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
luda_lava [24]
3 years ago
12

If dy/dx equals xy squared and if y = 1 when x = 0, then when y = 3, x is equal to?

Mathematics
2 answers:
Ymorist [56]3 years ago
5 0
\displaystyle
\dfrac{dy}{dx}=xy^2\\
dy=xy^2 \, dx\\
\dfrac{1}{y^2}\, dy=x\, dx\\
\int \dfrac{1}{y^2}\, dy=\int x\, dx\\
-\dfrac{1}{y}=\dfrac{x^2}{2}+C\\\\
-\dfrac{1}{1}=\dfrac{0^2}{2}+C\\
C=-1\\\\-\dfrac{1}{3}=\dfrac{x^2}{2}-1\\
-2=3x^2-6\\
3x^2=4\\
x^2=\dfrac{4}{3}\\
x=\sqrt{\dfrac{4}{3}} \vee x=-\sqrt{\dfrac{4}{3}}\\
x=\dfrac{2}{\sqrt3} \vee x=-\dfrac{2}{\sqrt3}\\
x=\dfrac{2\sqrt3}{3} \vee x=-\dfrac{2\sqrt3}{3}




S_A_V [24]3 years ago
4 0
This is a separable differential equation, so let's start of there. Let's separate the variables to their own side with the respective differentials:
\frac{dy}{dx} = xy^2
dy = (xy^2) dx
\frac{1}{y^2} dy = x dx

Let's integrate both sides (it's separable, so we can do this):
\int\ { \frac{1}{y^2} } \, dy =  \int\ {x} \, dx
- \frac{1}{y} =  \frac{x^2}{2} + C

Now, let's plug in the values we are given to find the constant "C":
- \frac{1}{1}  =\frac{0^2}{2}+C
-1 = C

Let's rewrite the equation, with C in it, then solve for x because we need to ultimately find x:
- \frac{1}{y}  = \frac{x^2}{2} - 1
x =  \sqrt{2(- \frac{1}{y}+1)}

Let's plug in y = 3 and solve for x:
x = \sqrt{2(- \frac{1}{3}+1)} = \sqrt{ 2( \frac{2}{3}) } = \sqrt{ \frac{4}{3} }

Let's simplify and rationalize the denominator:
x =  \sqrt{ \frac{4}{3}} = 2 \sqrt{ \frac{1}{3}} = 2  \frac{ \sqrt{3} }{3}

So, your answer is D.

You might be interested in
Find the number of bricks to be laid in a square path of side 18cm if the side of each square bricks is 3cm
AlladinOne [14]

Answer:

36 bricks

Step-by-step explanation:

We are given;

  • Length of the square path as 18 cm
  • Length of the square brick as 3 cm

We are required to determine the number of bricks that would be laid on the square path.

Number of bricks = Area of the path ÷ area of one brick

Area of a square = l²

Therefore;

Area of the square path = (18 cm)²

                                        = 324 cm²

Area of square brick = (3 cm)²

                                   = 9 cm²

Therefore;

Number of bricks = 324 cm² ÷ 9 cm²

                             = 36 bricks

7 0
3 years ago
An angle measures 76° less than the measure of a complementary angle what is the measure of each angle
sergij07 [2.7K]

Answer:

0.86969

Step-by-step explanation:

1 : 26 soln 1 ÷ 26 1 ÷ 685 now ans 0.86969 the

5 0
3 years ago
If you are given a 2% raise and the inflatoin is 3%, you are
lozanna [386]
Making less money in today’s dollars (option c)
6 0
3 years ago
What ratio is equal to 30/75?
Diano4ka-milaya [45]
It would be: 30/75 = 6/15 = 2/5

So, it's reduced & most simple form is 2/5

Hope this helps!
8 0
3 years ago
PLEASE HELP ASAP<br> find JL
san4es73 [151]

Answer:

7

Step-by-step explanation:

3 0
3 years ago
Other questions:
  • What order do these numbers go in: <br> 0.7, 85% and 4/5
    14·1 answer
  • a profit of 24% was made when a book was sold for 34.10$ find the selling price that would have given a profit of 28%​
    7·2 answers
  • {15÷[(6+9)÷5]+3}= show work please
    11·1 answer
  • The answer choices below represent different hypothesis tests. Which of the choices are one-tailed tests? Select all correct ans
    9·1 answer
  • Solve. -15 = -6n – 3 + 6
    15·2 answers
  • Stuart paid $48.00 for a new tennis racket, which was 64% of the original price.
    10·2 answers
  • What is 2.7 kg in g. i need a simple answer
    12·1 answer
  • Whats 4x10^6 in standard form? for brainlist!
    10·2 answers
  • -3(x + 6) idk what the answer is. ​
    10·1 answer
  • Please help !!!!!!!!!!!!
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!