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KIM [24]
3 years ago
15

I need more math help, the!

Mathematics
1 answer:
BabaBlast [244]3 years ago
4 0
Track A takes 20 minutes
Track B takes 15 minutes
In 1 minute track be will do a fraction of 1/20, while track B will do 1/15
Both tracks in a minute = 1/20+1/15
                                      = 35/300
Therefore the two tracks will take 300/35 minutes to fill the 200 cubic feet
That is 300/35
           = 8.57  minutes
           ≈ 9 minutes
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(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

y''_p = 0

0 + 2(Ax + B) = 16x + 7

2Ax + 2B = 16x + 7

By inspection,

2B = 7 => B = 7/2

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

The particular solution y_p = Ax + B

is 8x + (7/2)

8 0
3 years ago
The graph of the function f(x) = (x - 3)(x + 1) is shown.
KonstantinChe [14]

Answer:

all real values of x where x < -1

Step-by-step explanation:

See attached graph.

6 0
1 year ago
A text font fits 12 characters per inch. Using the same font, how many characters can be expected per yard of text? There are 12
Bond [772]

Answer:

432 characters

Step-by-step explanation:

First we can convert 12 characters per inch in to characters per feet. Knowing that there are 12 inches per foot we know we have to multiply the 12 characters per inch by 12, giving us 144 characters per foot. Now we have to convert characters per foot to characters per yard. Knowing there are 3 feet per yard we know we have to multiply 144 characters per foot by 3, giving us a final answer of 432 characters per yard of text.

7 0
3 years ago
Pls help me I would be happy if do
Brilliant_brown [7]

Answer:

a prism is a three dimensional shape with the same width all the way through.

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Evaluate the following expression 2+(3-2×2)×1
neonofarm [45]
2•3=9 2•2=4 2•2=4 9+4+4=17 the answer is 17
7 0
3 years ago
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