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3 years ago

Polynomial of degree 3 with three distinct real zeros and a positive leading coefficient

Mathematics

1 answer:

horsena [70]3 years ago

7 0

Conjugate. i hoped that helped

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Find a solution to the initial value problem, y′′+18x=0,y(0)=5,y′(0)=1.

Serga [27]

We want to find a solution to the initial value problem:

$y'' + 18x = 0 \qquad,\qquad y(0) = 5 \qquad,\qquad y'(0)=1.$

We can start by integrating the equation once:

$\dfrac{\textrm{d}^2 y}{\textrm{d}x^2} + 18 x = 0 \iff \dfrac{\textrm{d}^2 y}{\textrm{d}x^2} = -18 x \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -18\displaystyle\int x\textrm{ d}x \iff \dfrac{\textrm{d}y}{\textrm{d}x}=-18\dfrac{x^2}{2} + C \iff\\\\\iff \dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + C.$

Using the initial condition $y'(0) = 1$ , we can determine the integration constant $C$ :

$\dfrac{\textrm{d}y}{\textrm{d}x}\Big\vert_{x= 0} = 1 \iff -9 \times 0^2 + C = 1 \iff C = 1.$

Therefore, we have:

$\dfrac{\textrm{d}y}{\textrm{d}x} = -9x^2 + 1$

We can now integrate again:

$y(x) = \displaystyle\int\dfrac{\textrm{d}y}{\textrm{d}x}\textrm{ d}x = \int\left(-9x^2+1\right)\textrm{d}x = -9\int x^2\textrm{ d}x + \int\textrm{d}x =\\\\= -9\dfrac{x^3}{3} + x + K = -3x^3 + x + K.$

The integration constant $K$ is determined by using $y(0) = 5$ :

$y(0) = 5 \iff -3 \times 0^3 + 0 + K = 5 \iff K = 5.$

Finally, the solution is:

$\boxed{y(x) = -3x^3 + x + 5}.$

7 0

3 years ago

Please help me answer this!

timofeeve [1]

Answer:

what?

Step-by-step explanation:

6 0

4 years ago

Your new dresser will be 2/5ths larger than your old dresser. Your old dresser can hold 6.25 cubic feet, how much cubic feet wil

marissa [1.9K]

Answer:

8.75 cubic feet

Step-by-step explanation:

Your new dresser will be $\frac{2}{5}^{ths}$ larger than your old dresser.

This means that your new dresser wil be

$1+\dfrac{2}{5}=\dfrac{5+2}{5}=\dfrac{7}{5}$

of your old dresser.

Your old dresser can hold 6.25 cubic feet, so your new dresser can hold

$\dfrac{7}{5}\cdot 6.25=7\cdot 1.25=8.75\ ft^3$

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3 years ago

(5)

cricket20 [7]

no ane boys are not in the club

8 0

3 years ago

What is cos X? picture provided below

olasank [31]

SOH-CAH-TOA
Sine = Opposite over Hypotenuse, Cosine = Adjacent over Hypotenuse and Tangent = Opposite over Adjacent

Hey Dewild,

Remember this for cosign or cos. COS = Adjacent over Hypotenuse

24/26 = 0.92

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3 years ago

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