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X^5 - X^3    is  just that

The problem states the student made the error so

(500-499.7)/500 x 100 = .06 %   

We can use this formula:

A = A₀ * 2 ^-t/h      where A  is the amount left after t hours   A0 is the original amount    and h is the half-life in hrs.  ....so we have....

A = 18 * 2 ^-60/15    

A = 18 * 2^-4       

A = 18/ 16   =   9/8  grams 

Press "2nd" first, the "asin" key followed by = sign.

Sodium-24 has a half-life of 15 hours. How much sodium-24 will remain in an 18.0 g sample after 60 hours?

60/15=4 half-lives,

2^-4 X18=1.125 grams of Sodium-24 left after 60 hours.

The % error  is given by :

abs [ True Value - Estimated Value] /  [ True Value]  =

abs [ 499.7 - 500]  / 499.7    =  about .06%

WHAAAAAAA?

Correct if I'm wrong:

(96*7.50)-(96*6)-(1.2*96*0.25)=576/5=115.2

He made $115.2

(parentheses don't change problem, but useful for order)

-7s = 938        divide both sides by -7

s = 938 / -7   =   - 134

-e3.4e^(2-2n)-9=-4  THIS EQUATION HAS ONLY COMPLEX SOLUTION:

Solve for n:
-9-9.24216 e^(2-2 n) = -4

-9-9.24216 e^(2-2 n) = -9-9.24216 e^(2-2 n):
-9-9.24216 e^(2-2 n) = -4

Add 9 to both sides:
-9.24216 e^(2-2 n) = 5

Divide both sides by -9.24216:
e^(2-2 n) = -0.540999

Take reciporicals of both sides:
e^(2 n-2) = -1.84843

Take the natural logarithm of both sides:
2 n-2 = 0.614338+i pi (2 k+1)  for  k element Z

Add 2 to both sides:
2 n = 2.61434+i pi (2 k+1)  for  k element Z

Divide both sides by 2:
Answer: |  n = 1.30717+1/2 i pi (2 k+1)  for  k element Z
 

Is 100^500 bigger or 1000^300?

1000^300=[(100)^1.5]^300=100^450, Therefore

100^500>100^450.

Another way of comparing is to take their logs as follows:

Log:100^500=1,000

Log: 1000^300=900, therefore

1,000>900

goes as following:

10⁰=units (unsure, actualy)

10¹=tens

10²=hundreds

10³=thousands

10⁶⁼millions

10⁹= billions

10¹²=trillions

10¹⁵=quadrillions

10¹⁹=septillions? 

ect. ect.

Reasoning for the answer:

61-(25+16)

=61-41

=20

Easy enough

How can I know that     cos(1/6)pi = cos30 ?

2 DUH

No problem, Shades.....glad it helped.....

Thank you so much! It was extremely helpful and explanatory for me. Thanks again.

2 log₂ x - log₂ (x-1/2) = -log_1/3 3       note  that     - log_1/3 3     actually evaluates to  -[ -1 ]   = 1

So we have

2 log₂ x - log₂ (x-1/2)   = 1       and we can write

log₂ x²  - log₂ ( x - 1/2)   = 1       and by a property of logs  we have

log₂  [ ( x^2 ) / (x - 1/2)]    =  1    and in exponential form we have

2^1  =  ( x^2 ) / (x - 1/2)

2  = ( x^2) / ( x - 1/2)         multiply both sides by  x - 1/2

2( x - 1/2)  = x^2

2x - 1   = x^2       simplify

x^2 - 2x + 1  =  0        factor

(x -1 ) ( x - 1)  = 0      and setting each factor to 0   .....we have that   x = 1

Check that

2 log₂ (1) - log₂ (1-1/2)   = 1 

2 * 0   -  log₂ (1/2)  = 1

0  -  (-1)   = 1

1  =   1

Let me show you in an example.

First, take the denominator and see how many times it goes in the numerator.

Ex. 13/5

5 goes into 13 2 times.

Then, take that number (in this case 2) and make it your whole number.

Ex. 2 13/5

Finally, multiply the denominator by the number of times it fits into the numerator...

Ex. 5*2=10

...and subtract that from the numerator!

Ex.

13-10=3

Finish it off by putting it together!

Ex. 2 3/5

That's great, Hayley!

Let me show you her work...

72/514=approximately 0.14007

0.14007*100=14.007

If you round, you get 14.

Very nice, Riddler and Anonymous4338....5 pts.....!!!!

Okay, let's do this step by step.

First, find the LCD of each.

4/5: 5, 10, 15, 20, 25, 30, 35, 49, 45

2/9: 9, 18, 27, 36, 45

It's 45! 45 is your new denominator.

Multiply the numerator of each fraction by the first denominator of the other.

4*9=36

2*5=10

This is the new numerator. So...

36/45+10/45=a

I think you should be able to figure out the rest. 

4/5=36/45

2/9=10/45

10/45+36/45=46/45

46/45=1 1/45

Thanks, Melody for that answer....

Here's another way to evalute this for    i    raised to any  "n"   positve integer

n mod 4  =  1    →   i

n mod 4  =  2   →   -1

n mod 4  = 3   →   - i

n mod 4  = 4   →    1

So

i^61  =      61 mod 4   = 1    →   i            just as Melody found   !!!

congruent means equal shape and size.

It is like equal but it is used for geometry things.

So two triangles are congruent if they have the same lenght sides and the same angles.

If the sides are the same the angles will be the same anyway. (not tho other way around though:/ )