Find the point on the line y = 4x + 5 that is closest to the origin.

Step 1

Find the equation of the line perpendicular to that pas through the origin

we know that

the slope of the equation is

if two lines are perpendicular

then

the product of their slopes is equal to

the slope of the line perpendicular is equal to

with m2 and the origin find the equation of the line

Step 2

Solve the system

---> equation

-----> equation

Multiply equation by

Adds equation and equation

the solution is the point

=

therefore

the answer is

the point is

see the attached figure

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

irrational, cannot