Determine the graph of the polar equation r=4/(1-1/2cosx(theta))

  see below

Step-by-step explanation:

We assume you want the graph of ...

A graphing calculator or spreadsheet is useful for this.

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You know cos(θ) = cos(-θ), so the graph is symmetrical about the x-axis. You can evaluate the function at a few points to find the general outline.

  r at 0° = 8

  r at 30° ≈ 7.05

  r at 45° ≈ 6.19

  r at 60° ≈ 5.33

  r at 90° = 4

  r at 120° = 3.2

  r at 135° ≈ 2.96

  r at 150° ≈ 2.79

  r at 180° ≈ 2.67

i assume that by 5 you mean 5 gallons.

(20)(0.25) = 15

removing 15 gallons reduces the tank from 20 to 5.

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.