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]
2 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]2 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]2 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
Solve for x.<br><br> 3x - 13 = 2<br><br> (SHOW YOUR WORK)
Eddi Din [679]

3x-13=2

move -13 to the other side

sign changes from -13 to +13

3x-13+13=2+13

3x=2+13

3x=15

divide both sides by 3 to get x by itself

3x/3=15/3

cross out 3 and 3, divide by 3 and then becomes 1*1*x=x

x=15/3

x=5

answer:

x=5

7 0
3 years ago
Regular hexagon FGHIJK shares a common shares a common center with square ABCD on a coordinate plane .
timurjin [86]

Answer:

<h3>"The answer is the yellow lines in the attached figure. </h3>

Step-by-step explanation: As shown in the attached figure, regular hexagon FGHIJK and square ABCD shares common centre on the co-ordinate plane and AB || FG.

We are to find the line across which the combined figure will reflect onto itself.

In the attached figure, we see two lines which are yellow in colour. We can easily detect that the figure will be reflected onto itself if these two lines acts as a mirror separately.

Hence these yellow lines are the required lines."

<h3><u>Hope this helps!</u></h3>

6 0
2 years ago
How do you write 5 out of 6 in a fraction. Show how you got the answer.
antiseptic1488 [7]

Answer:

5/6

Step-by-step explanation:

bro ok this it ok okik

6 0
2 years ago
Read 2 more answers
Kiran scored 223 fewer points in a computer game than Tyler. Kiran scored 409 points. Which equation would Kiran use to determin
LenKa [72]

Answer:

The equation is:

409 = T - 223

And the solution is:

T = 632

Step-by-step explanation:

Given

Represent Kiran with K and Tyler with T

Kiran score is represented as:

K = 409

Also, Kiran scored 223 less than Tyler.

This is represented as:

K = T - 223

Substitute 409 for K

409 = T - 223

Make T the subject

T = 409 +223

T = 632

5 0
2 years ago
Find the 5th term in the geometric sequence, given the first term of 5 and common ratio of -3
Archy [21]

Answer:

5-3-3-3-3-3= -10

7 0
2 years ago
Other questions:
  • Estimate the sum to the nearest tenth: (-2.678) + 4.5 + (-0.68)
    7·2 answers
  • There are 50 students in the fifth grade at clark school one day 20% of them were absent how many fifth graders were in school t
    7·2 answers
  • Someone help me and remember to show your work so I know how to do it!
    13·1 answer
  • Tim has 30 jellybeans, with equal numbers of three flavors—raspberry, pineapple, and orange. He likes raspberry the best. So far
    5·2 answers
  • The width of a rectangle is 5 times the length. If the perimeter is 72, find the dimensions of the rectangle.
    10·1 answer
  • The area of a plot of land is 2496 square meters. A small part of the land is fenced. The ratio of the area of the plot of land
    9·1 answer
  • A particular style of sunglasses costs the retailer $70 $⁢70 per pair. At what price should the retailer mark them so he can sel
    14·1 answer
  • HELP ME PLZ AND I WILL SHOW YOU MY KITTTTY
    15·1 answer
  • A shop sells bag of peanuts for two dollars and a bag of walnuts for five dollars at nine bags of purchase for total cost of $36
    7·1 answer
  • Simplify (ab)2 + (b3 - a2) if a = -2 and b = 4
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!