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Anarel [89]
2 years ago
11

Simplify using the Distributive Property (enter your answer with no

Mathematics
2 answers:
Nady [450]2 years ago
8 0

Answer:

12e - 6f + 20g

Step-by-step explanation:

2(6e - 3f + 10g) is the given equation. Because of the grouping, we know  that the entire part in parentheses is multiplied by two. Now the distributive property helps us by letting us multiply each individual part of the parentheses by two.

6e becomes 12e

-3f becomes -6f

and 10g becomes 20g

Now when we put those together, it becomes 12e - 6f + 20g

Hope this helped!

umka21 [38]2 years ago
6 0

Answer:

2(6e-3f+10g)

Answer (I think): 12e-6f+20g

Step-by-step explanation:

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3 years ago
(a) By inspection, find a particular solution of y'' + 2y = 14. yp(x) = (b) By inspection, find a particular solution of y'' + 2
SOVA2 [1]

Answer:

(a) The particular solution, y_p is 7

(b) y_p is -4x

(c) y_p is -4x + 7

(d) y_p is 8x + (7/2)

Step-by-step explanation:

To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the nonhomogeneous part of the differential equation.

(a) Given y'' + 2y = 14.

Because the nonhomogeneus part of the differential equation, 14 is a constant, our trial function will be a constant too.

Let A be our trial function:

We need our trial differential equation y''_p + 2y_p = 14

Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.

y'_p = 0

y''_p = 0

Substitution into the trial differential equation, we have.

0 + 2A = 14

A = 6/2 = 7

Therefore, the particular solution, y_p = A is 7

(b) y'' + 2y = −8x

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x

2Ax + 2B = -8x

By inspection,

2B = 0 => B = 0

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x

(c) y'' + 2y = −8x + 14

Let y_p = Ax + B

y'_p = A

y''_p = 0

0 + 2(Ax + B) = -8x + 14

2Ax + 2B = -8x + 14

By inspection,

2B = 14 => B = 14/2 = 7

2A = -8 => A = -8/2 = -4

The particular solution y_p = Ax + B

is -4x + 7

(d) Find a particular solution of y'' + 2y = 16x + 7

Let y_p = Ax + B

y'_p = A

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By inspection,

2B = 7 => B = 7/2

2A = 16 => A = 16/2 = 8

The particular solution y_p = Ax + B

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8 0
3 years ago
Solve for x.<br><br> -3x = 15
castortr0y [4]

Answer:

x = -5

Step-by-step explanation:

1.  Divide both sides by -3

2. Simplify 15/-3 to 5

( 15 divided by -3 is -5)  

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3 years ago
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