A rectangular box with a square base is to be constructed from material that costs $9 per ft2 for the bottom, $5 per ft2 for the top, and $4 per ft2 for the sides. Find the box of greatest volume that can be constructed for $204. Round your answer to 2 decimals. slader -g

Step-by-step explanation:

Let

Side of square base=x

Height of rectangular box=y

Area of square base=Area of top=

Area of one side face=

Cost of bottom=$9 per square ft

Cost of top=$5 square ft

Cost of sides=$4 per square ft

Total cost=$204

Volume of rectangular box=

Total cost=

Substitute the values of y

Differentiate w.r.t x

It takes positive because side length cannot be negative.

Again differentiate w.r. t x

Substitute the value

Hence, the volume of box is maximum at x=2.2 ft

Substitute the value  of x

Greatest volume of box=

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

the class and exam medians are closely related, and it looks like the low outlier on the exam did pull the median lower. [tex][/tex]

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2