Find the points on the given curve where the tangent line is horizontal or vertical. (Assume 0 ≤ θ ≤ 2π. Enter your answers as a comma-separated list of ordered pairs.) r = 1 − sin(θ)

Tangent line is horizontal at points : and vertical at points : .

Step-by-step explanation:

Given,

where

Let, and . Then,

Now, to find tangent , we have to find,

Therefore,

The numerator of is 0 implies the tangent line is horizontal. That is,

or,

or,

Now, implies that there exist a vertical tangent at .

And the denominator of is 0 implies the tangent line is vertical. That is,

When,

Hence, tangent line is,

horizontal at points :

vertical at points :

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: 94

step-by-step explanation: 79+91+92+94+94 = 450 divided by 5 (since there are 5 number that are being added) = 90