Chung and his Food truck

Question

1.) to build a rectangular box for his pineapple fried rice, Chung uses a flat piece of cardboard with length l and width w. he cuts out four identical squares from the corners then folds the cardboard into the box.
The equation V = (l * 2s)(w * 2s)s represents the volume of the box.
*interpret the meaning of the expression (w - 2s)
*which feature of the folded box does the product (l *2)(w * 2s) represent?
2.) Chung writes down the number of customers he has for the first hour.
At 9 a.m. Chung opens his food truck.
Between 9 and 10 a.m. there are 10 customers.
He gets so busy he cannot write down the number of customers.
Chung is given the equation y= -x^2 + 10x + 1 which approximates the number of customers and how many there were, Chung transforms the equation into vertex form.
Step 1: y= x^2 +10x +1
Step 2: y-1 = -x^2 + 10x
Step 3: y= -1 = (x^2 + 10x +25) +25
Step 4: y= 26 = -(x + 5)^2
Step 5: y= - (x + 5)^2 + 26
*determine whether Chung made a mistake, if so, identify the step and show the steps to fix the process to create the correct vertex form.
* determine which hour Chung has the most customers and the number of customers he had during that hour.

3.) Chung starts a college fund with $200. Each month he deposits the same amount of money. Chung’s aunt wants to help out. She buys $200 of a stock that grows at a rate of 15% per month. (assume these conditions continue.)
*determine for which month(s) Chung account has a higher value than his aunts stock value.
*show all work that leads to and justifies your determination.

Answer 1

Hi

width of the box = w, length = l

1. The box is cut in the corners, assuming the length cut on each corner = s,

so. now width = w-2s and length = l-2s

now if you make this cut sheet into a box, it will a cuboid whose volume = length*breadth*height = (l-2s)*(w-2s)*s

area = length*breadth = (l-2s)*(w-2s)

 

2. I think this question wants you to isolate x and y terms and give a tidy equation like (x-5)^2 + 26 = y^2

only can you correctly give the original equation , is it -x^2 +10x or x^2 +10x

 

3. for each month, he saves 200, so in 1 year he will save 12*200 and if t= years he keeps saving, he will have 200*12t as his savings

 

what his aunt does is compound interest, compounded monthly for a time t where the boy's and aunt's contributions match

a= 200*12t = 200(1+ (0.05/12))^12t

12t = (1+ (0.05/12))^12t

if you solve this equation, you get the answer

 

:)

 

 

Answer 2

This isn't an answer (sorry!) but I'm wondering if something was typed incorrectly. The equation you included in the problem says  V = (l * 2s)(w * 2s)s and then it says to interpret the meaning of (w - 2s). So I'm wondering if either the equation or the expression needs to be edited. I would think they would be the same. Basically, as it's written now, you're being asked to interpret an expression that doesn't exist in the equation.