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3 years ago

Find the solution to the initial value problem (1 + x^{5}) y' + 5 x^{4} y = 5 x^{8}

1 answer:

8 0

$(1+x^5)y'+5x^4y=5x^8$
$\bigg((1+x^5)y\bigg)'=5x^8$
$(1+x^5)y=5\displaystyle\int x^8\,\mathrm dx$
$(1+x^5)y=\dfrac59x^9+C$
$y=\dfrac{5x^9+C}{9(1+x^5)}$

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AleksandrR [38]

Answer: 57 ft

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2 years ago

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What is the directrix of the parabola defined by `(1)/(4)(y + 3) = (x − 2)^2`?

Sauron [17]

The directrix of the parabola is $y = \frac {-49}{16}$

<h3>How to determine the equation of the directrix?</h3>

The parabola equation is given as:

$\frac 14(y + 3) = (x -2)^2$

A parabola is represented as:

$4p(y - k) =(x -h)^2$

By comparing both equations, we have:

4p = 1/4 ==> p = 1/16

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The directrix is represented as:

y = k - p

So, we have:

$y = -3 - \frac 1{16}$

Take the LCM

$y = \frac {-16 * 3- 1}{16}$

Evaluate

$y = \frac {-49}{16}$

Hence, the directrix of the parabola is $y = \frac {-49}{16}$

Read more about parabola at:

brainly.com/question/1480401

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1 year ago

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Mama L [17]

Answer:

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3 years ago

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Mumz [18]

Answer:

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Step-by-step explanation:

We need to calculate the slope of each of the given sets of points until we find the set associated with a slope of 3/4:

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