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Basile [38]
3 years ago
5

Write the standard form of the line that passes through the given points. Include your work in your final answer.

Mathematics
1 answer:
Amanda [17]3 years ago
3 0

Answer:

hope this will help u.. :-)

Step-by-step explanation:

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If xy + y² = 6, then the value of dy/dx at x= -1 is<br>​
mylen [45]

Hi there!

\large\boxed{\text{At (-1, -2), }\frac{dy}{dx} = -\frac{2}{5}}}

\large\boxed{\text{At (-1, 3), }\frac{dy}{dx} = -\frac{3}{5}}}

We can calculate dy/dx using implicit differentiation:

xy + y² = 6

Differentiate both sides. Remember to use the Product Rule for the "xy" term:

(1)y + x(dy/dx)  + 2y(dy/dx) = 0

Move y to the opposite side:

x(dy/dx) + 2y(dy/dx) = -y

Factor out dy/dx:

dy/dx(x + 2y) = -y

Divide both sides by x + 2y:

dy/dx = -y/x + 2y

We need both x and y to find dy/dx, so plug in the given value of x into the original equation:

-1(y) + y² = 6

-y + y² = 6

y² - y - 6 = 0

(y - 3)(y + 2) = 0

Thus, y = -2 and 3.

We can calculate dy/dx at each point:

At y = -2: dy/dx = -(-2) / -1+ 2(-2) = -2/5.

At y = 3: dy/dx = -(3) / -1 + 2(3) = -3/5.

5 0
3 years ago
The equation of this line in point-slope form is y -8 = -3/4(x-16). What is the equation of the line written in slope-intercept
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Answer: y= -\frac{3}{4}x +20

Step-by-step explanation:

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Maslowich

Answer:

Step-by-step explanation:

B

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