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3 years ago

(-24, -8); (-12, -6); (0 ,-4); (12, -2); (24, 0) slope intercept form

Mathematics

1 answer:

FromTheMoon [43]3 years ago

4 0

a. y=-24x-8

b. y=-12x-6

c. y=0x-4

d. y=12x-2

e. y=24x+0

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Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2/3 + y2/3 = 4 (−3 3 , 1)

vovikov84 [41]

Answer with Step-by-step explanation:

We are given that an equation of curve

$x^{\frac{2}{3}}+y^{\frac{2}{3}}=4$

We have to find the equation of tangent line to the given curve at point $(-3\sqrt3,1)$

By using implicit differentiation, differentiate w.r.t x

$\frac{2}{3}x^{-\frac{1}{3}}+\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=0$

Using formula : $\frac{dx^n}{dx}=nx^{n-1}$

$\frac{2}{3}y^{-\frac{1}{3}}\frac{dy}{dx}=-\frac{2}{3}x^{-\frac{1}{3}}$

$\frac{dy}{dx}=\frac{-\frac{2}{3}x^{-\frac{1}{3}}}{\frac{2}{3}y^{-\frac{1}{3}}}$

$\frac{dy}{dx}=-\frac{x^{-\frac{1}{3}}}{y^{-\frac{1}{3}}}$

Substitute the value x= $-3\sqrt3,y=1$

Then, we get

$\frac{dy}{dx}=-\frac{(-3\sqrt3)^{-\frac{1}{3}}}{1}$

$\frac{dy}{dx}=-(-3^{\frac{3}{2}})^{-\frac{1}{3}}=-\frac{1}{-(3)^{\frac{3}{2}\times \frac{1}{3}}}=\frac{1}{\sqrt3}$

Slope of tangent=m= $\frac{1}{\sqrt3}$

Equation of tangent line with slope m and passing through the point $(x_1,y_1)$ is given by

$y-y_1=m(x-x_1)$

Substitute the values then we get

The equation of tangent line is given by

$y-1=\frac{1}{\sqrt3}(x+3\sqrt3)$

$y-1=\frac{x}{\sqrt3}+3$

$y=\frac{x}{\sqrt3}+3+1$

$y=\frac{x}{\sqrt3}+4$

This is required equation of tangent line to the given curve at given point.

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4 years ago

What is 1/12x(4+6x3)-9?

sertanlavr [38]

Your answer is -43/6

1/12(4+6x3)-9
=1/12(22)-9
=11/6-9
=11/6-54/6
=-43/6

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3 years ago

a) The family likes peaches and other fruits. The local farmer’s market is selling fresh peaches at a discounted price. If the f

s344n2d4d5 [400]

Answer:

step one got to bathroom

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Step-by-step explanation:

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3 years ago

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What is the midpoint of (-1,-6), (-6, 5)

kirill115 [55]

<h3>Answer:</h3><h3>-3.5,-0.5</h3>

Step-by-step explanation:

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4 years ago

Please i need help on this question?!?!

anzhelika [568]

Answer:

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3 years ago