Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with...
Given any Cartesian coordinates, (x,y), there are polar
coordinates (?,?)(r,θ) with −?2<?≤?2.−π2<θ≤π2.
Find polar coordinates with −?2<?≤?2−π2<θ≤π2 for the
following Cartesian coordinates:
(a) If (?,?)=(18,−10)(x,y)=(18,−10) then
(?,?)=((r,θ)=( , )),
(b) If (?,?)=(7,8)(x,y)=(7,8) then
(?,?)=((r,θ)=( , )),
(c) If (?,?)=(−10,6)(x,y)=(−10,6) then
(?,?)=((r,θ)=( , )),
(d) If (?,?)=(17,3)(x,y)=(17,3) then
(?,?)=((r,θ)=( , )),
(e) If (?,?)=(−7,−5)(x,y)=(−7,−5) then
(?,?)=((r,θ)=( , )),
(f) If (?,?)=(0,−1)(x,y)=(0,−1) then (?,?)=((r,θ)=( ,))
3) Find a polar equation of the conic in terms of r
with its focus at...
3) Find a polar equation of the conic in terms of r
with its focus at the pole. ( r=???)
a)(4, π/2) (parabola)
b) (4, 0), (12, π) (eclipse)
c) (8,pi/2), (16,3pi/2) (eclipse)
The integral ∫-1(bottom) to 0 ∫sqrt(−1−x2)(bottom) to 0
−4/(−5+sqrt(x^2+y^2)dydx is very hard to do. If you...
The integral ∫-1(bottom) to 0 ∫sqrt(−1−x2)(bottom) to 0
−4/(−5+sqrt(x^2+y^2)dydx is very hard to do. If you put it in polar
form it's much easier, ∫ba∫dc f(r,θ)r drdθ it's much easier, but
you need to work out the new limits. Find a,b,c,d and the value of
the integral.
a=
b=
c=
d=
∫-1(bottom) to 0∫-sqrt(1−x^2)(bottom) to 0
a/(b+sqrt(x^2+y^2)dydx=