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natima [27]
4 years ago
7

Differential Equations Solve the initial-value problem dydx=e2x/5y4,y(0)=4. y(x)=

Mathematics
1 answer:
solniwko [45]4 years ago
5 0

Answer:

y(x) = \sqrt[5]{\frac{e^{2x}}{2} + \frac{2047}{2}}

Step-by-step explanation:

\displaystyle\frac{dy}{dx} = \displaystyle\frac{e^{2x}}{5y^4}

Cross multiplying, we have,

5y^4 dy = e^{2x} dx

Integrating both sides,

\int 5y^4 dy = \int e^{2x}dx

We obtain,

y^5 = \frac{e^{2x}}{2} + C, where C is the constant of integration.

y(x) = \sqrt[5]{\frac{e^{2x}}{2} + C }

We know that y(0) = 4

Putting these value in the above equation, we get C = \frac{2047}{2}

Thus,

y(x) = \sqrt[5]{\frac{e^{2x}}{2} + \frac{2047}{2}}

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A rose garden is formed by joining rectangle and a semicircle, as shown below. The rectangle is 29 ft long and 21 ft wide. If th
Iteru [2.4K]

Answer:

The answer to your question is 116.53 ft

Step-by-step explanation:

Data

length = 29 ft

width = 21 ft

π = 3.14

Process

1.- Calculate perimeter of the rectangle and subtract 1 length

Perimeter of the rectangle = 2l + 2w - l

Perimeter of the rectangle = 2(29) + 2(21) - 29

                                            = 58 + 42 - 29

                                            = 71 ft

2.- Calculate the perimeter of a semicircle

Perimeter = 2πr/2 = πr

radius = r = 29/2

               = 14.5 ft

Perimeter = (3.14)(14.5)

                 = 45.53 ft

3.- Calculate the total length of the fence

fence = 45.53 + 71

          = 116.53 ft

7 0
3 years ago
What is a possible equation for a function with an x-intercept of (-5,0) and a y-intercept of (0,3)?
Feliz [49]

Answer:

The equation of a straight line is

-3 x+5 y=15

Step-by-step explanation:

Given x - intercept of (-5,0) and y- intercept is (0,3)

here (-5,0 ) point lie on x- axis and (0,3) this point lie on y- axis

we know that the x- intercept  'a' and y- intercept 'b'  formula is

\frac{x}{a} +\frac{y}{b} = 1

so given x - intercept a =-5 and y- intercept is b= 3

now the straight line equation is \frac{x}{-5} +\frac{y}{3} =1

now simplify \frac{-3 x+5 y}{15} =1

-3 x+5 y=15

5 0
3 years ago
Solve for x. <br>can someone answer this please ​
tangare [24]
I think it has to be 76
4 0
3 years ago
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Which statement is an example of the distributive property? 3 + (2)(15) = 3(2) + 3(15) 3(2 + 15) = 3 + 2(3) + 15 3(2 + 15) = 3(2
natka813 [3]
It would be 3(2+15)= 3(2) + 3(15)
Hope this helps❤️
5 0
4 years ago
Read 2 more answers
How many times would that person's heartbeat if he/she ran a 5K
7nadin3 [17]
Not sure, goodluck tho!!
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3 years ago
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