Find the arc length from (-3,4) clockwise to (4,3) along the circle
x^(2) + y^(2) = 25. Show that the result is one-fourth the circumference of the circle.
Use the arc length formula!!
2007-02-04 12:25:44 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
And show you work, please!!!!!
2007-02-04 12:26:23 · update #1
KZ, you got the points!!! Thank you so much for explaining it!!!!
2007-02-04 12:46:41 · update #2
put this equation into y= form
y= Sqrt(25-x^2) (because we are only dealing with the top half of the circle, we dont' need to use the plus or minus)
use the arc length formula
Arc length = Integral from -3 to 4 of Sqrt(1+(d/dx (Sqrt(25-x^2)))^2) dx
the derivative of the Sqrt(25-x^2) is -x/(25-x^2)^.5
plugging this back into the original equation gives you
Arc length = integral from -3 to 4 of Sqrt(1+(x^2/(25-x^2)) dx
integrating this gives you 5Pi/2
show that the result if 1/4 the circumference:
well you have 5Pi/2
the circumference is 2Pi(radius), radius= Sqrt(25)=5
so circumference = 10Pi
10Pi/4=5Pi/2
2007-02-04 12:35:57 · answer #1 · answered by kz 4 · 1⤊ 0⤋
x*y^2nd pwr 2*2=12*2+1
2007-02-04 12:30:03 · answer #2 · answered by Anonymous · 0⤊ 0⤋
ya right i flunk
2007-02-04 12:37:33 · answer #3 · answered by TMC 2 · 0⤊ 1⤋