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vredina [299]
3 years ago
5

Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inv

ersely proportional to y4
Mathematics
1 answer:
vazorg [7]3 years ago
7 0
The statement "<span>The rate of change of y with respect to x is inversely proportional to y^4" can be written mathematically as dy/dx = k/y^4

To solve the differential equation, we use variable saparable method.
y^4 dy = kdx
Integrating both sides gives,
y^5 / 5 = kx + A
y^5 = 5kx + 5A = Bx + C; where B = 5k and C = 5A
y= \sqrt[5]{Bx+C}</span>
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Answer:

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Step-by-step explanation:

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7 0
2 years ago
The maximum value of 12 sin 0-9 sin²0 is: -​
jeka57 [31]

Answer:

4

Step-by-step explanation:

The question is not clear. You have indicated the original function as 12sin(0) - 9sin²(0)

If so, the solution is trivial. At 0, sin(0) is 0 so the solution is 0

However, I will assume you meant the angle to be \theta rather than 0 which makes sense and proceed accordingly

We can find the maximum or minimum of any function by finding the first derivate and setting it equal to 0

The original function is

f(\theta) = 12sin(\theta) - 9 sin^2(\theta)

Taking the first derivative of this with respect to \theta and setting it equal to 0 lets us solve for the maximum (or minimum) value

The first derivative of f(\theta) w.r.t \theta is

                        12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right)

And setting this = 0 gives

12\cos\left(\theta\right)-18\cos\left(\theta\right)\sin\left(\theta\right) = 0

Eliminating cos(\theta) on both sides and solving for sin(\theta) gives us

sin(\theta) = \frac{12}{18} = \frac{2}{3}

Plugging this value of sin(\theta) into the original equation gives us

12(\frac{2}{3}) - 9(\frac{4}{9} ) = 8 - 4 = 4

This is the maximum value that the function can acquire. The attached graph shows this as correct

3 0
1 year ago
Pls help I will give brainliest ​
Radda [10]

its B. 50°

Triangle Have 180°

  • 180 - 90 = 90
  • 90 × 2 = 180

Half of triangle Have 90°

  • 90° - 40° = 50°

5 0
2 years ago
I dont know how to solve this does anybody?
postnew [5]

Answer:

3x + 7 + 5

Step-by-step explanation:

I could be wrong... there are 3 x's so that would be 3x, and then the 7 and 5. sorry if i'm wrong

5 0
3 years ago
Read 2 more answers
What is the unit of time (t) when calculating interest?
Ymorist [56]

Answer:

t = time in decimal years; e.g., 6 months is calculated as 0.5 years. Divide your partial year number of months by 12 to get the decimal years.

Step-by-step explanation:

 

7 0
2 years ago
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