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a couple of math problems?
Please explain how you get the answer for both.
1. Two cylinders have the same volume. If the radius of cylinder I is 3 times the radius of cylinder II, then the height of cylinder II is how many times the height of cylinder I?
A. 12
B. 9
C. 6
D. 3
2. Every weekend, Phil drives from his home to his favorite amusement park, a distance of 60 miles.
a. If he averages 40 mph for the first half of the trip, what must his average speed for the second half of the trip in order for him to average 50 mph for the entire trip?
b. Suppose that on the trip home, Phil decides to stop a 30 minute dinner break. If he averages 45 mph for the first half of this return trip and 60 mph for the second half of this trip, how many more MINUTES will the return trip take compared to the trip going to the park? (be sure to account for his dinner break.)
4 Answers
- ranjankarLv 78 years agoFavorite Answer
1) Let the radius of 1st cylinder be x and height h1
Volume = pi *x^2 *h1
Radius of second cylinder = 3x
Volume = pi 9x^2 h2
pi 9x^2 h2 = pi x^2 h1
9h2 = h1
h2 = h1 /9
ANSWER 9 times
2) Let the total distance be x
and y be the speed for second half
x / 40 + x /y = 2x /50 = x /25
x/25 - x/40 = x/y
(8x - 5x)/ 200 = x /y
3x / 200 = x /y
3xy = 200x
3y = 200
y = 200/3 = 66.67 mph ANSWER
b) 60/50 = 1 hour 12 minutes = 72 minutes
30/45= 2/3 = 40 minutes
30/60 = 1/2 = 30 minutes
40 +30 +30 = 100 minutes
ANSWER = 100-72 = 28 minutes extra
- MojoMajLv 68 years ago
Volume of a cylinder I
= pi * r^2 * h
Volume of cylinder II = pi*(1/3*r)^2 *h and h of cylinder II must be nine times the height of cylinder I
2a. Speed on the first half of the trip = 40mph = distance (60 miles) / 1.5 hours
Average speed of 50 mph for 120 miles equals 2.4 hours
The difference between the two times {2.4 - 1.5) = 0.9 hours
Please note that any answer more accurate than two significant digits is not justified. Least accurate measurement given is two significant digits, 30 minutes.
Therefore the average speed for the second half of the trip, 60 miles = distance/ time = 60/0.9 = approximately 67 mph. (66.67 mph would not be justified by the number of significant figures provided)
b. 60 miles/45 mph = 1 hour and 20 minutes for the first half of the trip; 1 hour and 30 minutes for the second half of the trip and the total time including dinner break is 90 minutes. The difference in minutes between the trip to the amusement park and the trip home is 10 minutes.
Source(s): www.purplemath.com http://www.physics.uoguelph.ca/tutorials/sig_fig/S... - WarmongerLv 48 years ago
V=pi*r^2*h
Since volumes are the same...set equal to each other...cancel pi...
h2 is height of cylinder 2...
r^2 * (h2) = (3r)^2 * (h1)
r^2 cancels...
h2 = 9*h1
Total time = 120/50 = 2.4 hours
First leg's time = 60/40 = 1.5 hours...
Last leg's rate = (2.4-1.5)x = 60
X = 60/.9 = 66.67 mph
Last legs time = 30/45 + 0.5 + 30/60 = 1 hour 40 minutes
So, 10 minutes longer...
- Anonymous4 years ago
next time once you get assignments like those, you may only ask google. only variety interior the hunt field "28.35 grams to oz" additionally, solid luck with this, you would be changing imperial gadgets for the the remainder of your existence. 0.5 mile = half of one mile 28.35 grams = a million.00001682 ouncesNow, bypass do your homework ;)
