All Answers 358117 Answers

Well spoken, Miss Kitty. Well spoken.

Kitty just gave proof that the pen is mightier than the claw. She also gave (almost) everyone points.

So, pigeons, you should return the favor. Start clicking! Her last fifteen posts should be a good start. This will do two things. This will demonstrate our good will toward Kitty and it will make reinout-g sweat a little. That will teach him to curse CPhill!

About overlooking the small element in the answers: Yes, I can do that. I have been doing it for years and it should not be a problem to continue. (I would have said, “small elephant” though). This post was somewhat of an anomaly. I usually do not ware that hat because it might never come off.

This was a perfect storm: The proper post, optimal timing, and great feedback from CPhill. Drawing you into this was a – as it turns out, a fortuitous event --sort of like finding wild catnip.

Most math websites have their Newtons, Eulers, and Fermats, but very few have an Austen, Bronte, or Wolfe. This site is a unique exception. (There are few dogs here, but that is not the same as a Wolfe). This site is unique in many ways. Most of the young people here are pleasant. Rosala is like springtime and flowers, even for parts of the world that are going into winter. Zegros and Ninja have entertaining banter. They all answer questions and do well, too.

You and Melody are the central points and anchors of this site. Your join dates are nine days apart. Currently, three quarters of the posts are after this point. Melody is the Queen and you are the Princess. I hope you do not dislike the title so much that that you abdicate. Every kingdom needs a Queen and Princess (just ask Disney). The king is often away or works behind the scenes.

I have been a ghost on here since this site was 8 days old. Those were desolate days. (Log into the French, Spanish or Russian site to get an idea). I found many back doors and secret passages. I watched the pawns come and stab at a few questions then fade. There was a bishop for a while, but he acted more like a rook and left after the Queen’s coronation.

With the arrival of the Queen and Princess, this place came alive!

The nobility came: reinout-g as jonkheer, esquire; Rom, Alan, Bertie, as patricians, knights; Then CPhill as patrician, knight, and then as Seigneur: Knight of the manor. There are the lesser known, who visit often. The knights are often on duty, especially Sir CPhill, who carries the sword of Excalibur, and is powered by a modern nuclear battery. (The EverReady bunny has nothing on him).

There are, of course, the court jesters –sometimes called fools, they include those who have license because of brilliance, and those who are simply excused because they can’t help it. (For some, I may fit in that category). If their posts are too off base, they are usually deleted without ceremony. Sometimes the execution is public, like this one by Sir CPhill

No problem, ND......we traveled different highways but arrived at the same destination...!!! Points and Thumbs from me on your answer ......!!!

This works just like "long  division".......we have

                      x^2   - 4x  + 2  

         ----------------------------

x+5  ) x^3 +   x^2 - 18x +  2

          x^3  + 5x^2

         ----------------------------

                   -4x^2  - 18x

                   -4x^2  - 20x

                   ---------------

                                 2x  +  2

                                 2x  + 10

                                 -----------

                                          -8

So, there's our answer......  x^2 - 4x  + 2  with a "remainder" of -8 /(x+5)

Note that if we can factor the numerator/denominator, this sometimes "cancels" terms and division might not be necessary at all, but that wasn't possible here.

I haven't learned about the equation you used CPhill.

I probably made it harder than it needed to be, but we both got the same answer so that's the important thing. :)

$$\mathrm{\ }$$Well, if you have a graph handy, I would just plot the points and go from there.

If you don't have a graph, ask yourself...what's the difference between these two lines?

From the point (1,-4), you go over 4 and up 6 to get to the next point.

So, our slope is 6/4 or 3/2.

In the slope intercept form, we have Y=3/2X+b

b is the Y intercept.

How do we figure out b?

From point (1,-4) we could go over 1 to get to the Y intercept., and our slope is up 3 over 2 (or 3/2)

If we divide the top and bottom by 2, we get 1.5 over 1. Meaning, to go over one, we need to go down 1.5

Now we have our completed slope intercept form of a line: Y=3/2X -5 ½

There we go!

It would have been alot easier to do this with a graph. The only problem with this though, is that you wouldn't have known exactually where it intercepted the Y axis, you would have had to estimate...but you probably would have figured out it's about -5 ½

(1,-4) (5,2)

We first need to find the slope. This is just the change in the y coordinates divided by the change in the x coordinates. Note that y changes from -4 to 2 so that's 6. And x changes from 1 to 5 and that's 4.

So (change in y)/ (change in x)   =   6/4  =  3/2   and that's the slope.

To write the equation of the line we can use one of the points and the slope. Using the "point-slope" form, we have

y - y₁ = m(x -x₁)    where m is the slope and x₁ and y₁ are the coordinates of one of the points.

I'll use (5,2) since there is no negative involved (but I could have used either point)....so we have

y - 2 = (3/2)(x - 5)       simplify the right side

y - 2 = (3/2)x - 15/2       add 2 to both sides

y =  (3/2)x - 15/2 + 2   simplify the right side

y = (3/2)x - 11/2

And there's the equation of the line in "slope-intercept" form.

I like this form because the slope tells me if the line 'falls or rises" from "left to right" and I can also see the y intercept (0, 11/2) right away.

I got no pictures but im still dope though!

I see...I think I misinterpreted the question.

I thought it was 

-3(X-4)²⁺¹³ 

but I think you meant

-3(X-4)²+13 

My bad.

-10x-8y=7

30x+24y=-20

We can quickly see that this sytem has no solution....if we multiply the first equation by -3 on both sides, we get:

30x  + 24y = -21

This says that the left side = -21

But the second equation says that the same left side = -20.

And this is impossible. Adding two terms together can't produce two different answers.

Correct.

$$-10x - 8y = 7$$

$$30x + 24y = -20$$

If you rearrange the first equation you get:

$$y = \frac{7+10x}{-8}$$

Substituting that into the second equation gives you:

$$30x + 24(\frac{7+10x}{-8}) = -20$$

Expanding and simplifying the bracket gives you:

$$30x - 21 - 30x = -20$$

The two 30x terms cancel out leaving you with -21 = -20, and so the equation is unsolvable. Changing the -20 in the second equation to a -21 would make it work, however.

EDIT: actually, going back and doing it with 21 doesn't give a definite solution, since then the two equations simplify down to the exact same thing, meaning you've only really got one equation to work with.

   It's the economy. . .

The chemical formula for Chalcopyrite is CuFeS₂. This compound corresponds to a molecular mass of 183.54.

The distribution of mass for this compound is

Iron      Fe  55.845 (1) 30.430%

Copper Cu  63.546 (1) 34.626%

Sulfur S      32.065 (2) 34.944%

Cu – copper represents 34.626% of the total mass of this compound

To mine 425g of pure copper, requires a quantity of Chalcopyrite equal to

$$\frac{425g}{0.34626} =1227.4g }{}$$

~~D~~

-2(3x +5) = -3(4x + 3)

Simplifying on the right and the left, we have

-6x -10 = -12x - 9

Add 12x to both sides

6x - 10 = -9    

Add 10 to both sides

6x = 1

Divide both sides by 6

x = 1/6

Let's check this in the original problem to make sure it "works"

-2[3(1/6) +5] = -3[4(1/6) + 3]    ???

-2[1/2 + 5] = -3[2/3 + 3]  ???

-2[11/2] = -3[11/3]   ???

- 11  =  -11   ....and that's true !!!

Let's examine how we can arrive at  Alan's  answer,  since it might not be immediately intuitive........

Note that  log 3⁵⁰⁰   asks.........What power do we raise 10 to in order to obtain 3⁵⁰⁰  ???

By a property of logs, we can write

log 3⁵⁰⁰    as   500*log3 .........and evaluating this gives us......... 238.56062735983122

Now....note that the "whole number" part of this tells us what power (exponent) will be on the "10" in the scientific notation representation of 3⁵⁰⁰ , and 10 raised to the decimal part will tell us what some of the first few digits of that number will be (within a certain degree of accuracy).

So 10^{.56062735983122} = 3.63602917958700501  (Only the first 12 digits of this are accurate for 3⁵⁰⁰ ... see below)

Thus, in scientific notation we would have......

3.63602917958 X 10²³⁸   

This number is actually 239 digits in length and Alan's answer of   3.636×10²³⁸   is good enough !!!!

However....if you insist.....we have

3636029179586993684238526707954331911802338502600162304034603583258060019158389548419850

8262979388783308179702534403855752855931517013066142992430916562025780021771247847643450

125342836565813209972590371590152578728008385990139795377610001

 I think I'll stick with the scientific notation........

15% means 15/100, so 15% of 334 is (15/100)*334

$$\left({\frac{{\mathtt{15}}}{{\mathtt{100}}}}\right){\mathtt{\,\times\,}}{\mathtt{334}} = {\frac{{\mathtt{501}}}{{\mathtt{10}}}} = {\mathtt{50.1}}$$

The Anonymous answer is almost correct, except that he/she should have added 13 rather than subtracting it.

3⁵⁰⁰ ≈ 3.636×10²³⁸

-3(X-4)^2+13

-3(x-4)^15

-3x^15*12^15

So that wouldbe your simplified version... or you could write it as

-3x^15*15,407,021,574,586,368

-3(X-4)^2+13 =-3(x^2-8x+16)-13=-3x^2+24x-48-13=-3x^2+24x-61

I'm going to my answer my own question. I figured it out after looking closely at the calculator.

There is a 2nd button and it activates the ^-1 on the sine key.

You're dull and uninteresting, biderman......nobody is paying any attention to your (supposedly) humorous posts....disappear back to troll land.......where your posts will actually display.......