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
Karolina [17]
3 years ago
6

Consider the differential equation dy/dx = (y - y^2)/x.

Biology
1 answer:
Vika [28.1K]3 years ago
7 0
We need to show that y = x/(x + c) is a solution of dy/dx = (y - y^2)/x. Then, 

<span>dy/dx = ((x + c) * 1 - x * 1)/(x + c)^2 </span>
<span>= (x + c - x)/(x + c)^2 </span>
<span>= c/(x + c)^2 </span>

<span>and </span>

<span>(y - y^2)/x = (x/(x + c) - x^2/(x + c)^2)/x </span>
<span>= (x(x + c) - x^2)/(x(x + c)^2) </span>
<span>= (x^2 + cx - x^2)/(x(x + c)^2) </span>
<span>= cx/(x(x + c)^2) </span>
<span>= c/(x + c)^2 </span>

<span>which proves the equality. </span>
You might be interested in
What is fusion and how does it relate to e=mc squared?
trasher [3.6K]
E = mc2 Meaning

At the beginning of the 20th century, the notion of mass underwent a radical revision. Mass lost its absoluteness. One of the striking results of Einstein’s theory of relativity is that mass and energy are equivalent and convertible one into the other. Equivalence of the mass and energy is described by Einstein’s famous formula E = mc2. In words, energy equals massmultiplied by the speed of light squared. Because the speed of light is a very large number, the formula implies that any small amount of matter contains a very large amount of energy. The mass of an object was seen to be equivalent to energy, to be interconvertible with energy, and to increase significantly at exceedingly high speeds near that of light. The total energy of an object was understood to comprise its rest mass as well as its increase of mass caused by increase in kinetic energy.

In special theory of relativity certain types of matter may be created or destroyed, but in all of these processes, the mass and energy associated with such matter remains unchanged in quantity. It was found the rest mass an atomic nucleus is measurably smaller than the sum of the rest masses of its constituent protons, neutrons and electrons. Mass was no longer considered unchangeable in the closed system. The difference is a measure of the nuclear binding energy which holds the nucleus together. According to the Einstein relationship (E = mc2) this binding energy is proportional to this mass difference and it is known as the mass defect.

7 0
2 years ago
All I ask is for ☝️one favor please. Describe how limiting factors has an impact on population of species
andrew-mc [135]

Answer: It can decrease or increase a population of species.

Explanation: Limiting factors include the availability of food, water, shelter, and etc. When a population of species are limited in any of these, they either move or adapt to their environment. So, population tends to decrease. The population that may finds an abundance of resources will find that their numbers tend to increase. This cycle is repeated over and over again.

Hope this helps!!!

7 0
3 years ago
HELPPP ASAPPPP PLEASSSEEEEEEE
mezya [45]
I think the answer is D) Precipitation. Hope this helps!! Please mark me Brainiliest!!
4 0
2 years ago
How do organisms use different types of carbon compounds?
fgiga [73]
<span>Carbon is the building blocks of all living molecules. With the ability to form carbon-carbon bonds, many different compounds formed into different structures can be used for different purposes such as macromolecules.  </span>
6 0
3 years ago
use the base pairing rules to write the sequence that would pair with the following sequence: Agatcct
lukranit [14]

Answer:

TCTAGGA

Explanation:

The deoxyribonucleic acid (DNA) molecule consists of two single-strands, which are composed of four different types of nucleotide bases: Adenine (A), Thymine (T), Guanine (G) and Cytosine (C). These two DNA strands run in an anti-parallel direction to each other. According to the base-pairing rules, Adenine always pairs with Thymine, while Guanine always pairs with Cytosine. In DNA, Thymine and Adenine form two hydrogen bonds between them, while Guanine and Cytosine form three hydrogen bonds between them.

8 0
2 years ago
Other questions:
  • ATP Has phosphate,and ADP has
    6·1 answer
  • after light excites electrons and they leave Photosystem II to travel down the first electron transport chain. How are these ele
    6·1 answer
  • Name the journal that regularly publishes research articles dealing with exercise physiology.
    8·1 answer
  • Total these measurements. Your answer should indicate the proper accuracy. Include units.
    7·1 answer
  • A plant using the sun to grow leaves; this is an example of
    13·2 answers
  • An energy pyramid is a graphical model of energy flow in a community. The different levels represent different groups of organis
    8·2 answers
  • What influences the path that surface currents take?
    6·2 answers
  • It was found that the C4 protein promotes synaptic pruning during brain development in the teenage years. This is a normal proce
    11·1 answer
  • For your club’s fundraiser, you decided to hold a bake sale. In order to make bakery items, you had to purchase 12 pounds of sug
    5·1 answer
  • In the early 19th century capturing merchant ships as prizes of war was the primary purpose of what navy vessels?
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!