radomes.openskiesproject.org
afghanifarouq
afghanifarouq afghanifarouq
  • 28-07-2016
  • Mathematics
Answered

Find the length of the cardioid r=5+5cosθ.

Verified Answer :

caylus
caylus caylus
  • 28-07-2016

Hello,

r=5(1+cos t)

r'=5(-sin t)

r²+r'²= 25[(1+cos t)²+(-sin t)²]=50(1-cos t)=50 sin² (t/2)
Between 0 and π, sin x>0 ==>|sin x|=sin x
\(l= 2*5* \int\limits^{\pi}_0{sin( \frac{t}{2} )} \, dt= 5[-cos (t/2)]_0^{\pi}\\\\ =5(0+1)=5\)

Here is the method but i may have make some mistakes.






Answer Link

Related Questions

what is the fraction mixed number of 31 over 6
Jack has 25 to spend at the mall Write an inequality that expresses symbology the amount of money m that jack can spend
The steps to solve the given equation for $x$ are shown below. Given: $\quad \frac{4}{5}+4 x=\frac{1}{2}+\frac{3}{10} x$ Step 1: $\quad \frac{4}{5}+4 x+\lef
How does the excerpt relate to the premises of Brown v Board of Education
If tan x 34 and 0 x 90 then cos x Please explain the work behind the solution
Given y 3x 4 What is the xintercept 0 4 0 43 43 0
is a rock with a fine dark texture that makes up the oceanic crust
You earn a fixed salary working as a sales clerk making 11 per hour You get a weekly bonus of 100 Your expenses are 60 per week for groceries and 200 per week f
what are some steps in research
Why do you think the colonists believed that these laws were intolerable