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Alborosie
4 years ago
12

What is equivalent expression 9y+y

Mathematics
1 answer:
andrew11 [14]4 years ago
4 0

Answer:

10y

Step-by-step explanation:

9y+y=

10y

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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
State the slope and the y- intercept for the graph of 2x + y = 3.
Ksenya-84 [330]
We need to put ur equation in y = mx + b form ...and  the m will be ur slope and the b will be ur y int
so basically, we solve for y...

2x + y = 3....subtract 2x from both sides
y = -2x + 3

y = mx + b
y = -2x + 3......slope(m) = -2 and y int (b) = 3 <==
4 0
4 years ago
Please answer asap!! <br><br> write this in standard form: x^2+y^2+2x-18y+18=0
cricket20 [7]

Answer: x^2+y^2+2x-18y+18=0 in standard form is (x+1)^2+(y-9)^2=64

7 0
3 years ago
X + 2y = 10
Crazy boy [7]

Answer:

(-12,11)

Step-by-step explanation:

x + 2y = 10

3x + 4y = 8

(-2)x + (-2)2y = (-2)10

3x    + 4y       = 8

-2x - 4y = -20

3x  + 4y = 8

Add to eliminate:

x = -12

Substitute x to solve y:

x + 2y = 10

(-12) + 2y = 10

-12 + 2y = 10

2y = 10 + 12

2y = 22

y = 22 ÷ 2

y = 11

Check:

x + 2y = 10

(-12) + 2(11) = 10

-12 + 22 = 10

10 = 10

8 0
3 years ago
Read 2 more answers
Which of the following numbers is rational?
Viefleur [7K]

Answer:

Step-by-step explanation:

C:27

Plzz give me brainliest

8 0
3 years ago
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