Use implicit differentiation to find an equation of the tangent line to the curve at the given point. x2 + 6xy + 12y2 = 28, (2, 1) (ellipse)

The equation of the tangent line is .

Step-by-step explanation:

Firstly, we obtain the equation for the slope of the tangent line by implicit differentiation:

(1)

If we know that , then the slope of the tangent line is:

By definition of tangent line, we determine the intercept of the line ():

(2)

If we know that and , then the intercept of the tangent line is:

The equation of the tangent line is .

use an equation of ratios to determine the amount of gas needed to fill the tank.

    0.2             0.8

  =    

288.75             x

                                                              231 gal

so, 0.2x = (0.8)(288.75 gal), and x = = 1155 gal.

                                                                0.2

it would take 1155 gal. to fill the tank.

the cost would be

1155 gal         $3

* = $3465   (answer)

      1           1 gal

hope this you

answer: 819.89 miles across america

step-by-step explanation: