1. [V] Plot the point with cylindrical coordinates, (r, θ, z) = (2, 4π/3, 1). Then find the rectangular and spherical coordinates of the point. 2. [V] Let P be the point whose rectangular coordinates are (x, y, z) = (−1, −1, 2) Find the cylindrical and spherical coordinates of P.
4. [V] Write the equation z = x^2 + y^2 in cylindrical and in spherical coordinates.
6. [V] Write the equation φ = π/2 in rectangular and in cylindrical coordinates.

u bout ugly as   a mf

step-by-step explanation: lol

answer: b

step-by-step explanation:

hello from mrbilldoesmath!

answer:   (7x + 6y) ( 49x^2 - 42xy + 36y^2)

discussion:

in general, the factorization of a^3 + b^3 is

a^3 + b^ 3 = (a + b) ( a^2 - ab + b^2)

in our case note that 343 = 7^3 and 216 = 6^3 so the equation becomes:

343x^3 + 216y^3 = (7x)^3 + (6y)^3

if you think of a (above) as 7x and b as 6y the factorization becomes

343x^3 + 216y^3 =

((7x + 6y) (   (7x)^2 - 7x*6y + (6y)^2)   =

(7x + 6y) ( 49x^2 - 42xy + 36y^2)

you,

mrb

(a + b) (a^2 - a b + b^2)