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aksik [14]
3 years ago
5

Answer asap thank you?!!!!! 1.

Mathematics
2 answers:
Lorico [155]3 years ago
8 0

Answer:

b

Step-by-step explanation:

i just did it

ale4655 [162]3 years ago
8 0

Answer:

Either B or D is my guess

Step-by-step explanation:

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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
Find the distance between the two points rounding to the nearest tenth (if necessary).
Evgesh-ka [11]

Answer:

approximately 8.5

Step-by-step explanation:

So you can use the distance formula: \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ which is derived from the Pythagorean theorem because normally x2-x1 would kind of give the distance length between x2 and x1 except sometimes it would be negative which wouldn't make much sense right? but it doesn't matter because it's being squared so the value ultimately becomes positive, and the same thing goes for the y-value. the distance between x2 - x1 really represents the base and y2-y1 represents the height and then adding them together gives the hypotenuse squared which is why you take the square root over the entire thing to find the distance, since the hypotenuse is the shortest distance between two points

Now all you have to do is plug the values in to get

\sqrt{(-7 - (-4))^2 + (-8 - 0)^2}\\\sqrt{(-3)^2 + (-8)^2}\\\sqrt{9 + 64}\\\sqrt{73}\\distance \approx 8.5

5 0
2 years ago
Find x in the following figure
Sloan [31]
The answer is 125. Hope it helps you
3 0
3 years ago
Read 2 more answers
(08.05 MC)
MissTica

Answer:

The rotation of the rectangle, of area 12 squared units, about y-axis produces a cylinder, with a volume of 48\pi cubic units.

Step-by-step explanation:

Rotation about x-axis or y-axis at an angle requires some general rules. When a 2D figure is rotated about a line a 3d figure would be produced. This can be done through a process called solid of revolution.

From the question, connecting the given coordinates produces a rectangle with a length of 4 units and width 3units.

Area of the rectangle = Length × width

                                   = 4 × 3

                                   = 12 square units

The required rule for rotation of a figure about y-axis is: (x, y) → (-y, x).

If the given rectangle is rotated about y-axis, a cylinder would be formed.

The volume of the cylinder = V = \pir^{2}h

where: r = 4 units and h = 3 units.

                V = \pi × (4)^{2} × 3

                   = 48\pi cubic units

Therefore, the rotation of the rectangle of area 12 squared units produces a cylinder with volume of 48\pi cubic units.

3 0
3 years ago
What is the value of n
Hunter-Best [27]

Answer:

B) n = 6

Step-by-step explanation:

4n + 12 = 8n - 12

Combine like terms

24 = 4n

n = 6

5 0
3 years ago
Read 2 more answers
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