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UNO [17]
3 years ago
14

Express x^4+1 ÷x ^3+9x in partial fraction​

Mathematics
1 answer:
Simora [160]3 years ago
3 0

Answer: The answer would be x ^4 + 1/x^3 + 9x, Good Luck!

Step-by-step explanation:

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Show that d^2y/dx^2=-2x/y^5, if x^3 + y^3=1
aalyn [17]

Answer:

y³ + x³ = 1

First, differentiate the first time, term by term:

{3y^{2}.\frac{dy}{dx} + 3x^{2}} = 0 \\\\{3y^{2}.\frac{dy}{dx} = -3x^{2}} \\\\\frac{dy}{dx} = \frac{-3x^{2}}{3y^{2}} \\\\\frac{dy}{dx} = \frac{-x^{2}}{y^{2}}

↑ we'll substitute this later (4th step onwards)

Differentiate the second time:

3y^{2}.\frac{dy}{dx} + 3x^{2} = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} + 6x = 0 \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{dy}{dx})^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{-x^{2} }{y^{2} })^{2} = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + 6y(\frac{x^{4} }{y^{4} }) = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} + \frac{6x^{4} }{y^{3} } = - 6x \\\\3y^{2}.\frac{d^{2} y}{dx^{2}} = - 6x - \frac{6x^{4} }{y^{3} } \\\\

3y^{2}.\frac{d^{2} y}{dx^{2}} =  - \frac{- 6xy^{3} - 6x^{4} }{y^{3}} \\\\\frac{d^{2} y}{dx^{2}} =  - \frac{- 6xy^{3} - 6x^{4} }{3y^{2}. y^{3}} \\\\\frac{d^{2} y}{dx^{2}} =  - \frac{- 2xy^{3} - 2x^{4} }{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} =  - \frac{-2x (y^{3} + x^{3})}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} =  - \frac{-2x (1)}{y^{5}} \\\\\frac{d^{2} y}{dx^{2}} =  - \frac{-2x}{y^{5}}

3 0
3 years ago
Help will give brainiest
son4ous [18]

Answer:

I'm pretty sure the answer is a

4 0
2 years ago
Read 2 more answers
Help plz if anybody know the answer
Tanzania [10]

Answer: x^2+29x+39

You would first have to set up an equation, which would be ((2x+9)⋅(x+6))-((x-5)⋅(x-3)) to find the area of both rectangles.

Then you can simplify it, which gives us 2x^2+21x+54-(x^2-8x+15)

Then simplify it even more which gives us 2x^2+21x+54-x^2+8x-15

Then we can get our answer: x^2+29x+39

Hope that helps :)

4 0
3 years ago
What is the value of y in the equation 2(2y − 12) = 0?<br><br> 4<br> 6<br> 7<br> 8
lesantik [10]
6 hope this helps :4
4 0
3 years ago
Read 2 more answers
Given the endpoint (4, −2)and midpoint (9, 4), find the other endpoint.
marissa [1.9K]

Answer:

Step-by-step explanation:

(x + 4)/2 = 9

x + 4 = 18

x = 14

(y-2)/2 = 4

y - 2 = 8

y = 10

(14, 10)

4 0
3 years ago
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