You work part-time at the “Pack-it and Mail-it” that sells containers used for shipping items. Your photography teacher asks you to recommend the best package to ship 35 mm film containers. The film containers are 1 inch in diameter and 2 inches in height, and they are to be shipped in groups of twelve.

A) Find the volume of twelve film containers. Round your result to two decimal places and show all calculations below.

B) Which container should be used to fit a dozen film containers with the least amount of wasted space? Explain your reasoning.

At work you get a list of package sizes. Your store has four box sizes that look like they might work. The sizes are given in the form l x w x h. They are 3 in. x 2 in. x 5 in., 4 in. x 3in. x 2 in., 5 in. x 6 in. x 5 in., and 3 in. x 2 in. x 3 in.

(a)18.85 Cubic Inches

(b)The box with dimensions of 4 in. x 3in. x 2 in.

Step-by-step explanation:

Part A

Volume of the 12 Containers

Height =2 Inches

Diameter=1 Inch

Radius=Diameter/2=1/2=0.5 Inch

Volume of a cylinder

Volume of the 12 Containers

Part B

To determine the container which should be used, we first determine the volume of the available boxes.

Volume of the boxes

Volume of box with dimension 3 in. x 2 in. x 5 in.=3X2X5=30 Cubic Inches

Volume of box with dimension 4 in. x 3in. x 2 in.=4X3X2=24 Cubic Inches

Volume of box with dimension 5 in. x 6 in. x 5 in.=5X6X5=150 Cubic Inches

Volume of box with dimension 3 in. x 2 in. x 3 in. =3X2X3=18 Cubic Inches

The box that should be used with the least amount of wasted space is he box with volume 24 Cubic inches. i.e. box with dimensions 4 in. x 3in. x 2 in.

This is because the volume of the box(18 cubic inches) with dimension 3 in. x 2 in. x 3 in. is less than what is required.

answer: solve 5\cdot 2^x=2405⋅2  

x

=2405, dot, 2, start superscript, x, end superscript, equals, 240.

solution

to solve for xxx, we must first isolate the exponential part. to do this, divide both sides by 555 as shown below. we do not multiply the 555 and the 222 as this goes against the order of operations!

\begin{aligned} 5\cdot 2^x& =240 2^x& =48 \\ \end{aligned}  

5⋅2  

x

2  

x

​    

=240

=48

​

step-by-step explanation:

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