Math Assignment Help

[NobodyAnyone]

1.
A factory stacks boxes according to their weights. To provide stability to the stacks of boxes, heavier boxes are placed at the bottom of the stack, and lighter boxes are placed at the top. However, because of the boxes’ material, a box can only be placed on top of another if its weight is exactly half the weight of the lower box. Also, due to the height of the warehouse ceiling, boxes can only be stacked 4 levels high. The factory director has asked for your help in answering some questions about these boxes.

a. Explain how you would find the weight of each stacked box if you knew the weight of the bottom box. Find the weight of each box in a stack of 4 boxes if the bottom box weighs 10 pounds.
b. Eventually, these stacks of boxes will go onto pallets for shipping. We need to know how much each stack weighs in order to know how many stacks we can put on each pallet, but the bottom boxes do not necessarily weigh 10 pounds. In fact, we don’t know how much they weigh at all! Write and simplify an expression to find the weight of one stack of 4 boxes based on the unknown weight of the bottom box.
c. Each stack needs to weigh less than 100 pounds. Write and solve an inequality to find the maximum weight of the bottom box. What would be the possible range of weights for this box? It may help you to consider a graph of the solution to your inequality.

 

[BigBeachBanana]

a) If the bottom box weighs 10 lbs, and the next one weighs half of that, meaning 10*(1/2)=5, continue for boxes 3 and 4.
b) Observe the pattern you did in part a), instead of letting the bottom box weighs 10lbs, let's say it weighs x lbs. Hint: Sum of geometric series.
c) Complete part b) first.

 

[NobodyAnyone]

a) If the bottom box weighs 10 lbs, and the next one weighs half of that, meaning 10*(1/2)=5, continue for boxes 3 and 4.
b) Observe the pattern you did in part a), instead of letting the bottom box weighs 10lbs, let's say it weighs x lbs. Hint: Sum of geometric series.
c) Complete part b) first.

Thx u so much but can you please explain briefly or at least make me a formula.

 

[Steven G]

Part c asks for a formula. Giving you the answer (ie the formula) is not something we do here. We want you to do the work on your own.
I will do part a for you.
10 lbs, then 10/2lbs = 5 lbs, then 5/2lbs = 2.50lbs, then 2.5/2lbs = 1.25 lbs.

Here is a hint for part b. You need to know that \(\displaystyle \dfrac{(\dfrac{a}{b})}{c} = \dfrac{a}{bc}\)

 

[NobodyAnyone]

Part c asks for a formula. Giving you the answer (ie the formula) is not something we do here. We want you to do the work on your own.
I will do part a for you.
10 lbs, then 10/2lbs = 5 lbs, then 5/2lbs = 2.50lbs, then 2.5/2lbs = 1.25 lbs.

Here is a hint for part b. You need to know that \(\displaystyle \dfrac{(\dfrac{a}{b})}{c} = \dfrac{a}{bc}\)

Alright. I’ll try it!