Which numbers complete the blanks when solving the equation cos(x+2π) = - √2/2 over the interval [0,2π]

x = 3π/4, 5π/4

Step-by-step explanation:

cos(x+2π) = -√2/2, [0,2π]

cos(x)cos(2π)-sin(x)sin(2π) = -√2/2

cos(x) = -√2/2

x = 3π/4, 5π/4

Remember that the cosine function is periodic, so cos(θ+2π)=cos(θ).

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)