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3 years ago

COMPLETE (s – r)(x) =

Mathematics

1 answer:

iren [92.7K]3 years ago

7 0

Answer:

sx-rx

Step-by-step explanation:

Since s, r, and x are unknown variables, you just multiply them. s × x = sx.

r × x = rx. then when you put the together, it will look like this:

sx-rx

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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

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

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3 years ago

Suppose the top surface of a balance beam is 16 feet 5 inches long and 3.9 inches wide. Find the area of the top surface of the

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Answer:

Option A would be your answer

Step-by-step explanation:

Had this question on Achieve3000

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2. What type of sequence is this?<br> 4,0-4,-8, -12,...<br> Arthimetic<br> Geometric<br> Neither

lora16 [44]

Answer:

Arithmetic

Step-by-step explanation:

Arithmetic is additive and geometric is multiplicative, and the numbers aren''t multiplying, they're adding.

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3 years ago

To join a gym, you have to pay an initial fee of $50 and $30 per month. Write an equation representing total cost (t).

Vladimir [108]

50+30m= t

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t: total

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3 years ago

Read 2 more answers

Find the volume of a cube with a side length of 4r3s2.

andrey2020 [161]

Answer:

V = 64 r^(9) * s^(6)

Step-by-step explanation:

The volume of a cube is given by

V = s^3 where s is the side length

V = ( 4r^3s^2) ^3

We know that ( ab) ^c = a^c * b^c

V = 4^3 * r^3^3 * s^2^3

V = 64 * r^3^3 * s^2^3

We know that a^b^c = a^(b*c)

V = 64 r^(3*3) * s^(2*3)

V = 64 r^(9) * s^(6)

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3 years ago