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mx-y=n and nx-m2y=my      m = 3   n = 9 

3x - y  = 9      ⇒   y  =  3x - 9    (1)

9x - 3*2y = 3y  ⇒  9x - 6y  = 3y  ⇒  9x = 9y  ⇒  x  = y   (2)

Sub (2)  into (1) for y  and we have that

x = 3x - 9

-2x  = 9

x  =  -9/2

And   since  x = y, then y = -9/2

Thanks, Manuel.....

2(x+4)(x-2p) .....expanding, we have

2 [ x^2 + (4-2p)x -8p] 

2x^2 + (8-4p)x - 16p

And the minimum will occur where the derivative is 0

Take the derivative of the function and set to 0

4x + 8 - 4p  = 0

x + 2 - p  = 0

x = p - 2

So.......subbing this back into the function, we have

2 ( p - 2 + 4)(p - 2 - 2p)  =  -18

-2 ( p + 2) (p + 2)  = -18

(p + 2)^2  =  9     

p + 2  = 3              or    p + 2  = -3

p = 1                            p = -5

Here's the graph to prove this : 

https://www.desmos.com/calculator/6dn053wdo2

Your explanation is good, Gh0sty   !!!!!

Well, Google says 1 fluid ounce = 0.0078125 gallons.

Make an equation. 

17h = amount of liquid leaked.

There are 24 hours in a day.

So 17*24=408

408 fluid ounces.

Convert that into gallons and you get 3.1875 gallons.

The pipe would leak 3.1875 gallons per day.

(Did I get this explanation wrong?)

The slope at any point on the parabola = 2x

The slope of the line is 3

So.....equating slopes, we have that     2x = 3 ⇒   x  =  3/2

So....at x = 3/2,  x^2  =  9/4  = y

So.......to find p we have

9/4  =  3(3/2) - p + 1

9/4  =  9/2 + 1 - p

9/4  = 22/4 - p

p = 13/ 4

Here's the graph : https://www.desmos.com/calculator/kzzakejx7h

Here are some things you can do:

1. Do extremely hard calculus.

2. Feed your homework to your dog.

3. Give your homework a bath.

4. Just Do It.

5. Do all of the above.

(I strongly recommend doing number 1 and 4...)

Well you can fall asleep and dream about being sucessful and making money but your dream is more likely to come true if you stop complaining and do your homework  

You are welcome and if you send private messages that is really nice of you.    

It is also nice and important that you thank people publicly because it sets an example for others.

If new people do not see anyone else saying thank you then they are more likely to think that they, for some bizarre reason they are not supposed to say thanks.  People copy the behaviours of others. :)

Welcome to the forum by the way.  I know you have been here for over a month but that still isn't all that long.    

Melody

I always say thank you to whoever answers my questions

but you don't see it because I always send the person a private message

Also, I forgot the give the others questioners points

And by the way, Thanks for the answer

Although, I would suggest at least attempting your homework, then you could use a site like that to verify your answers.

Evaluate:

Given: a=d/t2  and d=rt+1/2at2  

Find the values of a and t  when d=2 and r=3

\(Given: a=\frac{d}{t^2} \;\; and\;\;d=rt+\frac{1}{2}at^2\\\text{Find a and t when d=2 and r=3}\\~\\ a=\frac{2}{t^2}\;\;(1) \;\; and\;\;2=3t+\frac{1}{2}at^2\;\;(2)\\ at^2=2 \;\;\;(1b)\\ sub \;1b\;into\;2\\ 2=3t+\frac{1}{2}*2\\2=3t+1\\1=3t\\t=\frac{1}{3}\\ \text{sub back into (1)}\\ a=2\div\frac{1}{3^2}=2*9=18\\ so\;\;t=\frac{1}{3}\;\;and\;\;a=18 \)

Thanks CPhill! I appreciate it.

Hello Manuel,

Why is it that you give your own questions points but you almost never give the answerers any points?

Also,

Why is it that you always say please, which is very nice, but you never say thank you?

We all use Desmos, it is a beautiful graphing calculator :)

I don't understand the question either. 

It has been a long time since I have done questions like this but this is what I think.

n=81      p=0.477    q=1-p = 0.523

expected number of 1s and 2s in 81 invoices is   np = 81*0.477=38.637

\(\bar x=38.637\)

\(\sigma ^2= npq\\ \sigma ^2= 81*0.477*0.523\\ \sigma ^2= 20.2072\\ \sigma = 4.4952\\\)

Now there were 25 ones and twos.  This is below the expected mean of 38.637

38.637-25=13.637    It is below by this many in actual number but how many standard deviations below it is?

13.637/4.4952 = 3.0336803701726286

Mmm it is 3.0337 standard deviations below the expected mean. 

I think the probability of there being 25 or less ones or twos   is 0.0012 or    0.12%

You should try to learn from this old post 

Good luck with your maths test .. I hope we have helped :)

Here is a very old post that you may find very helpful.

The original question is a little different from yours so be a little patient with looking at the answers :)

43.9526 degrees (or hours)

=43degrees + 0.9526*60minutes

=43degrees + 57.156minutes

=43degrees + 57minutes + 0.156*60seconds

=43degrees + 57minutes + 9.36seconds

\(43.9526^\circ=43^\circ\;57'\;9.36''\)

"The line y= 3x-p+1 is a tangent to the parabola y= x²

Evaluate p "

.

What is x?

- 2(3x + 3) = 6    [ div:  / (-2)

3x + 3 = - 3        [ subtr:  3

3x = - 3 - 3

3x = - 6              [ div:  / 3

x = - 2

- 2 * (3 * (- 2) + 3) = 6 

- 2 * (- 6 + 3) = 6

- 2 * - 3 = 6

6 = 6

  !

Here is the problem explained

We have \(b=\sqrt{4ac}\)

Square both sides, \(b^2=4ac\)

Divide both sides by \(4c\) to get \(a={b^2\over4c}\)