All Answers 358110 Answers

To find the number of protons given those assumptions, divide the mass of the Earth by the mass of a single proton.

As an order of magnitude estimate, divide 10²⁴ by 10^-27:   10²⁴ / 10^-27  =  10^{24 - -27}  =  10^?

For a more exact answer:    (5.98 x 10²⁴) / (1.67 x 10^-27)  =  (5.98/1.67) x 10^{24 - -27}  =  ?

Exponential growth formula:  A  =  Pe^rt

A = final amount = 53     P = beginning amount = 50     r = rate (as a decimal)    r = time = 10

--->   53  =  50·e^r·10

--->   53  =  50·e^10r

--->   1.06  =  e^10r

--->   ln(1.06)  =  ln(e^10r)

--->   ln(1.06)  =  10r

--->   ln(1.06) / 10  =  r

--->   r  =  0.00583   --->   r  =  0.583%

Population in 2010 (using base year as 1992):  r  =  0.00583  and  t  =  18

--->   A  =  50·e^{0.00583 · 18}

--->   A  =  50·e^0.10494

--->   A  =  55.5 million  

D = r·t

Divide both sides by t:     D/t  =  r     --->     r  =  D/t

D = 120 km  and  t  = 2.5 hr:     r  =  120 km / 2.5 hr  =  48 km/hr

1) Just multiply the first equation by 3 and the second equation by 5 the add them together .

That will eliminate the ys.

2)Solve for x

then

3) sub the x value back into any of the equations and solve for y.

@@ End of Day Wrap      Mon 15/12/14       Sydney,   Australia      Time 12:30 am   (Really Tues morn)        ♬

Hi everyone,

Lots of great answers today from Alan, Geno3141, CPhill, Saseflower, Nauseated, shadew, sorasyn and Heureka.

Geno seemed to answer a great many interesting questions.   There were a lot of absolute value questions.  I have only included a couple in the interest posts but maybe I should have saved a few more of the post addresses.      Thanks Geno.

There are a number of unanswered questions. 

Now for some interest posts:

1) I liked Nauseated's answer to this one - it was funny.  Thanks Nauseated.

Tues 16/12/14

1) flflvm97's daily logic puzzle -  Thanks flflvm97   

What about it?

$${\mathtt{a}}{\mathtt{\,-\,}}{\frac{{\frac{{\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\times\,}}{\mathtt{b1}}}{{\mathtt{6}}}}{\mathtt{\,\times\,}}{\mathtt{c2}}}{{\mathtt{9}}}}$$

Is this your intended question?

Your question doesn't make sense but I think that you are asking for this to be solved.

$$\\1600x^3+1200x^2+800x = 4000\\
4x^3+3x^2+2x = 10\\
4x^3+3x^2+2x-10 = 0\\$$

The only real answer (from the graph) is

approx = 1.05

Pet therapy does not seem to have made you placid.

That’s true, but I do wag my tale more, especially since I became a Royal S.O.B.:)

the question asks  " How many more dollars ...." that implies  a subtraction and a worked answer.

okay anon - you have been very patient with us :)

$$\\$monthly weight lose $\ge \frac{35-28}{6}\\\\
$monthly weight lose $\ge \frac{7}{6}\;lbs\\\\$$

Pet therapy does not seem to have made you placid.  I guess nothing works all the time.  

Thanks Geno, that looked like a challenge  

Thank you Alan, this was a great question and answer :))

You should not use that kind of language on the forum.  There are children about.

You really are just so Nauseating    

Type it into the site calc as  

asin(4/6)   you may need to press = on the actual calc.

asin is the same as inverse sine. 

Make sure the calc is set to degrees  (toggle button on the bottom left)

$$\\y = -2 (x - 6)^2 + 8\\
y=-2(x^2-12x+36)+8\\
y=-2x^2+24x-72+8\\
y=-2x^2+24x-64\\$$

A career change may be in order.

One thing I like about dogs is they rarely nauseate me – even when they roll in carrion. The very few that do manage to, I feed to my cats. They usually just barf them up, though. I guess the cats are nauseated too.    :)

This is the main website that we use for graphs.

It is a beautiful graphing calculator

If you become a member (which is free) you can save your graphs and  share them with other people.

This sounds like excellent advice Nauseated.  

Do you work as a canine pschycholgist?   

If not then perhaps you should consider it.

This could be of dual benefit.  

Pet therapy is known to have great benefits, it is very soothing.