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A(0) =[6 x 10^23) x 2^-(d/1), solve for d

A(0) =Log[6 x 10^23) / Log(2)

d =~78.9893 days - when you will have 1 atom left !!!.

3x(x+1) + 7(x+1)

Since both of the values in the parenthesis are equal, we can combine.

(3x+7)(x+1)

Notice the parenthesis. If i had just done 3x+7(x+1), then only 7 would be multiplied by x+1.

So (3x+7)(x+1) is your final answer.

R plus 10 equals J

J*2=S

Subsitute equations

(R+10)*2=S

2R+20=S

2R-S=-20

This would be our final answer unless....

you would give us more info

Though I think im missing somthing..... anybody want to add on to my equation???

All triangles are under the same height

If AWX  = 30......and AYZ  = 20....we have that

(1/2)WX * height   =  30

(1/2)YZ * height  = 20

Which implies that    WX =  (3/2)YZ

Which implies that

WX + XY = 9       and

YZ +  XY = 7        so

(3/2)YZ + XY  = 9

YZ        + XY = 7     subtract these two equations

(1/2)YZ  =  2      ⇒  YZ  =  4       ⇒ XY = 3

And the height is   (1/2)YZ  * height = 20    ⇒  (1/2)4 * height = 20  ⇒ height = 10

So.....the area of AXY  =  (1/2) XY * height  = (1/2) * 3 * 10   =  15 units^2

Bite the coin

Im almost running out of time, please can you finish up quicker (not to be rude)

what do you mean by "equations"?

P.S. Im a middle schooler (7th grade) and this problem is pretty easy to solve for me (no offence)

CPhill can you solve #2..... Im really stumped on the secound one, and i would like to see how you would do it.

Meters per second is speed...meters per second per second  is acceleration.  

Id solved #1 and got 15

People has different thoughts about the question 'math'. However, math is all over the world. Jest send me anything and I’ll explain it in 'math'.

thats the unit of Speed

Hectitar's answer was more concise.....I told my ghost not to be so long-winded!!!!!

Also! 

Let's call side CD, which is the base of triangle CDA,  " b "  .

Let's call the area of CDA  " a " .

(1/2)(b)(7 + 5)  =  a

(1/2)(b)(12)  =  a

6b  =  a

b  =  a/6

(1/2)(b)(7)  =  a - 15

(7/2)(b)  =  a - 15

(7/2)b + 15  =  a

                                 Plug in  a/6  for  b .

(7/2)(a/6) + 15  =  a

(7/12)a + 15  =  a      Multiply through by  12 .

7a + 180  =  12a

180  =  5a

  36  =  a

Thanks, hectitctar!!!......there is a sligtly faster way of finding the missing area

Using hectictar's diagram [ along with a theorem from Euclid ]

        area of ab *  area of dc =   area of bd * area of ac

               4        *         5            =         3        *    area of ac

                      20                      =          3        *    area of ac      

                                Divide both sides by 3

                                20 / 3   =  area of ac   

Parallel to CD, draw line EF through B

We have four triangles EBA, FBA, EBC and FBD....and their combined area is 15

And because triangle EAF  is similar to triangle CAD.....then EB = 5/12 CE  and BF = 5/12 ED ....and the height of EBA and FBA = BA = 5, while the height of EBC and FBD = EB = 7

So we have

Area EBA          +  Area of FBA   +       Area of EBC      +  Area of FBD  =    15

(1/2)(5/12)CE*BA + (1/2)(5/12)ED *BA  + (1/2)(5/12)CE *EB  + (1/2)(5/12)ED *EB  =  15

(1/2)(5/12)CE*5 + (1/2)(5/12)ED *5  + (1/2)(5/12)CE *7  + (1/2)(5/12)ED *7  =  15

[ (1/2)(5/12) CE * (5 + 7) ]  + [ (1/2)(5/12) ED * (5 + 7) ]  = 15

[ (1/2)(5/12) CE * (12) ]  + [ (1/2)(5/12) ED * (12) ]  = 15

[ (1/2)(5/12)* 12  [ CE + ED]  =  15

(60/24) [ CD]  = 15

CD  = 15 * (24/60) =   (1/4) * 24  =  6

So.....area CDA =  (1/2)CD * EA =   (1/2) * 6 * 12  =  36 units^2

half life of 1 day

Hmmm!!

I kind of cheated to get this, but I found out that  ln( e^i2π ) ≠ i2π . As for why that is....it beats me!!

And on the second one...(I didn't cheat on this one!)....    e^ix  =  e^i2x    when  x = 0  ....?? 

Is CPhill's ghost composing an answer right now? Because apparently, CPhill can compose answers while not being online... LOL

Let's see... we have a desk that's 25 in. long and 18 in. wide, and another geometrically similar desk that's 60 in. long and x in. wide. Now, the special property of similar shapes is that the ratios of their sides will always be the same. Doing that gives us \({25\over 60}={18\over x}\), which, using basic algebra gets us: 

\(25x=18*60=1080\)

\(x={1080\over 25}=43.2\) inches, which is the width of the second desk.

Q.E.D. 

You have to give the half-life of the radioactive substance, which can range from microseconds to billions of years!!. Then, we can easily figure out how long would it take to completely disappear.

ab  =  4     →     a  =  4 / b

bd  =  3

cd  =  5     →     c  = 5 / d

area of remaining rectangle  =  ac  =  \(\frac4b\cdot\frac5d=\frac{20}{bd}=\frac{20}{3}\)

863,636,276,372,636,726,363,000,000,000,000,000,000,000,000

The answer is 51 because you take 17*300 = 5100 and then you move your decimal over two places and get 51.00 Drop the zeros and you have just plain and simple 51, but on other questions you will have to work out the whole problem becuase it won't be as simple as multiplying 3 by 17. 

17% of 100  =  17

So.......17% of 300 must be three times as much  = 3 * 17 =  51