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
Vlada [557]
3 years ago
7

A function y(t) satisfies the differential equation dy dt = y4 − 6y3 + 5y2.

Mathematics
1 answer:
mojhsa [17]3 years ago
8 0

\dfrac{\mathrm dy}{\mathrm dt}=y^4-6y^3+5y^2=y^2(y-1)(y-5)

a. If y(t) is constant, then the derivative 0, which means we would have

y=0\text{ or }y=1\text{ or }y=5

as constant solutions.

Next, we have 4 possible intervals to consider where the derivative doesn't vanish:

  • for t, we have \frac{\mathrm dy}{\mathrm dt}>0 (consider the sign of the derivative for, say, y=-1);
  • for 0, we have \frac{\mathrm dy}{\mathrm dt}>0;
  • for 1, we have \frac{\mathrm dy}{\mathrm dt};
  • and for t>5, we have \frac{\mathrm dy}{\mathrm dt}>0

Taking all these facts together, we see that ...

b. y is increasing on the interval (-\infty,0)\cup(0,1)\cup(5,\infty), and

c. y is decreasing on the interval (1,5).

You might be interested in
Which relation is a function<br>​
DENIUS [597]

What do you mean? Which relation is a function do you mean fraction and if yes then where are the options.

4 0
4 years ago
Can some one please help me!!! I really don't understand and plz explain
igor_vitrenko [27]
Length = l
width = 1/3 of length = l/3

perimeter = 2(l + l/3)
Answer is option B

-----------------------------------
2(l+ l/3) = 56
⇒ 8l/3 = 56
⇒ l = 3*56/8
⇒ l = 21 inch
width = 21/3 = 7inch

Area = 21*7 inch² = 147 inch²
5 0
3 years ago
14 + 35 = 7(2 + ___)
xz_007 [3.2K]

Answer:

5

Step-by-step explanation:

Hope this helps and pls mark me brainliest:)

3 0
3 years ago
Read 2 more answers
What is 4x+3 = 5x <br> :))
Butoxors [25]

Answer:

x = 3

Step-by-step explanation:

4x + 3 = 5x

4x = 5x - 3

4x - 5x = -3

(4 - 5)x = 1x

-1x = -3

x = -1 × (-3)

<u>x</u><u> </u><u>=</u><u> </u><u>3</u>

8 0
3 years ago
Read 2 more answers
Clarissa has just completed her second semester in college. She earned a grade of Upper D in her 4​-hour linear algebra ​course,
adell [148]
Well if they are only talking about grade point if she earned D in all of her 4 classes than it would be a 4 point average but if they are asking about every hour than it would be 14 point credit
4 0
4 years ago
Other questions:
  • A high speed computer printer prints a page in 1/6 of a second. Using this printer, how long would it take to print 30 pages?
    6·1 answer
  • I need help please no one helps me :((
    11·1 answer
  • How do you calculate the bearing?
    13·1 answer
  • Solve the system: <br> 2/x - 3/y =-5; 4/x + 6\y =14
    8·1 answer
  • Which statement is false ?
    6·1 answer
  • Let x and y represent the tens digit and ones digit of a two digit number, respectively. The sum of the digirs of a two digit nu
    10·1 answer
  • 1/2 inch= 3 feet what is the length for 7 inches
    10·2 answers
  • What offer is the best price per square inch pizza?
    11·1 answer
  • - 2.4f + 0.4f - 12-5=
    14·2 answers
  • A dictionary is opened to a random page; the probability that the page is numbered 103.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!