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
olga_2 [115]
3 years ago
13

A mass of 100 grams of a particular radioactive substance decays according to the function m(t)=100e−t850

Physics
1 answer:
AleksandrR [38]3 years ago
8 0

Answer:

After 1023.4 years the mass of the substance will be 30 g.

Explanation:

Hi there!

Let´s write the function (according to what I found on the web):

m(t) = 100e^{-t/850}

We have to find the time "t1" at which the mass of the substance is 30 g. Mathematically:

m(t1) = 30

Then:

30 = 100e^{-t1/850}

Let´s solve the equation for t1. First, divide by 100 both sides of the equation:

0.3 = e^{-t1/850}[/tex]

Apply ln to both sides of the equation:

ln(0.3) = ln(e^{-t/850})

Use the logarithm property: ln (aᵇ) = b ln(a)

ln(0.3) = -t/850 · ln (e)             (ln (e) = 1)

ln(0.3) = -t/850

850 ln(0.3) = -t

t = -850 ln(0.3)

t = 1023.4

After 1023.4 years the mass of the substance will be 30 g.

You might be interested in
Two astronauts, each with a mass of 50 kg, are connected by a 7 m massless rope. Initially they are rotating around their center
kiruha [24]

Answer:

The angular  velocity is w_f =  1.531 \ rad/ s

Explanation:

From the question we are told that

     The mass of each astronauts is  m =  50 \ kg

      The initial  distance between the two  astronauts  d_i  =  7 \  m

Generally the radius is mathematically represented as r_i  =  \frac{d_i}{2} = \frac{7}{2}  =  3.5 \  m

      The initial  angular velocity is  w_1 = 0.5 \  rad /s

       The  distance between the two astronauts after the rope is pulled is d_f =  4 \  m

Generally the radius is mathematically represented as r_f  =  \frac{d_f}{2} = \frac{4}{2}  =  2\  m

Generally from the law of angular momentum conservation we have that

           I_{k_1} w_{k_1}+ I_{p_1} w_{p_1} = I_{k_2} w_{k_2}+ I_{p_2} w_{p_2}

Here I_{k_1 } is the initial moment of inertia of the first astronauts which is equal to I_{p_1} the initial moment of inertia of the second astronauts  So

      I_{k_1} = I_{p_1 } =  m *  r_i^2

Also   w_{k_1 } is the initial angular velocity of the first astronauts which is equal to w_{p_1} the initial angular velocity of the second astronauts  So

      w_{k_1} =w_{p_1 } = w_1

Here I_{k_2 } is the final moment of inertia of the first astronauts which is equal to I_{p_2} the final moment of inertia of the second astronauts  So

      I_{k_2} = I_{p_2} =  m *  r_f^2

Also   w_{k_2 } is the final angular velocity of the first astronauts which is equal to w_{p_2} the  final angular velocity of the second astronauts  So

      w_{k_2} =w_{p_2 } = w_2

So

      mr_i^2 w_1 + mr_i^2 w_1 = mr_f^2 w_2 + mr_f^2 w_2

=>   2 mr_i^2 w_1 = 2 mr_f^2 w_2

=>   w_f =  \frac{2 * m * r_i^2 w_1}{2 * m *  r_f^2 }

=>    w_f =  \frac{3.5^2 *  0.5}{  2^2 }

=>   w_f =  1.531 \ rad/ s

       

3 0
2 years ago
The ________ on the axis (c2) forms a pivot point with the atlas (c1) that allows you to nod a "no."
grandymaker [24]
The dens or the odontoid process of the axis or the second cervical spine forms a pivot point with the atlas or the first cervical vertebrae that is responsible for the nodding and the rotational movements of the head. This is reinforced by ligaments and the atlanto-occipital joint that allows the head to make a nodding or up and down movement on the vertebral column.
3 0
3 years ago
The gravitational force strength on the moon is 1.63N/Kg if the rock on the moon weighs 200N how much does the same rock weigh o
FromTheMoon [43]

m = Q(on moon) * G(on moon) = 200N * 1.63N/kg = 326kg

Q(Earth)= g * m = 10m/s2 * 326kg = 3260N

8 0
2 years ago
a lump of putty and a rubber ball have equal mass. both are thrown with equal speed against a wall. the putty sticks to the wall
RUDIKE [14]
The bouncy ball experiences the greater momentum change.

To understand why, you need to remember that momentum is actually
a vector quantity ... it has a size AND it has a direction too.

The putty and the ball have the same mass, and you throw them
with the same speed.  So, on the way from your hand to the wall,
they both have the same momentum.
Call it " M in the direction toward the wall ".

After they both hit the wall:

-- The putty has zero momentum.
    Its momentum changed by an amount of  M .

-- The ball has momentum of " M in the direction away from the wall ".
    Its momentum changed by an amount of  2M .
5 0
3 years ago
Read 2 more answers
How do the prefixes micro,<br> nano and pico relate to each<br> other?
In-s [12.5K]

Answer:

because they are same and their properties

8 0
3 years ago
Other questions:
  • Which of the follwoing is not an example of an abiotic factor?
    11·2 answers
  • An ostrich can run at a speed of 43 mi/hr. How much ground can an ostrich cover if it runs at this speed for 15 minutes? (Hint:
    8·1 answer
  • Which is a consequence of the third law of thermodynamics Energy is not always conserved. Engines cannot discharge waste heat. H
    13·2 answers
  • What is the calculation for elastic potential?
    12·1 answer
  • Which produces more gravitational force on your textbook: you or the earth?
    12·1 answer
  • 9<br>How can you prove that air has weight​
    12·2 answers
  • You toss a rock of mass mm vertically upward. Air resistance can be neglected. The rock reaches a maximum height hh above your h
    13·2 answers
  • An early submersible craft for deep-sea exploration was raised and lowered by a cable from a ship. When the craft was stationary
    6·1 answer
  • What is the mass of a vehicle that has 50,000 N and 25M/S/S
    9·1 answer
  • Suppose the battery in a clock wears out after moving thousand coulombs of charge through the clock at a rate of 0.5 Ma how long
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!