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Naddika [18.5K]
3 years ago
15

A toxic radioactive substance with a density of 9 milligrams per square centimeter is detected in the ventilating ducts of a nuc

lear processing building that was used 55 years ago. If the​ half- life of the substance is 20 ​years, what was the density of the substance when it was deposited 55 years​ ago?
Mathematics
2 answers:
Nutka1998 [239]3 years ago
5 0
<span>60.5 milligrams per square centimeter First, determine how many half lives have expired by dividing the time by the half-life. So: 55/20 = 2.75 That means that only 2^(-2.75) = 0.148650889 = 14.8650889% of the original substance remains. So just divide the amount remaining by 0.148650889 to get the original amount. 9 / 0.148650889 = 60.5445419 So originally, there was 60.5 milligrams per square centimeter 55 years ago.</span>
omeli [17]3 years ago
5 0

Answer:

<em>The density of the substance when it was deposited 55 years​ ago was </em><em>60.54 mg/cm³</em>

Step-by-step explanation:

The exponential function for growth and decay is,

y(t)=a(1\pm r)^t

where,

y(t) = the amount after time t

a = initial amount

r = rate of change

t = time period

+ is used for growth and - is used for decay.

As this is the case of decay, so the function becomes,

y(t)=a(1- r)^t

Given,

y(55) = 9 mg/cm³

r = 50% = 0.5  (as the substance is getting halved)

t = \dfrac{55}{20} = 2.75   (as the half life is 20 years and we have convert time in terms of half life)

Putting the values,

\Rightarrow 9=a(1- 0.5)^{2.75}

\Rightarrow 9=a(0.5)^{2.75}

\Rightarrow a=\dfrac{9}{(0.5)^{2.75}}

\Rightarrow a=60.54\ mg/cm^3

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3 years ago
A convertible is traveling at 45 miles per hour, and its wheels have a diameter of 48 inches. How many complete revolutions do t
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To answer this question you will need to know how many inches the car travels Per minute.

1. To find this out you will first divide 45 miles by 60 to get the number of miles per minute.

The convertible travels 0.75 mi./min.

2. Next you will convert this number of miles to inches.

There are 63,360 inches per mile.

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7 0
3 years ago
Read 2 more answers
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TEA [102]

Based on the data given, the length of line segment AC is 2.29

<h3>What is the length of side AC?</h3>

Based on the given data:

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  • AB=3
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The triangle ABC is an isosceles triangle.

The line segment AC is the hypotenuse of the the triangle ACD.

The length of AD = 3/2

AC = \sqrt{(\sqrt{3)^{2}} + (\frac{3}{2})^{2}}= 2.29

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An expression for the total cost of the daycare for Lucy's dog this week is T = 3F + 2H and the total cost is equal to $114.

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In this exercise, you're required to write an expression for the total cost of the daycare for Lucy's dog this week. Thus, we would assign a variable to the cost for full-day and half-day day care as follows:

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