Yes, sorry, that is what I mean. Decimal approximation is not allowed as far as I know and I'm not even aware that leaving it as arctan(-5/3) is allowed. It does not specify, but all the other problems have had pi in the theta value so I have no idea how it is to be submitted. I guess that is...
Homework Statement
The Cartesian coordinates of a point are given. (3,-5)
(i) Find polar coordinates (r, θ) of the point, where
r > 0 and 0 ≤ θ < 2π.
(ii) Find polar coordinates (r, θ) of the point, where
r < 0 and 0 ≤ θ < 2π.
Homework Equations
r^2=x^2+y^2
tanθ=(y/x) →...
EDIT: Figured it out. Stupid me. I should have solved in terms of x, giving me x=1-(y+3)^2 as my answer.
Homework Statement
x= 1−t^{2}, y= t−3, −2 ≤ t ≤ 2
Eliminate the parameter to find a Cartesian equation of the curve for
−5 ≤ y ≤ −1
Homework Equations
N/A
The Attempt at a Solution...
Ok, that's what my question at the end was about. I wasn't sure if I was supposed to subtract the radii from 5. I'll try it out and see how it goes. Thanks!
Homework Statement
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.
y = 5x, y = 5\sqrt{x} about y = 5
Homework Equations
A(x)=∏(R2-r2)
The Attempt at a Solution
A(x)=∏(5x)2-(5\sqrt{x})2)
A(x)=∏(25 x2 -...
Correct. So, basically I found the area below 1/2x by finding the anti derivative and integrating from 4 to 25. Then I did the same for sqrt(x) and subtracted. Is that not correct?
Well, it looks like part of this may be my own fault for believing this graph? The homework claims this (attached document) is the correct graphing of the two curves, which intersect at (4,2). Which would mean integrating from 4 to 25, correct? Sorry, and it goes on to say (at the bottom) to...
I hope you guys can help. I feel like I know how to do this, but I keep getting the same answer no matter what I do, which is wrong.
Sketch the regions enclosed by the given curves.
y=√x, y=1/2x, x=25
Find its area.
The attempt at a solution
∫4,25 ((1/2x)-(√x))dx
[(1/4x2)-(2/3x3/2)]...