Melody

Hi  MathyGoo13,

I am glad that you are being persistent with asking for help, and saying you don't understand.  :)

It is what I encourage people to do.   I will take a look for you.

Now that i have done it, I don't think that this is a brain dead question at all.

I think questions like this can be really confusing. 

The temperature changed throughout a certain day at a steady rate of
- 3 ° C every hour. If it was -8° C sometime between 2 pm and 2:20
pm, then the temperature was 9° C in the time interval

2pm to 2:20pm        -8 degrees    (at some point)

1pm to 1:20pm        -8+3 = -5

12pm to 12:20pm        -5+3 = -2

11am to 11:20am        -2+3 = 1

10am to 10:20am        1+3 = 4

* 9am to 9:20am        4+3 = 7

* 8am to 8:20am        7+3 = 10

Ok, now what?

In an hour it decreases 3 degrees so in 20 minutes it decreases 1 degree.   (I am going forward in time now, its less confussing, I hope.)

so now I have

* 8am to 8:20am        7+3 = 10                  turns 10 degrees

8:20am to 8:40am        turns 9 degrees.

So it turns 9 degrees somewhere between 8:20 and 8:40 am   

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

How could I have done this more quickly?

1 degree in 20 minutes

-8+ 17  = 9

17 lots of 20 minutes = 17/3hours  = 5 hours and 40 minutes

The start time was  2pm to 2:20pm

5 hours ago it was  9am to 9:20am

40 minutes before that was   8:20am to 8:40am

---------

I got the same answer 2 different ways.  That is always a good sign 

2573 = 31*83

This is a composite number.  It has 4 factors.   1, 31, 83 and 2573

I discovered this by entering    

factor(2573) =       into the web2.0calc.   

It is good that you have shared your answer but why not tell us what you think  f(-2)  and g(-2) are .....

Let A be the point (0,0)

Let B be the point (22,0)

the line equidistance from thes points is x=11,  the centre will line on this line

now AC=12 and BC=14   Find C using locus

\(x^2+y^2=144\qquad (x-22)^2+y^2=196\\ subtract\\ (x-22)^2-x^2=196-144\\ -44x+484=52\\ x=9.\bar{81}\\ x^2=96\frac{48}{121}\\ x^2+y^2=144\\ y^2=144-96\frac{48}{121}\\ y^2=47\frac{73}{121}\\ y^2=\frac{5760}{121}\\ y^2=\frac{2^7*3^2*5}{121}\\ y^2=\frac{2^6*3^2*5*2}{121}\\ y=\frac{24\sqrt{10}}{11}\\ C(\frac{108}{11}, \frac{24\sqrt{10}}{11})\)

The centre will be the point on the line x=11 that is equidistant to  A(0,0), B(22,0)  and  C  let the point be Q(11,y)

I think I will let you take over from there.

Here is the pic

LaTex:

x^2+y^2=144\qquad (x-22)^2+y^2=196\\
subtract\\
(x-22)^2-x^2=196-144\\
-44x+484=52\\
x=9.\bar{81}\\
x^2=96\frac{48}{121}\\
x^2+y^2=144\\
y^2=144-96\frac{48}{121}\\
y^2=47\frac{73}{121}\\
y^2=\frac{5760}{121}\\
y^2=\frac{2^7*3^2*5}{121}\\
y^2=\frac{2^6*3^2*5*2}{121}\\
y=\frac{24\sqrt{10}}{11}\\
C(\frac{108}{11}, \frac{24\sqrt{10}}{11})

You can do this on the web2.0calc!

just enter

factor(2023) and hit enter.

factor(2023)= = 7*17^2

How about presenting your question properly, without the unrendered LaTex.

This will happen when 

x^2-5x+2 = 0      ( so long as x^2-4x+2 isn't 0 as well. )

use the quadratic formula

I don't know either ......

You have made 2 mian logic errors here.

1) You have said that all the numbers can be used more than once, which they can't.

2) You also said that order chosen counts, you already understand that you made that mistake.  

Learning is a journey :)

 g(x) = sqrt((x - 3)^2 - (x - 18)^2)

\( g(x) = \sqrt{(x - 3)^2 - (x - 18)^2}\\ g(x) = \sqrt{(x^2 - 6x+9) - (x^2 -36x+ 324)}\\ g(x) = \sqrt{ - 6x+9 +36x- 324}\\ g(x) = \sqrt{ 30x- 315}\\ 30x-315\ge 0\\ 30x\ge315\\ x\ge 10.5\)