(y+2)=1/4(x-4) is the answer because you use the formula (y-y1)=slope(x-x1)
If
is an integer, you can use induction. First show the inequality holds for
. You have
, which is true.
Now assume this holds in general for
, i.e. that
. We want to prove the statement then must hold for
.
Because
, you have
and this must be greater than
for the statement to be true, so we require
for
. Well this is obviously true, because solving the inequality gives
. So you're done.
If you
is any real number, you can use derivatives to show that
increases monotonically and faster than
.
The fare of $(20 - 2.5) = $17.5 will maximize the total fare.
<h3>What is Differentiation?</h3>
Differentiation means the rate of change of one quantity with respect to another. The speed is calculated as the rate of change of distance with respect to time.
Here, The operator for a round-trip fare of $20, carries an average of 500 people per day.
It is estimated that 20 fewer people will take the trip, for each $1 increase in fare.
for $x increase in fare, 20x less people will take the trip and at that time the total fare F is given by
f(x) =(20 + x)(500 - 20x)
f (x) = 10000 + 100x - 20x²
For f(x) to be maximum, the condition is dy/dx = 0
100 - 40x = 0
⇒ x = 2.5
Thus, the fare of $(20 - 2.5) = $17.5 will maximize the total fare.
Learn more about Differentiation from:
brainly.com/question/24062595
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Answer:
2/3 = 0.666666667
<em><u>hopefully i helped :)</u></em>
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