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
Delicious77 [7]
3 years ago
5

Solve the equation. StartFraction dy Over dx EndFraction equals5 x Superscript 4 Baseline (1 plus y squared )Superscript three h

alves An implicit solution in the form ​F(x,y)equalsC is nothingequals​C, where C is an arbitrary constant.
Mathematics
1 answer:
dangina [55]3 years ago
5 0

Answer:

Step-by-step explanation:

To solve the differential equation

dy/dx = 5x^4(1 + y²)^(3/2)

First, separate the variables

dy/(1 + y²)^(3/2) = 5x^4 dx

Now, integrate both sides

To integrate dy/(1 + y²)^(3/2), use the substitution y = tan(u)

dy = (1/cos²u)du

So,

dy/(1 + y²)^(3/2) = [(1/cos²u)/(1 + tan²u)^(3/2)]du

= (1/cos²u)/(1 + (sin²u/cos²u))^(3/2)

Because cos²u + sin²u = 1 (Trigonometric identity),

The equation becomes

[1/(1/cos²u)^(3/2) × 1/cos²u] du

= cos³u/cos²u

= cosu

Integral of cosu = sinu

But y = tanu

Therefore u = arctany

We then have

cos(arctany) = y/√(1 + y²)

Now, the integral of the equation

dy/(1 + y²)^(3/2) = 5x^4 dx

Is

y/√(1 + y²) = x^5 + C

So

y - (x^5 + C)√(1 + y²) = 0

is the required implicit solution

You might be interested in
How do you make the colored lines short enough to make a "K"?
earnstyle [38]
Hmmm wait let me try to do it
8 0
3 years ago
Help me with khan geometry. (Explain or give answer no link to answer thx)
NikAS [45]

Answer:

\boxed{\sf 200\pi}

Step-by-step explanation:

We know that the volume of a cone:-

\boxed{\sf  \pi r^2\cfrac{h}{3}}

(r = 10) (h = 6)

\sf \pi \times 10^2\times\cfrac{6}{3}

<u>Divide numbers:-</u>

\sf \cfrac{6}{3}=\boxed{2}

\sf 10^2\times \:2\pi

\sf 100\times \:2\pi

<u>Multiply numbers:-</u>

\boxed{\sf 200\pi}

Therefore, your answer is 200π³

We could also multiply 200 by 3.14 which will give you 628 units³.

7 0
2 years ago
SOLVING INEQUALITIES UNIT PORTFOLIO
noname [10]

Answer:

Step-by-step explanation:

I don't really know sorry I am not smart I only sign up to see the answers

6 0
2 years ago
Jill collected a total of 19 gallons of honey. If she distributed all of the honey equally between 9 jars how much will be in ea
Ratling [72]
There would be 2g in each jar
8 0
3 years ago
Which of the following is NOT a way to determine if a piece of art is a reproduction or an original?
sergij07 [2.7K]

Answer:

its either family history or morellian analysis , im not sure

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Other questions:
  • Simplify the expression and write without negative exponents:
    9·1 answer
  • Find the qoutient of 24/8
    11·2 answers
  • PLEASE HELP, URGENT!!
    12·1 answer
  • Which answer is the equation of the line represented in function notation?
    7·1 answer
  • at 12pm there are 855 people in the zoo by 5pm 4/5 of the children have left and ³/₄ of the adults have left. There are now 36 m
    6·1 answer
  • If f(x) = x-3/x, g(x) = x+3, and h(x) = -2x+1, what is (gohof)(x)
    11·1 answer
  • How many quart are 8/1/4 gallons
    11·1 answer
  • A 20ft ladder is leaning against a building. If the base of the ladder is 6ft from the base of the building. What is the angle o
    9·1 answer
  • Determine what type of model best fits the given situation: A. none of these B. exponential C. linear D. quadratic
    5·1 answer
  • F(x)=cos(x). Find the x-intercepts of f(x) on [0, 2).
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!