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Vladimir79 [104]
3 years ago
9

Element X decays radioactively with a half life of 14 minutes. If there are 760 grams of Element X, how long, to the nearest ten

th of a minute, would it take the element to decay to 11 grams?
Mathematics
1 answer:
Mkey [24]3 years ago
4 0

Answer:

85.5 minutes

Step-by-step explanation:

The amount of an element that will remain after time t can be expressed as a function of initial amount N0, time t, and half life th as;

Nt = N0 × e^(-λt)

Where;

Decay constant λ = ln(2)/th, substituting into the equation;

Nt = N0 × e^(-ln(2)t/th)

We need to make t the subject of formula;

Nt/N0 = e^(-ln(2)t/th)

ln(Nt/N0) = -ln(2)t/th

t = ln(Nt/N0) ÷ -ln(2)/th

Given;

Initial amount N0 = 760g

Final amount Nt = 11 g

Half life th = 14 minutes

the nearest tenth of a minute, would it take the element to decay to 11 grams can be derived using the formula;

t = ln(Nt/N0) ÷ -ln(2)/th

Substituting the given values;

t = ln(11/760) ÷ -ln(2)/14

t = 85.5 minutes

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By using the concept of uniform rectilinear motion, the distance surplus of the average race car is equal to 3 / 4 miles. (Right choice: A)

<h3>How many more distance does the average race car travels than the average consumer car?</h3>

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s' = (v' - v) · t

Where:

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Please notice that a hour equal 3600 seconds. If we know that v' = 210 mi / h, v = 120 mi / h and t = 30 / 3600 h, then the distance surplus of the average race car is:

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The perimeter of the rectangle is 146 units. What is the length of the longer side?
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we know that

the perimeter of the rectangle is equal to

P=2W+2L

where

P is the perimeter of the rectangle

W is the width of the rectangle

L s the length of the rectangle

In this problem

P=146\ units \\ W=2x\\ L=3x+3

Substitute the values in the formula above

P=2W+2L\\ 146=2*(2x)+2*(3x+3)\\ 73=2x+3x+3\\ 5x=70\\ x=14\ units

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therefore

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the length of the longer side of the rectangle is equal to 45\ units

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