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Is this function correct?
A stone is dropped in a lake and creates a ripple that moves outward at a rate of 60cm/second. Write the area of this ripple as of function of t (seconds). My book says the answer is A(t)=3600pi(t)^2 but i got A(t)=900pi(t)^2 because the radius is half the diameter the first second. So am I right or the book is right? If I'm wrong, where did I thought wrong?
Thank you seanchasworth, I don't what I was thinking but yea that's where I went wrong thanks!
Alot of correct answers thanks!
10 Answers
- lcmcpaLv 71 decade agoFavorite Answer
Glad so many of these people could help you. I had to pass on this one.
- 1 decade ago
Sorry, but the book is correct. The radius of the circle after one second is 60 cm. -- not 30 cm. After one second the ripple has moved 60 cm from the center --- in all directions. The diameter of the ripple is actually 120 cm. So, the area as a function of time is 3600 pi t^2.
Source(s): Trust me. I have a degree in math. - organicchemLv 51 decade ago
We know area of a circle is (pi)(radius)^2
The radius in your case is 60t because at t = 1s, the radius is 60 cm, at t = 2s the radius is 120 cm, at t = 3s the radius is 180 cm......since the ripple travels 60cm/second.
Thus area of the circle is (pi)(60t)^2 = 3600 (pi)(t)^2. I think you used 60t as the diameter instead of radius in order to get 900 (pi)t^2. The ripple moving outward at a rate of 60cm/second means the radius is 60cm after 1 second.
- just♪wonderingLv 71 decade ago
Area = (pi)(r)^2
r is changing as a function of time, starting from zero, so r(t) = 60t cm because the circle moves out in all directions at the rate of 60 cm/sec.
So Area = (pi)(60t)^2 = 3600(pi)t^2
That makes the book right.
The problem does not say that the diameter of the ripple is growing at the rate of 60 cm/sec. It just says the ripple is moving outward at that rate. That's where you made your mistake.
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- 1 decade ago
I read it this way...the ripple moves outward at a rate of 60 cm/s. It must move outward from something...so that would be the center. Therefore, after a second, it has moved outward from the center 60 cm. It has NOT stretched to a diameter of 60, but to a diameter of 120. It must stretch outward from one point that stays constant, in this case the center.
- Anonymous1 decade ago
the book is right.... the rate that the ripple moves outwards at (60 cm/second) is the radius of the ripple, not the diameter. i hope this helps.
- PolymathLv 51 decade ago
I prefer the 3600. The radius is expanding at 60cm/s, not the diameter. The ripple is moving outward from the center, not the other ripple.
That's just my take on things, though.
- Anonymous1 decade ago
Area = pi * radius squared.
But, the radius changes with time and that rate of change is
radius/time = 60 [cm/sec]
The actual radius = rate * time = 60 [cm/sec] * t [sec]
r = 60t [cm]
Plug into area equation:
Area =A(t) = pi * (60t [cm])^2
= 3600pi(t)^2 [cm^2]
- peveheadLv 41 decade ago
if the answer was wrong it would be a typo. it wouldnt be that far off.
one thing i do notice however is that your answer is 1 quarter of the correct one. could you have just made is simple miscalculation?
