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Simora [160]
2 years ago
8

Find the second derivative of 2x^3-3y^2=8​

Mathematics
1 answer:
Umnica [9.8K]2 years ago
5 0

Answer:

\frac{d^2y}{dx^2}=\frac{x(2y-x^3)}{y^3}

Step-by-step explanation:

<u>Find the first implicit derivative using implicit differentiation</u>

<u />2x^3-3y^2=8\\\\6x^2-6y\frac{dy}{dx}=0\\ \\-6y\frac{dy}{dx}=-6x^2\\ \\\frac{dy}{dx}=\frac{x^2}{y}

<u>Use the substitution of dy/dx to find the second derivative (d²y/dx²)</u>

<u />\frac{d^2y}{dx^2}=\frac{(y)(2x)-(x^2)(\frac{dy}{dx})}{y^2}\\ \\\frac{d^2y}{dx^2}=\frac{2xy-(x^2)(\frac{x^2}{y})}{y^2}\\\\\frac{d^2y}{dx^2}=\frac{2xy-\frac{x^4}{y}}{y^2}\\\\\frac{d^2y}{dx^2}=\frac{x(2y-x^3)}{y^3}

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A and B can fill a cistern in 4 hours. A and C can fill
kirill [66]

Answer:

20 hours

Step-by-step explanation:

We can work easier if we think in terms of an hour

the first equation that we can write is

A + B = 1/4 (its meaning is that in an hour A and B fill 1/4 of the cistern)

the second equation we can write is

A + C = 1/5 (its meaning is that in an hour A and C fill 1/5 of the cistern)

the third equation that we can write is

B = 2C  (its meaning is that in an hour B fill 2 times C the cistern)

now we can substitute the value of B in the first two equations

A + 2C = 1/4

A + C = 1/5

A = 1/5 - C

1/5 - C + 2C = 1/4

C = 1/4 -1/5

C = (5-4)/20

C = 1/20 (this means that in an hour C will fill 1/20 of the cistern, so it takes 20 hours to fill the entire cistern)

A = 1/5 - 1/20

A = (4-1)/20 = 3/20

B = 1/20 *2 = 1/10

4 0
2 years ago
The diagram shows a triangle.<br><br> What is the value of z?
Damm [24]

Answer:

z=31°

Step-by-step explanation:

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z=180-149

z=31°

<h2>stay safe healthy and happy.</h2>
6 0
3 years ago
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D. x-6
That is the correct answer.
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