual insight. 

I always knew he was clever from when he first started posting.

Unfortunately I am not likely to remember this.  How sad.

Question 1

Jenny, the circumference of a circle is 2pi*r

r stands for radius but it can also stand for radians.

So in a complete circle there are 2pi radians and 360 degrees.

So long as you know that you can work all the others out for yourself.

\(\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}\\~\\ =\frac{2*9^{\frac{1}{3}}}{1 +3^{\frac{1}{3}} +9^{\frac{1}{3}}}\\~\\ =\frac{2*3^{\frac{2}{3}}}{1 +3^{\frac{1}{3}} +3^{\frac{2}{3}}}\\~\\ let\;\; x=3^{1/3}\\~\\ =\frac{2x^2}{1 +x +x^2}\\~\\ =\frac{2x^2}{x^2+x+1}\\~\\ \)

I really do not see this simplifying very nicely

coding:

\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}\\~\\ 
=\frac{2*9^{\frac{1}{3}}}{1 +3^{\frac{1}{3}} +9^{\frac{1}{3}}}\\~\\
 =\frac{2*3^{\frac{2}{3}}}{1 +3^{\frac{1}{3}} +3^{\frac{2}{3}}}\\~\\ 
let\;\; x=3^{1/3}\\~\\ 
=\frac{2x^2}{1 +x +x^2}\\~\\ 
=\frac{2x^2}{x^2+x+1}\\~\\ 
 

Hi OldTimer,

Ok so I was looking at it correctly after all.....

Thanks Tiggsy.     

Mine was completely correct.

I did not give you the final answer.   I only gave you P(pop)  

You finished it yourself, which is great,  but you should have understood that my answer was purposefully not complete.

Billy and Bobbi each selected a positive integer less than 200. Billy's number is a multiple of 18, and Bobbi's number is a multiple of 24. What is the probability that they selected the same number? Express your answer as a common fraction.

200/18 = 11.1111111111111111                  integer part 11

200/24=  8.3333333333333333               integer part 8

factor(18) = 2*3^2

factor(24) = 2^3*3 

lowest common muultiple = 2^3* 3^2 = 8*9 = 72

So there is 2 commmone factors less than 200,       72 and 144

Probability that they both chose 72 = 1/11 * 1/8 = 1/88

Probability that they both chose 144 = 1/88

Probability that they both chose the same number = 2/88   =  1/44

Answering guest:  Why do you think that this is incorrect?

I just read this from Google

"Tracheids are present in all vascular plants whereas vessels are confined to angiosperms. Tracheids are thin whereas vessel elements are wide. Tracheids have a much higher surface-to-volume ratio as compared to vessel elements. Vessels are broader than tracheids with which they are associated.M....

NOW.

If you do not know what an angiosperm is then google it.  

So without checking till afterwards.

y= 3-4sinx 

Q  What is the least confusing way to write this?  What number does the minus sign belong to?

What will be the main features of this graph?

Q What is the y intercept?    Is the y intercept on the centre line?  

From the y axis will the graph start going up or down?  How can you tell this from the equation?  (in the positive x direction of course)