then its circumference is expandinf at a constant rate. Justify your anwer with a formula if its TRUE or FALSE
2006-12-30 08:41:37 · 7 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
c=2πr
affter time /\t
c+/\c=2π(r+/\r)
the change is
c+/\c-c=2π(r+/\r)-2πr
/\c=2π/\r
as long as /\r is comstant, /\c will also be constant
so TRUE
2006-12-30 08:47:53 · answer #1 · answered by yupchagee 7 · 16⤊ 0⤋
To work a problem like this, first make sure that you know the relationship between the things involved:
How is circumference and radius related?
C=2*pi*R
Since 2 and pi are constants, if you plot C vs R it's a straight line. Slope is
change in C / change in R , which is constant.
This can be considered a calculus problem but it is so simply that I don't think that it is.
2006-12-30 16:49:50 · answer #2 · answered by modulo_function 7 · 0⤊ 0⤋
The formula for circumference is C = 2Ïr
Because neither the circumference nor the radius has an exponent (both raised to a power of one) and they are direct functions of each other -- that is, only separated by the multiplication/division function, they increase at the same rate.
That according to the formula -- but they expand at a constant rate because they both express distance (as opposed to area or volume) -- your practical proof or check. :)
2006-12-30 16:44:40 · answer #3 · answered by Shanny 2 · 0⤊ 0⤋
True.
The formula for a circumference (2*pi*r) is linear; as r increases at a constant rate, so too does the circumference.
(By contrast, the area formula, pi*r^2, is not linear; so the area increases as the square of the radius, rather than the radius itself. This geometric progression is not constant.)
2006-12-30 16:44:43 · answer #4 · answered by Tim P. 5 · 0⤊ 0⤋
The circumference C is just 2*PI*radius. So, C is linearly proportional to the radius.
C=2*PI*r
dC/dt = 2*PI*dr/dt (because 2 and PI are constants).
So the circumference increases at a rate 2*PI times faster than the radius.
2006-12-30 16:47:27 · answer #5 · answered by NMAnswer 2 · 0⤊ 0⤋
True.
The circumference of a circle is equal to 2(pi)r. That's 2 multiplied by pi multiplied by the radius. If the radius increases, then so does the circumference.
2006-12-30 16:45:06 · answer #6 · answered by Silas 2 · 0⤊ 0⤋
Call the radius 'r'.
Call the constant rate 'k'.
So dr/dt = k.
Call the circumference 'C'.
Radius is related to circumference in this way:
C = 2r*pi.
So, r = C/(2*pi).
Differentiate both sides (w.r.t. time):
dr/dt = 1/(2*pi) dC/dt.
Thus, 1/(2*pi) dC/dt = k,
dC/dt = 2*pi*k, which is indeed constant (how boring).
2006-12-30 16:52:24 · answer #7 · answered by Bugmän 4 · 0⤊ 0⤋