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Vsevolod [243]
3 years ago
7

Bernoulli equation xy’+3y=x^5y^(1/3) Please solve this step by step

Mathematics
1 answer:
s344n2d4d5 [400]3 years ago
4 0

Answer:

y=(x^5/8+Cx^{-3})^{3/2}

Step-by-step explanation:

xy’+3y=x^5y^(1/3)

rewrite in:

y^{-1/3}\frac{dy}{dx} +3x^{-1}y^{2/3}=x^4

substitute: v=y^{2/3}\\

\frac{dv}{dx}=\frac{d}{dx}y^{2/3}=y^{-1/3}\frac{dy}{dx}

The equation can be rewritten in:

\frac{dv}{dx}+3vx^{-1}=x^4

This is a first-order linear differential equation:

Can be solved by using integrating factor or variation of parameter:

integrating factor:

u(x)=exp(∫3/x \ dx) = x^3

v=u^{-1}∫u(x) x^4dx

v=x^{-3}(∫x^4x^3dx)

y^{2/3}=v=x^{-3}(x^8/8+C)

y=(x^5/8+Cx^{-3})^{3/2}

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Keith is trying to figure out the area of his pool section in his backyard he knows that his pool is 20 feet long and 9 feet wid
Nata [24]

Answer:

The total area of the pool section of Keith's backyard is 390 square feet.

Step-by-step explanation:

Since Keith is trying to figure out the area of his pool section in his backyard, and he knows that his pool is 20 feet long and 9 feet wide, and he also knows the sidewalk is 3 feet wide all around the floor, to determine what is the total area of the pool section of Keith's backyard, the following calculation must be performed:

(20 + 3 + 3) x (9 + 3 + 3) = X

26 x 15 = X

390 = X

Therefore, the total area of the pool section of Keith's backyard is 390 square feet.

3 0
4 years ago
List the numbers that have 30 as a multiple
Yuki888 [10]
30 has Infinite amount of multiples but a few are 60,90,120,150,180,210,240

In simpler terms multiples are what numbers go into
7 0
3 years ago
below is a diagram showing a regular hexagon and a regular Pentagon. Each shape has a lengths of two sides shown in the terms of
Strike441 [17]
To solve this, we work out the perimeter of the hexagon, by finding x,  and we work out the perimeter of the pentagon by find y, and the compare them:

Perimeter of the Hexagon:
Since it is a regular hexagon, all the sides are the same: This means we can say that:

4x - 2 = x + 4       (Now lets solve this)
4x = x + 6             ( Add both sides by 2 to get 4x alone)
3x = 6                   (Subtract both sides by x, to collect the x values)
x = 2                     (Divide both sides by 3 to get what just x is)

Now we work out the length of one side by substituting the value for x in
x + 4 = 2 + 4
= 6 

Now that we know the length of one side, we can multiply that by 6 to get the perimeter, because a hexagon has six sides.

6 * 6 = 36

Perimeter of the Pentagon
Since it is a regular Pentagon, all the sides are the same, just like the hexagon. This means we can say that:

5y - 8 = 2y + 1         (Now we solve this like we did before)
5y = 2y + 9               ( Add both sides by 8 to get 5y alone)
3y = 9                       (Subtract both sides by 2y, to collect the y values)
y = 3                         (Divide both sides by 3 to get what just y is)

Now we work out the length of one side by substituting the value for x in
2y + 1 = (2 * 3) + 1
= 7

Now that we know the length of one side, we can multiply that by 5 to get the perimeter, because a pentagon has 5 sides.

5 * 7 = 35


Since the perimeter of the hexagon is 36, and the perimeter of the pentagon is 35, we can see that:

The hexagon has the larger perimeter.
5 0
4 years ago
Please help me with this one
vlada-n [284]

polynomial which has no real root is

x {}^{2}  + 2x + 3

8 0
4 years ago
Use the information on the right to determine which students will have positive z-scores. Aaliyah, who completed the exam in 55
Y_Kistochka [10]

Answer:

B and C, Benjamin and Cynthia.

Step-by-step explanation:

Next part (Cynthia's score) is 0.2

4 0
3 years ago
Read 2 more answers
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