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Travka [436]
3 years ago
13

If dy / dx = xy2 and x = 1 when y = 1, then y = ?

Mathematics
1 answer:
kykrilka [37]3 years ago
7 0

Answer:

y = \dfrac{2}{3-x^2}

Step-by-step explanation:

Given that:

\dfrac{dy}{dx} = xy^2

and x = 1 when y = 1

<u>by integrating: </u>

first distribute all x variables on one side and all y variables on the other side.

\dfrac{dy}{y^2} = xdx

now integrate both sides

\displaystyle\int {\dfrac{1}{y^2}}\,dy=\displaystyle\int {x} \, dx\\ \dfrac{-1}{y}=\dfrac{x^2}{2}+c

to find the value of c, we can use the conditions given to us that x = 1 when y = 1.

-\dfrac{1}{y} = \dfrac{x^2}{2}+c\\-\dfrac{1}{1} = \dfrac{1^2}{2}+c\\c = -1-\dfrac{1}{2}\\c = -\dfrac{3}{2}

now that we have our c, we can plug it into our integrated expression.

-\dfrac{1}{y} = \dfrac{x^2}{2}-\dfrac{3}{2}

now simply rearrange the equation to make y the subject.

-\dfrac{1}{y} = \dfrac{x^2}{2}-\dfrac{3}{2}\\-y = \dfrac{2}{x^2-3}\\y = \dfrac{2}{3-x^2}

this is the equation of y

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B) f(x)=x(x-4)

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Frances gets 6 paychecks in 12 weeks. how many paychecks does she get in 52 weeks?
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In this question it is important to look at all the information's that are given. Based on those given information's, the answer to the question can be very easily deduced. Now let us concentrate on the problem in hand.
The number of paychecks that Frances gets in 12 weeks = 6
Then
The number of paychecks that Frances gets in 1 week = (6/12)
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The number of paychecks that Frances gets in 52 weeks = (1/2) * 52
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