How do I solve 7 1/5 divided by 2 1/15? (Pls show all steps like simplify, common denominator,etc)

Mathematics

2 answers:

Basile [38]3 years ago

5 0

If you scroll up I answered a previous question like this in the same subject

professor190 [17]3 years ago

5 0

Answer:

= 2 106/217

Step-by-step explanation:

7 1/5 / 2 1/15

turn into improper fractions

multiply by denominator and add to numerator

7 1/5 = 7 x 5 + 1

= 35 + 1

= 36

2 1/15 = 2 x 15 + 1

= 30 + 1

= 31

36 / 31

7 15

multiply by the reciprocal

36 x 15 = 540

7 31 217

= 2 106/217

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The half-life of a certain tranquilizer in the bloodstream is 22 hours. How long will it take for the drug to decay to 90% of

nasty-shy [4]

Answer:

It will take approximately 3.34 hours for the drug to decay to 90% of the original dosage

Step-by-step explanation:

As suggested, we use the formula for exponential decay:

$A(t)=A_0\,e^{-k\,t}$

From the given information, the half life of the drug in blood id 22 hours, so that means that it takes that number of hours to go from the initial value $A_0$ , to a final value equal to $A_0/2$ . Using this information we can find the decay rate "k" by solving for this parameter in the formula, and using the natural log function to bring the exponent down:

$A(t)=A_0\,e^{-k\,t}\\\frac{A_0}{2} =A_0\,e^{-k\,*22}\\\frac{A_0}{A_0*2} =e^{-k\,*22}\\\frac{1}{2} =e^{-k\,*22}\\ln(\frac{1}{2})=-k\,*22\\ k=-\frac{ln(\frac{1}{2})}{22} \\k=0.0315$

Now we use this value for the decay rate "k" to calculate how long it would take to decay to 90% of the original dose;

$A(t)=A_0\,e^{-0.0315\,t}\\0.9*A_0} =A_0\,e^{-0.0315\,t}\\\frac{0.9*A_0}{A_0} =e^{-0.0315\,t}\\0.9 =e^{-0.0315\,t}\\ln(0.9)=-0.0315\,t\\ t=-\frac{ln(0.9)}{0.0315} \\t=3.3447\,hours$