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zhannawk [14.2K]
3 years ago
5

Finding Derivatives Implicity In Exercise, find dy/dx implicity. x2 - 3 ln y + y2 = 10

Mathematics
1 answer:
Veseljchak [2.6K]3 years ago
8 0

Answer:

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

Step-by-step explanation:

We are given that

x^2-3lny+y^2=0

Differentiate w.r.t x

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

By using formula

\frac{dx^n}{dx}=nx^{n-1}

\frac{d(lnx)}{dx}=\frac{1}{x}

\frac{dy^n}{dx}=ny^{n-1}\frac{dy}{dx}

\frac{dy}{dx}(-\frac{3}{y}+2y)+2x=0

\frac{dy}{dx}(-\frac{3}{y}+2y)=-2x

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

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

Hence, the derivative of function

\frac{dy}{dx}=-\frac{2xy}{2y^2-3}

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3 years ago
The base of this regular right pyramid is a square. What is its surface area?
zubka84 [21]

Answer:

○ A) 21 ft.²

Step-by-step explanation:

{a}^{2} + 2a  \sqrt{ \frac{ {a}^{2}}{4} + {h}^{2} } = S. A. \\  \\ {3}^{2} + 2(3) \sqrt{ \frac{ {3}^{2} }{4} +  {2}^{2}} = 24 \\  \\ 24 ≈ 21

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3 years ago
(ANSWER FOR FREE BRAINPOINTS!) (FIRST TO ANSWER GETS BAINLIEST) The local park has a rectangular swimming pool that measures 40
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Answer:

9 yards

Step-by-step explanation:

Since both pools are similar, therefore the ratio of their length and width would be equal. That is:

Length of the current swimming pool : length of the new swimming pool = width of the current swimming pool : width of the new swimming pool

Thus, we can set up a proportion as shown below:

Let the width of the new swimming pool be x.

40 : 24 = 15 : x

\frac{40}{24} = \frac{15}{x}

Cross multiply

40*x = 15*24

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Divide both sides by 40

x = \frac{360}{40}

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The width of the new swimming that is smaller would be 9 yards.

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2 years ago
If cosA+sinA=√2, then prove A=45°.
Lyrx [107]

Answer:

1/2 now substitute 45 degrees

Step-by-step explanation:

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Sliva [168]

Answer:

416mm^{3}

Step-by-step explanation:

Volume is found by Length x Width x Height

10.4 x 5 x 8      

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