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Black_prince [1.1K]
3 years ago
15

Find the solution to the initial value problem (1 + x^{5}) y' + 5 x^{4} y = 5 x^{8}

Mathematics
1 answer:
natali 33 [55]3 years ago
8 0
(1+x^5)y'+5x^4y=5x^8
\bigg((1+x^5)y\bigg)'=5x^8
(1+x^5)y=5\displaystyle\int x^8\,\mathrm dx
(1+x^5)y=\dfrac59x^9+C
y=\dfrac{5x^9+C}{9(1+x^5)}
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The middle side of a triangle is half of 3 times the length of the shortest side. The longest side is 2 centimeters longer than
USPshnik [31]

<u>Answer:</u>  

The difference between the longest and shortest sides of the triangle is 4 cm.

<u>Explanation:</u>

<em>Step Number One:</em>

Let the shortest side of the triangle have a length of x.

The middle side of the triangle has a length that is half of 3 times the length of the shortest side. This can be written as 1/2*3x, which equals 3/2x.

The longest side of the triangle has a length that is 2 centimeters longer than the length of the middle side. This can be written as 3/2x + 2.

<em>Step Number Two: </em>

The perimeter of the triangle, which can be found by adding the lengths of all of the sides of the triangle, is 18 centimeters. This can be shown by the following equations:

Shortest Side + Middle Side + Longest Side = Perimeter

x + 3/2x + 3/2x + 2 = 18

4x + 2 = 18

4x = 16

x = 16/4

x = 4

<em>Step Number Three: </em>

This means that the shortest side of the triangle has a length of 4 centimeters and the longest side of the triangle has a length of 8 centimeters.

8 cm - 4 cm = 4 cm

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Are you still confused? Not feeling confident in your ability to solve these types of problems? Some helpful topics to practice are listed below!

<u>Still confused on ...</u>

Step 1 - Practice equation solving!

Step 2 - Practice perimeter!

Step 3 - Practice addition and subtraction!

Remember: Certain problems may be tricky, but practice makes perfect!

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<em>Answer by Math_Is_Me_123         </em>

7 0
3 years ago
87 times 422 divided by 4
Lynna [10]

Answer:

9178.5

Step-by-step explanation:

Follow PemDas

From Left to Right, you multiply 87 x 422, which is 36,714

Then, thake that number and divide it by 4, giving you 9,178.5

8 0
3 years ago
A peice of fabric costs $5.29 a yard which is an estimated cost of 16.3 yards of fabric?
DerKrebs [107]

Answer:

90

Step-by-step explanation:

$5.29  * 16.3 = $86.227

=$86.23

86.23 could be rounded up to 90

6 0
3 years ago
Jane paid 40$ for an item after
ad-work [718]

Answer:

after what.................. ???

3 0
3 years ago
A music company offers a loan to buy a drum set for $1500. The simple interest is 11.8% and the loan will be paid in equal month
Mrrafil [7]
Simple interest<span> is determined by multiplying the daily </span>interest<span> rate by the principal by the number of days that elapse between payments. It is expressed as:

I = Prt

I = 1500(.118)(2) = 354

Total amount to pay = $1854
Monthly payment = $77.25

Hope this answers the question. Have a nice day.</span>
3 0
3 years ago
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