Answer: 16.5 hours
Step-by-step explanation:
distance=rate*time
132=8*x
Divide by 8 on both sides
x=16.5
26*2=52 cards each
52/15 = 3.4 cards
52/13 = 4 cards
52/18 = 2.8 cards
52/16 = 3.25 cards
Answer: 15 rows of 4 cards each
Given:
The data points are:
(1, 0), (2, 3), (3,1), (4,4), (5,5)
To find:
The equation of best fit line in the form of and then find the value of b.
Solution:
The general form of best fit line is:
...(i)
Where, m is the slope of best fit line and b is the y-intercept of the line.
Using the graphing calculator, we get the equation for the best fit line and the equation is
...(ii)
On comparing (i) and (ii), we get
Therefore, the value of b is equal to -0.7.
A)
y=C₁(v)=Fuel cost for the trip as a linear function of the average speed, v.
x=v= average speed.
Data:
When: v=60 mph ⇒ C(v)=$30
When: v=120 mph ⇒ C(v)=$42
We have two points (60,30) and (120,42), therefore we have to calculate the equation of the line passes through these points.
1) We calculate the slope of the function:
Given two points (x₁,y₁) and (x₂,y₂) the slope of the line passes through these points will be:
m=(y₂-y₁)/(x₂-x₁)
In our case, the points are (60,30) and (120,42) and the slope will be:
m=(42-30)/(120-60)=12/60=0.2 ($0.2 per mile)
slope-intercept form of a line: we need a point (x₀,y₀) and the slope:
y-y₀=m(x-x₀)
We know the slope (m=0.2) and we can choose either of the points known, the result is always the same with any of these points known. Therefore:
(60,30)
m=0.2
y-y₀=m(x-x₀)
y-30=0.2(x-60)
y-30=0.2x-12
y=0.2x-12+30
y=0.2x+18
y=C(v)
x=v
C₁(v)=0.2v+18
Answer (a)= the fuel cost ( C(v) ) for the trip as a linear function of the average speed, v would be: C₁(v)=0.2v+18
b)
y=C₂(v)=no- fuel cost of the trip en function of the average speed (v).
v=average speed
time=distance / speed
C₂(v)=$20 per hour (distance /speed)
C₂(V)=$20 / hour(100 miles / speed)
C₂(v)=2000/ v
For example:
if v=60 mph ⇒ C₂(v)=2000 /60≈$33.33
if v=120 mph⇒C₂(v)=2000/120≈$16.67
Other way
We have to calculate the time spend with the two speeds known.
if average speed=60 mph ⇒time=100 miles/(60 miles/hour)=5/3 hour.
if average speed=120 mph ⇒time=100 miles/(120 miles/hour)=5/6 hour.
non-fuel cost if v=60 mph =$20 per hour(5/3 hour)≈$33.33
non-fuel cost if v=60 mph =$20 per hour(5/6)≈$16.67
Answer (b): the function of the non-fuel cost for the trip will be :
C₂(v)=2000/v. The non-fuel cost for the speeds given are:
non-fuel cost if v=60 mph ≈$33.33
non-fuel cost if v=120 mph ≈$16.67
c)
C(v)=total cost for the trip
C(v)=C₁(v)+C₂(v)
C(v)=(0.2v+18)+(2000/v)
or
C(v)=(0.2v²+18v+2000)/v
1) We have to do the first derivative of this function:
C´(v)=0.2-2000/v²
C´(v)=(0.2v²-2000)/v²
2) We have to find the values of "v" when C´(v)=0
Then:
0.2v²-2000=0
v=√(2000/0.2)=100
3)We have to do the second derivative:
C´´(v)=4000/v³
C´´(100)>0 ⇒ we have a minimum at v=100
The total cost of the trip will be:
C(100)=0.2(100)+18+2000/100=$58
Answer (c): the average seed that minimizes the total cost of the trip will be 100 mph.