What term applies to a line that intersects two other lines?

The slope of the line tangent to the curve y^2 + (xy+1)^3 = 0 at (2, -1) is ...?

Lina20 [59]

$\frac{d}{dx}(y^2 + (xy+1)^3 = 0)
\\
\\\frac{d}{dx}y^2 + \frac{d}{dx}(xy+1)^3 = \frac{d}{dx}0
\\
\\\frac{dy}{dx}2y + \frac{d}{dx}(xy+1)\ *3(xy+1)^2 = 0
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\\\frac{dy}{dx}2y + \left(\frac{d}{dx}(xy)+\frac{d}{dx}1\right)\ * 3(xy+1)^2 = 0
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\\\frac{dy}{dx}2y + \left(\frac{d}{dx}xy+x\frac{d}{dx}y+\frac{dx}{dx}\right)\ * 3(xy+1)^2 = 0
\\
\\\frac{dy}{dx}2y + \left(\frac{dx}{dx}y+x\frac{dy}{dx}+\frac{dx}{dx}0\right)\ * 3(xy+1)^2 = 0
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\\\frac{dy}{dx}2y + \left(y+x\frac{dy}{dx}\right)\ * 3(xy+1)^2 = 0$
$\frac{dy}{dx}2y + \left(y+x\frac{dy}{dx}\right)\ * 3(xy+1)^2 = 0
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\\\frac{dy}{dx}2y + \left(3y+3x\frac{dy}{dx}\right) (xy+1)^2 = 0
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\\2y\ y' + \left(3y+3x\ y'\right) (xy+1)^2 = 0
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\\2y\ y' + \left(3y+3x\ y'\right) ((xy)^2+2xy+1) = 0
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\\2y\ y' + \left(3y+3x\ y'\right) ((xy)^2+2xy+1) = 0
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\\2y\ y' + 3x^2y^3 +6xy^2+3y+(3x y' +6x^2y y'+3x^2y y') = 0
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\\3x^2y^3 +6xy^2+3y+(3x y' +6x^2y y'+3x^2y y'+2yy' ) = 0
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\\y'(3x +6x^2y+3x^2y+2y ) = -3x^2y^3 -6xy^2-3y

$
$y' = \frac{-3x^2y^3 -6xy^2-3y}{(3x +6x^2y+3x^2y+2y )};\ x=2,y=-1
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\\y' = \frac{-3(2)^2(-1)^3 -6(2)(-1)^2-3(-1)}{(3(2) +6(2)^2(-1)+3(2)^2(-1)+2(-1) )}
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\\y' = \frac{-3(4)(-1) -6(2)(1)+3}{(6 +6(4)(-1)+3(4)(-1)-2 )}
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\\y' = \frac{12 -12+3}{(6 -24-12-2 )}
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\\y' = \frac{3}{( -32 )}$

7 0

3 years ago

Find the value of g(-1)

Anna11 [10]

Answer:

g(-1) = -3

Step-by-step explanation:

g(-1) is the y value of the graph when x = -1

when x=-1 y=-3

g(-1) = -3

6 0

3 years ago

Help meee pleasee!!!<br><br><br><br><br> thank you <3

julsineya [31]

The equation of the newsletter function is C(x) = 75 + 0.25x and the function values are C(0) = 75, C(100) = 100, C(200) = 125 and C(300) = 150

<h3 /><h3>How to determine the newsletter function?</h3>

From the question, the given parameters are

Initial charge = $75.00

Rate per copy = $0.25 per copy

The equation of the newsletter function is then calculated as

Total = Initial charge + Rate per copy x Number of copies

Let x represents the number of copies

So, we have

Total = Initial charge + Rate per copy x x

This gives

C(x) = 75 + 0.25x

<h3>The function values for x = 0, 100, 200 and 300</h3>

When x = 0, we have

C(0) = 75 + 0.25 x 0 = 75

When x = 100, we have

C(100) = 75 + 0.25 x 100 = 100

When x = 200, we have

C(200) = 75 + 0.25 x 200 = 125

When x = 300, we have

C(300) = 75 + 0.25 x 300 = 150