Acellus 3
Find the maximum value of
C = 6x + 2y
Subject to the following constraints: *
x >0
x < 5
y>0
4x – y >1

the answer is 13 cm

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)

in 2010, the population of the state of california is 37.29 × 10⁶

step-by-step explanation:

population of los angeles = 3.79 × 10⁶

population of california = 9.84 × population of los angeles

                                        = 9.84 × 3.79 × 10⁶

                                        = 37.2936 × 10⁶

                                        = 37.29 × 10⁶

∴ in 2010, the population of the state of california is 37.29 × 10⁶

step-by-step explanation:

hihi so drawing these 2 triangles is fairly simple. all that's left is finding the height of each one. luckily, we have a side length and an angle, so there is a trig function we can use to solve for the height. the easiest one to use would be tangent, since we have 2/3 things needed to find and the third needed is what we are solving for. tan(73°) * 30 ~= 98.13 and tan(73°) * 35 ~= 114.45