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
Alex17521 [72]
3 years ago
12

Solve the initial value problem: y'(x)=(4y(x)+25)^(1/2) ,y(1)=6. you can't really tell, but the '1/2' is the exponent

Mathematics
1 answer:
goblinko [34]3 years ago
4 0

Answer:

y(x)=x^2+5x

Step-by-step explanation:

Given: y'=\sqrt{4y+25}

Initial value: y(1)=6

Let y'=\dfrac{dy}{dx}

\dfrac{dy}{dx}=\sqrt{4y+25}

Variable separable

\dfrac{dy}{\sqrt{4y+25}}=dx

Integrate both sides

\int \dfrac{dy}{\sqrt{4y+25}}=\int dx

\sqrt{4y+25}=2x+C

Initial condition, y(1)=6

\sqrt{4\cdot 6+25}=2\cdot 1+C

C=5

Put C into equation

Solution:

\sqrt{4y+25}=2x+5

or

4y+25=(2x+5)^2

y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4}

y(x)=x^2+5x

Hence, The solution is y(x)=\dfrac{1}{4}(2x+5)^2-\dfrac{25}{4} or y(x)=x^2+5x

You might be interested in
What is 1/10 of 6000
solong [7]

Answer: 600

Step-by-step explanation: Cancel the common factor of 10 to get 600.

3 0
3 years ago
I NEED HELP PLZ ASAP , I AM SO STUCK ON THIS.
Bezzdna [24]

Function

d. 4f(t)

=4(t²+9)

=4t²+36

e. (f(t))²+8

=(t²+9)² + 8

= t⁴+18t²+81+8

= t⁴+18t²+89

5 0
2 years ago
Whoever answers correctly gets brainlist.
trapecia [35]

Answer:

0.65

Step-by-step explanation:

Find a common denominator, but whatever you multiply it by, you must take the same number and multiply the numerator as well. I hope that helps- Good luck!

4 0
3 years ago
How many solutions exist for the given equation? 3x(x - 2) = 22 - x
Mila [183]
The solution exist for the given equation are
x=-2
and
x=11/3
5 0
4 years ago
SOLVE
Sauron [17]

Answer:

approximately

1623.6

Step-by-step explanation:

16 1/2%=.165 which is approximately equal to 1/6, so we can just multiply the original number by 6.

7 0
3 years ago
Other questions:
  • Select the correct answer What is the solution for in the equation? 4+ 5x-7 = 10+ 3x-2 * Y Lee R=###​
    13·1 answer
  • Will give brainliest! please answer correctly!
    5·1 answer
  • Triangle town wants to build a school that is equidistant from its three cities L, M, and N. Which construction correctly finds
    14·1 answer
  • A toy rocket is shot vertically into the air from a launching pad 9 feet above the ground with an initial velocity of 88 feet pe
    13·1 answer
  • H ( x ) { − 2 + 3 , i f x < 1 1 /2 x + 1 if x ≥ 1 }
    7·1 answer
  • Find the surface area of a rectangular prism with a height of 16 feet, a width of 10 feet, and a length of 13 feet.
    6·1 answer
  • MathWiz wya? I need some help with this...show your work <3
    13·1 answer
  • Pls help me and no links I am serious
    13·2 answers
  • Hola wiwehfvpadhf{aodjvopasdgvaeffb
    10·1 answer
  • How many minutes are there<br> from 19 to 7 until 17 past 7?
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!