Melody

Deleted

If h (t) = 20 · e1,5 t, then what is the value of h '(0)

\(h(t) = 20e^{1.5t}\\ h'(t) = 20*1.5*e^{1.5t}\\ h'(t) =30*e^{1.5t}\\ h'(0) =30*e^{1.5*0}\\ h'(0) =30*1\\ h'(0) =30 \)

Any time.  I will put the kettle on :))

Guest is right.  You do not need a fancy plotter to graph this.

He and i have both shown you how it is done.

It is good to become familiar with a 'fancy' plotter though because you can use it to check your answers and it can also help you develop an understandng of how graphs work :)

I thought I might expand a little on what i have already said.

Think about the most basic hyperbola example

\(y=\frac{1}{x} \)

Now you cannot divide by 0 so x cannot be 0.  x=0 is an asymptote.

Now, the right hand side cannot equal zero because 1 divide by any number cannt be 0 

SO      y cannot be zero either.                         y=0 is also an asymptote.

Lets look at the basic hyperbola formula with horizonal and vertical intercepts.

\(y-k=\frac{a}{x-h}\qquad where \;\;a\ne 0 \)

x-h cannot be 0        SO x cannot be h so      x=h is an asymptote

y-k cannot be 0         so  y cannot be k so      y=k is also an asymptote

Wed 11/11/15

1) Effective interest rate and an answer to "How do you know all this Melody"

I was hesitant to include this post because I do not want people thinking I am big noting myself.

I noted that there are a number of mathematicians working the forum and some are much better mathematicians than I am.  (I do not know all their qualifications but I know by the work they produce)

It is just that some of the question askers are wondering about the regular answerers' skills and I do not think it hurts to satisfy their curiosity and let them know that they are dealing with very knowledgable  people, who are  also being very generous with their time.  

http://web2.0calc.com/questions/hi-i-really-do-not-understand-this-question-calculate-the-effective-annual-interest-rate-for-20-p-a-compounded-every-4-months-could-someone-please#r3

2)  Introductory play with imaginary numbers.  Good for all levels.   Thanks Heureka and Maximillian.

     http://web2.0calc.com/questions/imaginary-numbers-1

3)  Good circle geometry question for junious.  Thanks guest and CPhill

     http://web2.0calc.com/questions/help-pl0x

4)  Meaning of "inductive" and  "deductive" reasoning.     Thanks Geno    

   http://web2.0calc.com/questions/geometry_25137#r3

5)  Finding the n'th term.    Thanks  CPhill, Heureka and Brodude.....

     (I am sorry Brodude, your name is just toooooooo long)     

   http://web2.0calc.com/questions/f-1-20-f-n-3-f-n-1-60-find-the-10th-term

6)  Use Newton's Method to estimate the maximum.   Thanks Alan and Melody

    http://web2.0calc.com/questions/use-newton-s-method-to-find-the-absolute-maximum-value-of-the-function-f-x-2x-sin-x-0-x-correct-to-six-decimal-places#r2

 7)  Understanding the hyperbola

      http://web2.0calc.com/questions/hi-this-is-juriemagic#r1

Hi Juriemagic,

Around the time you posted this I could see you logged on at the bottom of my page.  

I hope that cookie problem gets fixed soon.  

I am trying to help a grade 11 pupil prepare for his exam, and we have a question here that we know he is going to get. I have tried, but, yes, you guessed it, I'm tooooo stupid!!.  Its a hyperbola related problem. The equation given is k(x)=(a/(x-p))+q where D is the x-intercept (2,0). Now, the graph is given but I cannot plot it here for you. What I have additional is the Horizontal asymptote is Y=1 and the Vertical one is x=3. If someone would Please,..(sigh), walk the xtra mile and plot the graph, which I'm sure is possible to do using the info I have given, and then help me calculate a, p and q. Alland any help will be accepted with the utmost of humility and apreciation!..thank you all kindly.. 

\(k(x)=\frac{a}{(x-p)}+q\\ asymptotes \;\;y=1\;\;and\;\;x=3\\ x\;intercept = 2\)

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The equation of any hyperbola with with a vertical and horizonal axis is 

\(y-k = \frac{c}{x-h}\\ \mbox{The horizontal axis will be y=k and the vertical x=h}\\ \mbox{So we have h=3 and k =1}\\ \mbox{So far the equation of this hyperbola is }\\ y-1 = \frac{c}{x-3}\\ \mbox{Now this equation also passes through the point (2,0) so I will sub this point in to get c}\\ 0-1 = \frac{c}{2-3}\\ -1 = \frac{c}{-1}\\ c=1\\ \mbox{So the equation is } y-1 = \frac{1}{x-3}\\ or\\ y= \frac{1}{x-3}+1\\ \)

sorry, that is 

\(k(x)=\frac{1}{x-3}+1\)

So, a=1,  p=3  and q=1

check.     You shouold get familiar with Desmos graphing calculator.  It is a fabulous tool.

I am very pleased to help you :)

"How on earth do you know all these things?."

You asked so I will answer.     LOL

I have a BSc degree in Mathematics and a Diploma of Education.

I taught in high schools for years and I have also taught commercial mathematics, and other subjects, at College.

So....I guess I should know this stuff.      

I want to point out though that some of the other mathematicians here know far more than I do.     

It is a great honour to work with the other mathematicians and also an honour to work and play with all our regular members and guests.     

Thanks Everyone                    

                                                                                                     ♪ ♫       Melody    ♪ ♫        

@@ What is Happening?  [Wrap4]    Tues 10/11/15   Sydney, Australia Time 8:15pm   ♪ ♫

Hi everyone  

Our fabulous answers were delivered by Alan, CPhill, Will85237, Jeanne, Saseflower,  Heureka and guests.  Many thanks.   

Oh!  Saseflower has been with us for one whole year as of yesterday.  I hope that you are with us for many more years Saseflower, it is a joy to have you on the forum.    

Repeat request:

In the post below where I have invited people to discuss their views of the forum.  All sensible thoughts will be greatly appreciated.

-25i25

\(-25i^{25}\\=-25*i^{24}*i\\=-25*(i^{2})^{12}*i\\=-25*(-1)^{12}*i\\ =-25*((-1)^{2})^6*i\\ =-25*(1)^6*i\\ =-25*1*i\\ =-25i\)