A car starts a journey with a full tank of gas. The equation y=16 - 0.05x relates the number of gallons of gas, y, left in the t
1 answer:
We are given that a car starts a journey with a full tank of gas. The equation relates the number of gallons of gas (y) left in the tank to the number of miles the car has traveled(x).
A. We will find y intercept by substituting x=0 in our equation,
Now let us find our x-intercept by substituting y=0 in our equation,
Therefore, x-intercept is 320 and y-intercept is 16.
B. Our x-intercept represents that after travelling 320 miles there were 0 or none gallons of gas left in tank.
C. Our y-intercept represents that there were 16 gallons of gas in car tank when car started the journey.
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Let
where we assume |r| < 1. Multiplying on both sides by r gives
and subtracting this from gives
As n → ∞, the exponential term will converge to 0, and the partial sums will converge to
Now, we're given
We must have |r| < 1 since both sums converge, so
Solving for r by substitution, we have
Recalling the difference of squares identity, we have
We've already confirmed r ≠ 1, so we can simplify this to
It follows that
and so the sum we want is
which doesn't appear to be either of the given answer choices. Are you sure there isn't a typo somewhere?