# rectangular

1. ### Rectangular to trignometric form.

-4-4root(3)i therefore... it is going to be in the third quadrant. we find out that the hypotenuse is 8. we know that it is a 30-60-90 right triangle. so writing it in trigonometric form. 8[cos(4pi/3)+isin(4pi/3)] Question though... the textbook said assume that theta... is between 0...

3. ### r=tan(theta) convert to rectangular form

r=tan(theta) r^2=rtan(theta) x^2+y^2=r(y/x) .. problem... we cannot get rid of the "r" if we keep converting and squaring. x(x^2+y^2)=r*y.... x(x^2+y^2)=r*r sin(theta) x(x^2+y^2)=x^2+y^2((sin(theta)) wait a minute I did r= sin/cos therefore... r=(y/r)/(x/r) multiple r by both...
4. ### Conversion: Polar form to rectangular form.

r=2cos(theta) r=2(x/r) r^2=2x x^2+y^2=2x x= rcos(theta) the answer in the book is (x-1)^2+y^2=1
5. ### Conversion from Rectangular to Spherical

1. 2. 3. Formula:
6. ### A Lid made from a square shaped paper, must fit on a rectangular box (no lid).

The values of the rectangular box is given, the question is to determine the amount needed to be cut off from a 10x10cm paper with 1mm over lap and 1 cm folded edge which maximizes the volume of the box AND what the volume of the box underneath will be.
7. ### Double Integral over rectangular region.

Hello, I have the following question, and I disagree with its proposed answer. Here is what I did, am I correct? \int_1^2 \int_1^3 xe^{xy}dy dx = \int_1^2 (e^{xy})|_1^3 dx \int_1^2 (e^{3x}-e^{-x})dx = (\frac{1}{3}e^{3x}-e^x )|_1^2 = \frac{1}{3}e^6 - e^2 -\frac{1}{3}e^3 +e Thanks!
8. ### Simplifying the surface area formula for a rectangular box with a square base

Please refer to the image for my question
9. ### Convert from spherical coordinates to rectangular

Convert the spherical formula $ρ=\sinθ\sinϕ$ to rectangular coordinates and describe the surface defined by the formula (Hint: Multiply both sides by $ρ$.) Looks simple, but I couldn't figure it out. \begin{align*} \rho^2&=\sin\theta\sin\phi\cdot\rho\\ y&=\rho^2 \end{align*} What about the rest?
10. ### Need help finding maximum possible volume of a rectangular box

I think I might be over thinking this but I am not sure what to do to get the formulas.
11. ### Equation to a rectangular Prism

Hello, I am trying to understand the concept of solid geometry(spheres, cubes, polyhedra etc) as a function of their co-ordinates. for example, the general ellipsoid, is a quadratic surface which is given in Cartesian coordinates by: (x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1 a,b,c being the semi axis. -Is...
12. ### Among all rectangular solids defined by the inequalities find one with greatest flux

Among all rectangular solids defined by the inequalities 0 ≤ x ≤ a, 0 ≤ y ≤ b, 0 ≤ z ≤ 1, find the one for which the outward flux of F = (−x^2 − 4xy)i − 6yzj + 12zk outward through the six sides is greatest. What is this maximum flux? I am not sure how to proceed.
13. ### Average value of function over rectangular prism

There are two related problems im stuck on. Average value of: f(x)=ye^(-xy) Over the box [0,1]x[0,1]x[0,1] and over the prism [0,5]x[0,3]x[0,3]. I cant find a way around the #/0 problem... help please?

15. ### Finding average value using polar and rectangular coordinates of f(x,y)=x

I have to find the avg value of f(x,y)=x over the quarter of the unit circle in the first quadrant using rectangular and polar coordinates. I can do it by polar coordinates but I'm unsure how I would make it rectangular. I will include a photo of my written work shorty since I'm not very good at...
16. ### converting equations (cylindrical, rectangular, spherical)

I figured out the answer on my own, I don't know how to delete the post
17. ### converting rectangular to spherical coordinates

Question: Convert the point from rectangular coordinates to spherical coordinates. a. b. c. d. e. Relevant equations : tanθ = y/x ρ = √(x²+y²+z²) Φ = arccos(z/ρ) Solution attempt: ρ=√(7²+(7√3)²+14²) = 14√2 tanθ = 7√3/-7 = -√3 arctan(-√3) = -Π/3 Φ = arccos(14/14√2) =...
18. ### Rectangular Parallelepiped Length and Angle Problem Stuck:(!!

A rectanglar parallelepiped with square ends has 12 edges and six surfaces. If the sum of all edges is 176 cm and the total surface area is 1288 cm^(2) Find: A) the length of the diagonal of the parallelpiped (shown as bold line in figure) B) the angle the diagonal makes with the base...
19. ### Write the complex number in rectangular form.

Write the complex number in rectangular form. 3cis52degrees ( round to 3 decimal places)
20. ### Polar to rectangular

I am trying to help grand daughter express this is rectangular form: thetha = pi/3