1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zmey [24]
3 years ago
13

A radioactive substance decays exponentially: The mass at time t is m(t) = m(0)ekt, where m(0) is the initial mass and k is a ne

gative constant. The mean life M of an atom in the substance is M = −k [infinity] tekt dt. 0 For a radioactive isotope, the value of k is −0.000192. Find the mean life of the isotope's atom. (Round your answer to one decimal place.) yr

Mathematics
1 answer:
velikii [3]3 years ago
3 0

Answer:

M = 1/0.000121 = 8264.5 years

Step-by-step explanation:

M = − k ∫∞₀ teᵏᵗdt

To obtain this mean life, we'll use integration by parts to integrate the function ∫ teᵏᵗdt

∫udv = uv - ∫ vdu

u = t

du/dt = 1

du = dt

∫ dv = ∫ eᵏᵗdt

v = eᵏᵗ/k

∫udv = ∫ teᵏᵗdt

uv = teᵏᵗ/k

∫ vdu = eᵏᵗ/k

∫ teᵏᵗdt = (teᵏᵗ/k) - ∫eᵏᵗ/k

But, ∫eᵏᵗ/k = (1/k) ∫eᵏᵗ = (1/k²) eᵏᵗ = eᵏᵗ/k²

∫ teᵏᵗdt = (teᵏᵗ/k) - eᵏᵗ/k²

The rest of the calculation is done on paper in the image attached to this question

You might be interested in
Solve x2 + 4x − 4 = 0
hoa [83]

Answer:

third option

Step-by-step explanation:

Given

x² + 4x - 4 = 0 ( add 4 to both sides )

x² + 4x = 4

Using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(2)x + 4 = 4 + 4, that is

(x + 2)² = 8 ( take the square root of both sides )

x + 2 = ± \sqrt{8} = ± 2\sqrt{2} ( subtract 2 from both sides )

x = - 2 ± 2\sqrt{2}

7 0
3 years ago
Read 2 more answers
What's the pattern?<br> 1,2,4,8,16.....
Inessa05 [86]
You have to add the last number to itself. So the next number would be 32 because 16 + 16 equals 32. Then you add 32 + 32 so the next number would be 64
1, 2, 4, 8, 16, 32, 64, 128
7 0
3 years ago
Jason agreed to make 12 payments of $38.50 to buy a new T.V. SO far he has made 8 payment. How much more money does he owe?
alexira [117]

Answer:

154$

Step-by-step explanation:

8 0
2 years ago
A friend of yours was interested in determining whether the news media noticed campus events. Your friend decided to do a conten
anygoal [31]

The inference is that the person will tell the friend that he did manifest coding and he should have recorded the base.

<h3>What is an inference?</h3>

The options are:

He did manifest coding.

He did latent coding.

He should have recorded the base.

He did manifest coding and he should have recorded the base.

It should be noted that an inference simply means the conclusion that can be deduced based on the information given.

In this case, the friend was interested in determining whether the news media noticed campus events and decided to do a content analysis of the local paper.

Therefore, the the person will tell the friend that he did manifest coding and he should have recorded the base.

Learn more about inference on:

brainly.com/question/25280941

#SPJ12

8 0
1 year ago
Read 2 more answers
He collected a total of 120 coins . If ​72 % of the coins he collected were​ foreign, how many other did he​ collect?
dem82 [27]
33 other coins were collected
8 0
2 years ago
Other questions:
  • Which number belongs to the solution set of the equation below? x - 7 = 35 A. 41 B. 28 C. 22 D. 42
    8·1 answer
  • Determine the volume of this prism.
    5·1 answer
  • Bridget bought cupcakes for her sister's birthday party. 80% of the 45 cupcakes had sprinkles on top. How many cupcakes had spri
    11·2 answers
  • Order the following units of a capacity families to greatest gallon paint cup quart
    8·1 answer
  • Find the surface area of the figure below. (attached image)
    14·1 answer
  • Graph the compound inequality on the number line. x 3&lt;=-4 or x&gt;= 3​
    9·1 answer
  • What is the length of the missing leg? help me pleaseee die in 5 mins
    5·1 answer
  • Solve<br> -21 = -9 + 2/3b
    14·1 answer
  • Help im being timed plssss
    13·1 answer
  • How do I graph this linear function <br> x &lt; -1
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!