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
7

Normalize the equations

Physics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer:

Solution is in explanation

Explanation:

part a)

For normalization we have

\int_{0}^{\infty }f(x)dx=1\\\\\therefore \int_{0}^{\infty }ae^{-kx}dx=1\\\\\Rightarrow a\int_{0}^{\infty }e^{-kx}dx=1\\\\\frac{a}{-k}[\frac{1}{e^{kx}}]_{0}^{\infty }=1\\\\\frac{a}{-k}[0-1]=1\\\\\therefore a=k

Part b)

\int_{0}^{L }f(x)dx=1\\\\\therefore Re(\int_{0}^{L }ae^{-ikx}dx)=1\\\\\Rightarrow Re(a\int_{0}^{L }e^{-ikx}dx)=1\\\\\therefore Re(\frac{a}{-ik}[\frac{1}{e^{ikx}}]_{0}^{L})=1\\\\\Rightarrow Re(\frac{a}{-ik}(e^{-ikL}-1))=1\\\\\frac{a}{k}Re(\frac{1}{-i}(cos(-kL)+isin(-kL)-1))=1

\frac{a}{k}Re(\frac{1}{-i}(cos(-kL)+isin(-kL)-1))=1\\\\\frac{a}{k}Re(icos(-kL)+sin(kL)+\frac{1}{i})=1\\\\\frac{a}{k}sin(kL)=1\\\\a=\frac{k}{sin(kL)}

You might be interested in
Plz help i'm desperate! Why are all people on Earth members of the same biological Species?
Alex Ar [27]

Answer:

D.) All people can mate with one another and have children

Explanation:

7 0
3 years ago
A mass M suspended by a spring with force constant k has aperiod T when set into oscillations on Earth. Its period on Mars,whose
olchik [2.2K]

Answer:

C)T

Explanation:

The period of a mass-spring system is:

T=2\pi\sqrt\frac{m}{k}

As can be seen, the period of this simple harmonic motion, does not depend at all on the gravitational acceleration (g), neither the mass nor the spring constant depends on this value.

6 0
3 years ago
HELPPpPpPpPpPp!!!! ASAP !!!
DENIUS [597]

Answer:

50 N

Explanation:

8 0
2 years ago
Density of water is 1000 kg/m^3. What will be the volume of 35000 kg water?
d1i1m1o1n [39]
Volume = mass/density
Volume = 35000/1000
Volume = 35m^3
8 0
2 years ago
The weight of a block on the inclined plane is 500 N and the angle of incline is 30 degrees. What is the magnitude of the force
yanalaym [24]

Answer:

250 N

433 N

Explanation:

N = Normal force by the surface of the inclined plane

W = Weight of the block = 500 N

f = static frictional force acting on the block

Parallel to incline, force equation is given as

f = W Sin30

f = (500) Sin30

f = 250 N

Perpendicular to incline force equation is given  

N = W Cos30

N = (500) Cos30

N = 433 N

3 0
3 years ago
Other questions:
  • What is the mass number of a potassium atom that has 20 neutrons
    5·1 answer
  • A night-light uses 3 W.If the voltage is 120 V, what is the current? A.0.025A B.40 A C.360A D.0.25A
    13·1 answer
  • In the reaction C6H12 + ________ O2----> 6H20 + 6CO2, what coefficient should be placed in front of 02 to balance the reactio
    15·2 answers
  • PLZZ HELP <br> Explain how you can tell the difference between a physical and a chemical change.
    9·1 answer
  • A careful photographic survey of Jupiter's moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to
    9·1 answer
  • 2)
    10·1 answer
  • A 1kg object loses 20 j of gpe as it falls how far does it fall
    12·1 answer
  • A body floats at a volume of 2/5 when it is placed in oil, how dense the object is ....s=900km/m3​
    10·1 answer
  • Tell me the answer please
    11·2 answers
  • A race car completes race in 10 minutes. Its average speed is 200km/hr. How long is the racetrack?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!