How Do You Solve These Problems?
1.) A ball is thrown vertically upward from the ground with an initial speed of 80 ft/sec. Its height is given by h = 80t - 16t2. How high does the ball go? When does the ball hit the ground? 3.) A ferry service transporting passengers to an island charges a fare of $10 and carries 300 persons. The manager estimates that the company will lose 15 passengers for each increase in fare of $1. Find the fare that yields the greatest income.
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asked 2 years ago
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Velocity is derivative of position: 80-32t
Velocity= 0.
80-32t=0
32t=80
t=2.5 sec.
h=80*2.5-16*(2.5^2)=200-100
=100 ft.
when h=0:
0=80t-16t^2
-16t^2+80t-0=0
By quadratic formula:
t=(-80+/-sqrt(6400+0))/-32
=(-80+/-80)/-32
=0/-32, -160/-32
=0 sec., 5 sec.
Ball is at h=0 at 0 sec. And again at 5 sec. After being thrown.
3)
Let
"x" be the number of dollars the fare increases.
Income
to the company =(10+x)(300-15x)
-15x^2
+285x+3000 = 0
Solve
it with the help of quadratic formula a=-15 ; b=285 ; c=3000
Maximum
income occurs when x=-b/2a = -285/-30 =9.5
Putting
X= 9.5 in the equation
=(10+x)
=(10+(9.50)= (19.50)
The
fare when x=$9.50 is $19.50.
The
Income will be max when fare is $19.50
Velocity= 0.
80-32t=0
32t=80
t=2.5 sec.
h=80*2.5-16*(2.5^2)=200-100
=100 ft.
when h=0:
0=80t-16t^2
-16t^2+80t-0=0
By quadratic formula:
t=(-80+/-sqrt(6400+0))/-32
=(-80+/-80)/-32
=0/-32, -160/-32
=0 sec., 5 sec.
Ball is at h=0 at 0 sec. And again at 5 sec. After being thrown.
3)
Let
"x" be the number of dollars the fare increases.
Income
to the company =(10+x)(300-15x)
-15x^2
+285x+3000 = 0
Solve
it with the help of quadratic formula a=-15 ; b=285 ; c=3000
Maximum
income occurs when x=-b/2a = -285/-30 =9.5
Putting
X= 9.5 in the equation
=(10+x)
=(10+(9.50)= (19.50)
The
fare when x=$9.50 is $19.50.
The
Income will be max when fare is $19.50
0
1
(10+x) (300-15x) = 3000 +150x - 15xx; so x = 5; $15 far yields 15x225 or $3375. $19.50x(300-9.5(15)) = $3071.25
i mention that you will get the maximum income when the fare is $19.50... so the end result will be $3071.25.. i skipped the last part which you have done in the comment... and still you rated me bad for the whole procedure :( ,,, do you think it's fair??
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