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cricket20 [7]
2 years ago
5

Element X is a radioactive isotope such that every 9 years, its mass decreases by half. Given that the initial mass of a sample

of Element X is 70 grams, how long would it be until the mass of the sample reached 56 grams, to the nearest tenth of a year?
Mathematics
1 answer:
4vir4ik [10]2 years ago
5 0

Answer:

2.9 years

Step-by-step explanation:

Given that :

Half-life t1/2 = 9 years

Initial mass = I = 70 grams

A = final mass = 56 grams

t = time taken to reach final amount

Using the exponential half life relation :

A = I(0.5)^t/t1/2

56 = 70(0.5)^t/9

56/70 = 0.5^t/9

0.8 = 0.5^t/9

Log 0.8 = log 0.5^t/9

−0.096910 = −0.301029 * t/9

t/9 = 0.096910 / 0.301029

t/9 = 0.3219291

t = 0.3219291 * 9

t = 2.8973619

t = 2.9 years

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    2x + 5            3x + 5                  x + 1
---------------  - -----------------  - -------------------
   x(x - 3)         x (x+3)(x-3)       (x +3)(x - 3)

      (x + 3) (2x + 5)   -   (3x + 5)     -  x ( x + 1)
=  ---------------------------------------------------------
                         x (x+3)(x-3)   

      2x^2 +6x +5x + 15 -3x - 5 -x^2 - x
=  -----------------------------------------------
                         x (x+3)(x-3)      

     x^2 + 7x  + 10 
=  --------------------
      x (x+3)(x-3)     

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

or

      (x +5)(x+2) 
=  --------------------
         x^3 - 9

answer is A. first one


3 0
2 years ago
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