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
The greatest common factor of 15 and 45 is:<br> 03<br> 5<br> 015<br> 45
harkovskaia [24]

Answer:

15

Step-by-step explanation:

We can find the greatest common factor by listing the factors of the 2 numbers, that is

Factors of 15 are 1, 3, 5, 15

Factors of 45 are 1, 3, 5, 9, 15, 45

The common factors are 1, 3, 5, 15

The greatest common factor is 15

4 0
3 years ago
Solve the system of linear equations. separate the x- and y- values with a coma. 20x=-58-2y
lianna [129]
The best way to solve is by using elimination method.
20x = -58 - 2y
17x = -49 - 2y
Multiply second equation by -1
20x = -58 - 2y
-17x = 49 + 2y
Add equations.
3x = -9 
Divide.
x = -3
Plug in -3 into one of the equations.
17(-3) = -49 - 2y
-51 = -49 - 2y
Add 49 to both sides.
-2 = -2y
Divide.
1 = y
So your solution is (-3, 1).
I hope this helps love! :)

6 0
3 years ago
The perimeter of a rectangular park is 500 feet. The length of the park is 100 feet longer than the width. Find the length of th
lord [1]

Answer:

The length of the park is 175 feet

Step-by-step explanation:

Let us solve the question

∵ The perimeter of a rectangular park is 500 feet

∵ The formula of the perimeter of the rectangle is P = 2(L + W)

∵ L is the length and W is the width

→ Equate the rule of the perimeter by 500

∴ 2(L + W) = 500

→ Divide both sides by 2

∴ L + W = 250 ⇒ (1)

∵ The length of the park is 100 feet longer than the width

→ That means L is W plus 100

∴ L = W + 100 ⇒ (2)

→ Substitute L in (1) by (2)

∵ W + 100 + W = 250

→ Add the like terms

∵ (W + W) + 100 = 250

∴ 2W + 100 = 250

→ Subtract 100 from both sides

∵ 2W + 100 - 100 = 250 - 100

∴ 2W = 150

→ Divide both sides by 2

∴ W = 75

→ Substitute the value of W in (2) to find L

∵ L = 75 + 100 = 175

∴ The length of the park is 175 feet

6 0
3 years ago
PLEASE HELP PLEASE PLEASE PLEASE
sleet_krkn [62]

Answer:

oh no that's tough bro

hope you get through

8 0
2 years ago
What's the answer ? To this problem
Nataliya [291]
The answer is A. You can solve this by plugging the X values from the table into the equation and seeing if you end up with the right Y value.
3 0
3 years ago
Read 2 more answers
Other questions:
  • Evaluate the determinant for the following matrix 1, 4, 4, 5, 2, 2, 1, 5, 5
    8·1 answer
  • PLS ANSWER ASAP FASTTT
    9·2 answers
  • A strawberry farmer needs to water a strawberry patch of 1500 square yards is in the shape of a sector of a circle with a radius
    8·1 answer
  • Can someone help me with this problem please
    7·2 answers
  • A small airplane flies 1015 miles with an average speed of 290 miles per hour. 1.75 hours after the plane leaves, a Boeing 747 l
    6·1 answer
  • Solve for x. Round to the nearest hundredth.
    7·1 answer
  • If a1 = 7 and an = -2an-1 then find the value of a5
    13·1 answer
  • If tanx = 0.75, what is the value of cosx + sinx ?
    9·2 answers
  • Two out of every 5 jelly beans in a bag are green.
    15·2 answers
  • The second side of a triangular deck is 3 feet longer than the shortest side and a third side that is 3 feet shorter than twice
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!