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Elodia [21]
3 years ago
10

Find the solution to the initial value problem

Mathematics
1 answer:
Karo-lina-s [1.5K]3 years ago
3 0

Answer:

y = (11x + 13)e^(-4x-4)

Step-by-step explanation:

Given y'' + 8y' + 16 = 0

The auxiliary equation to the differential equation is:

m² + 8m + 16 = 0

Factorizing this, we have

(m + 4)² = 0

m = -4 twice

The complimentary solution is

y_c = (C1 + C2x)e^(-4x)

Using the initial conditions

y(-1) = 2

2 = (C1 -C2) e^4

C1 - C2 = 2e^(-4).................................(1)

y'(-1) = 3

y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)

3 = -4(C1 - C2)e^4 + C2e^4

-4C1 + 5C2 = 3e^(-4)..............................(2)

Solving (1) and (2) simultaneously, we have

From (1)

C1 = 2e^(-4) + C2

Using this in (2)

-4[2e^(-4) + C2] + 5C2 = 3e^(-4)

C2 = 11e^(-4)

C1 = 2e^(-4) + 11e^(-4)

= 13e^(-4)

The general solution is now

y = [13e^(-4) + 11xe^(-4)]e^(-4x)

= (11x + 13)e^(-4x-4)

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State the hundred thousands place for 7,832,906,215
juin [17]

Answer:

Step-by-step explanation:

6 is the thousands place

0 (right next to it) is the 10 thousands place

9 is the hundred thousands place. There is only 1 nine present so the answer is unique.

4 0
3 years ago
Draw a figure thats less than 1/6
HACTEHA [7]
1 Whole is bigger than a fraction
1 part of the 6 equal groups is shaded

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6 0
3 years ago
(Please help!)<br><br> Divide:<br> (4x² +33x+37) = (x+7)<br><br> Quotient:<br><br> Remainder:
Drupady [299]

Answer:

2

Step-by-step explanation:

4x² + 33 x + 37 = (4 x + 5) × (x + 7) + 2

5 0
3 years ago
A man drove his car at 80km per hr for 1 and a quarter hrs .He rested for 45mins and then covered 240km, at the same time. Calcu
prisoha [69]

Answer:

Probably 128 km/h, but maybe 98.5 km/h. See below.

Step-by-step explanation:

What does "at the same time" mean?

If it means that he covered the 240 km in the same time as he convered the 80 km, then this is how you solve it:

80 km in 1.25 hour

240 km in 1.25 hour

Total distance: 80 km + 240 km = 320 km

Total time: 1.25 hour + 1.25 hour = 2.5 hour

average speed = (total distance)/(total time) = 320 km / 2.5 hour = 128 km/h

If it means he covered the 240 km in the same time he covered the 80 km plus the rest, then this is how you solve it:

80 km in 1.25 hour

240 km in 1.25 hour + 45 min = 240 km in 1.25 houir + 0.75 hour = 240 km in 2 hour

Total distance: 80 km + 240 km = 320 km

Total time: 1.25 hour + 2 hour = 3.25 hour

average speed = (total distance)/(total time) = 320 km / 3.25 hour = 98.5 km/h

3 0
2 years ago
PLEASE HELP! I WILL MARK AS BRAINLIEST!! I REALLY NEED SOMEONES HELP!
Andrej [43]

Since this is subtraction, everything must be turned negative in the second polynomial.

(6x^2 - 5x) - (2x^2 + 3x - 2)

6x^2 - 5x - 2x^2 - 3x - (-2)

6x^2 - 5x - 2x^2 - 3x + 2

Now, reorder the terms to make it easier.

6x^2 - 2x^2 - 5x - 3x + 2

Now, just combine like terms.

4x^2 - 5x - 3x + 2

4x^2 - 8x + 2

There’s the answer!

Please consider marking this answer as Brainliest to help me advance.

4 0
3 years ago
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