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2 years ago

(2x^2+3x-8)+(3x^2+9x+17)-(5x^2-15)

Mathematics

1 answer:

Lelechka [254]2 years ago

6 0

Answer:

12(x+2)

Step-by-step explanation:

(2x^2+3x-8)+(3x^2+9x+17)-(5x^2-15)

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Solve the following differential equation: y" + y' = 8x^2

PtichkaEL [24]

Answer:

$y=y_p+y_h = \frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$

Step-by-step explanation:

Let's find a particular solution. We need a function of the form $y= ax^3+bx^2+cx+d$ such that

$y'= 3ax^2+2bx+c$ and

$y''= 6ax+2b$

$y'+y''= 3ax^2+2bx+c+6ax+2b = 3ax^2+x(2b+6a)+(c+2b) = 8x^2$

then, 3a= 8, 2b+6a =0 and c+2b = 0. With the first equation we obtain

a = 8/3 and replacing in the second equation 2b+6(8/3) = 2b + 16 = 0. Then, b = -8. Finally, c = -2(-8) = 16.

So, our particular solution is $y_p= \frac{8}{3}x^3-8x^2+16x$ .

Now, let's find the solution $y_p$ of the homogeneus equation $y''+y'=0$ with the method of constants coefficients. Let $y=e^{\lambda x}$

$y'=\lambda e^{\lambda x}$

$y''=\lambda^2e^{\lambda x}$

then $\lambda e^{\lambda x}+\lambda^2 e^{\lambda x} = 0$

$e^{\lambda x}(\lambda +\lambda^2)= 0$

$(\lambda +\lambda^2)= 0$

$\lambda (1+\lambda)= 0$

$\lambda =0$ and $\lambda)= -1$ .

So, $y_h = C_1 + C_2e^{-x}$ and the solution is

$y=y_p+y_h =\frac{8}{3}x^3-8x^2+16x+ C_1 + C_2e^{-x}$ .

5 0

2 years ago

2/3y=27<br> how do i figure out what 2/3y=27 is?

saveliy_v [14]

Answer:

y=40.5

Step-by-step explanation:

you need to get y out of a fraction, to do so multiply by the denominator on both sides

3(2/3y) = 3(27)

then divide to solve for y

2y = 81

y=40.5

8 0

2 years ago

Please help I will give brainliest to whoever explains step by step

Evgesh-ka [11]

Answer: In the exact order up to down: 80, 74, 110, 96, 80

Step-by-step explanation:

Do the equation

360=(x-6)+(x+30)+1.2x+x

we can simplify by doing

360=(x-6)+(x+30)+2.2x

=360=x-6+x+30+2.2x

=360=4.2x+24

=336=4.2x

=80=x

x=80

I just started brainly and I want to help more people with their questions please just give a thanks or a rating to keep me going and help more people.

4 0

2 years ago

44 is equal to 8 times a number minus 4. what is the number?

postnew [5]

Answer:

Step-by-step explanation:

Let "a number" = x

44 = 8x - 4

Simplify. Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First add 4 to both sides:

44 (+4) = 8x - 4 (+4)

44 + 4 = 8x

48 = 8x

Isolate the variable, x. Divide 8 from both sides:

(48)/8 = (8x)/8

x = 48/8

x = 6

6 is your answer.

3 0

2 years ago

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The fourth grade student at Riverside school are going on a field trip . There are 68 student on each of the four buses. How man

earnstyle [38]

This answer is 272 I know because I did it vertically

3 0

2 years ago

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