from a thin piece of cardboard 40 in by 40 in, square corners are cut out so that the sidescan be folded up to make a box. What dimensions will yield a box of maximum volume

20- max volume dimension

Step-by-step explanation:

since we don't know the amount of cardboard cut off, we'll take it as "x"^^

so the bottom of the box have dimensions of 40-2x(since squares are cut from both corners in a side) by 40-2x hence we can take area of base as

(40-2x)^2

since v=base*height

lets take height as x

x(40-2x) (40-2x)=v

(40x-2x^2)(40-2x)=v

4x^3-160x^2+1600x=v

take the derivitive: 12x^2-320x+1600

factor:

4(3x^2-80x +400)=0

4(3x-20)(x-20)=0

12x-80=0

x-20=0

x=20, 6.667(reduced from 6.66666666667)

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

the factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24. hope this ! mark brainliest! you v much! : )