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yangyang718
26.06.2020 •
Mathematics
A truck starts off 180 miles directly east from the city of Hartville. It travels due south at a speed of 45 miles per hour. After travelling 49 miles, how fast is the distance between the truck and Hartville changing
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Ответ:
11.82 mph
Step-by-step explanation:
The angle between the direction of travel and the direction to the city of Hartville is ...
arctan(180/49) ≈ 74.77°
The speed from the direction of Hartville is the the actual speed multiplied by the cosine of this angle:
speed from Hartville = (45 mph)×cos(74.77°) ≈ 11.82 mph
Comment on the solution
There are other approaches you can use to solve this. One is to compute the change in distance over a small period of time, such as 0.02 hours.
0.01 hours before the time of interest, the distance to the city is ...
d1 = √(180² +(49-.01(45))²) ≈ 186.4326 . . . miles
0.01 hours after the time of interest, the distance to the city is ...
d2 = √(180² +(49+.01(45))²) ≈ 186.6690 . . . miles
Then the rate of change of distance is ...
(d2 -d1)/(t2 -t1) = (186.6690 -186.4326)/0.02 = 11.82 . . . mi/h
__
Another is to write the distance equation and differentiate it. (You will find the solution looks very much like the trig solution above.)
d = √(180² +(45t)²)
dd/dt = 45²t/√(180² +(45t)²) . . . . . to be evaluated at t=49/45
rate of change = 45(49/√(180²+49²)) ≈ 11.82 . . . mi/h
Ответ:
total cost earn=$1360
adult sold =45
student sold =80
adult cost twice as student cost so we can say adult sold 45+45=90
so total sold=90+80=170
to get the cost of 1 meal we divide 1360 by 170
1360/170=8
one student meal cost=8$
one adult meal cost=8*2=16
total students meal cost=8*80=640$
total adult meal cost=16*45=720
640+720=1360