An open-top box is to be made from a 70-centimeter by 96-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. what size square should be cut out of each corner to get a box with the maximum volume? enter the area of the square and do not include any units in your answer. enter an improper fraction if necessary.

hello from mrbilldoesmath!

answer:

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

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

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

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

7x7=4 so if u carry the 9 it will be 33

step-by-step explanation: 4x12ft

• before the lesson, students attempt the assessment task individually. you then review students’

solutions and formulate questions that will them improve their work.

• during the lesson, students work collaboratively in pairs or threes, plotting graphs, completing

tables of values and deducing equations. then, based on the number of common solutions,

students link these representations.

• in a follow-up lesson, students receive your comments on the assessment task and use these to

attempt the similar task, approaching it with insights gained from the lesson.