End Test: I don't undestand these questions

[GreyMuta]

Ello!

Just this week, I just completed my end test, but I have problem understanding these two questions in the test. Can anyone help me?

Question 1: A box is to be formed from a rectangle piece of wood by cutting equal squares of 10 cm out of the corners and folding the sides. The piece of wood is thrice as long as it is wide. If the area of the box is 7680 cm^2. Determine the dimension of the original piece of wood.

Question 2: Jeffrey needs to maximize the area of a corral for his pet. However, there is a cliff on one side, so he only need to fence three sides. He has 1200 yards of fencing.
i) Show that the area, A m^2 is given by A = 1200 - 2x^2.
ii) Given the maximum value of x = -b/(2a), find the maximum value of A.

Regards,
AJ

 

[Deleted member 4993]

Ello!

Just this week, I just completed my end test, but I have problem understanding these two questions in the test. Can anyone help me?

Question 1: A box is to be formed from a rectangle piece of wood by cutting equal squares of 10 cm out of the corners and folding the sides. The piece of wood is thrice as long as it is wide. If the area of the box is 7680 cm^2. Determine the dimension of the original piece of wood.

Question 2: Jeffrey needs to maximize the area of a corral for his pet. However, there is a cliff on one side, so he only need to fence three sides. He has 1200 yards of fencing.
i) Show that the area, A m^2 is given by A = 1200 - 2x^2.
ii) Given the maximum value of x = -b/(2a), find the maximum value of A.

Regards,
AJ

Please tell us exactly where do you get lost in these questions.

 

[Harry_the_cat]

First step in all these sorts of questions is to draw a diagram with known measurements and defined variables.

 

[stapel]

Can anyone help me?

Sure, but we'll first need to know where you're having trouble! So, just like you saw in the "Read Before Posting" announcement, we'll need to see your work first.

Question 1: A box is to be formed from a rectangle piece of wood by cutting equal squares of 10 cm out of the corners and folding the sides. The piece of wood is thrice as long as it is wide. If the area of the box is 7680 cm^2. Determine the dimension of the original piece of wood.

Obviously, this exercise was slightly rewritten from a "cardboard" or "sheet of metal" exercise, since nobody can "fold up" wood to create the sides of a box. Duh! Maybe the author wasn't much familiar with the English language, and thought the terms were interchangeable...? In any case, you can get a good start by reviewing online examples such as the last example here.

Question 2: Jeffrey needs to maximize the area of a corral for his pet. However, there is a cliff on one side, so he only need to fence three sides. He has 1200 yards of fencing.

What picture did you draw? Assuming (as the author must have, but forgot to mention) that you use "x" as the variable for one of the matching sides (and, we'll say, "L" for the remaining side, parallel to the cliff), what "perimeter" equation did you get? Solving this for "L=", what expression did you get for L in terms only of x? What "area" equation did you create, using L and x? Subbing in for L, what "area" equation did you get, only in terms of x?

i) Show that the area, A m^2 is given by A = 1200 - 2x^2.

No; this equation is incorrect.

ii) Given the maximum value of x = -b/(2a), find the maximum value of A.

I'm guessing that they're expecting you to assume that they're referring to the generic quadratic form, "y = ax² + bx + c", and using the vertex-formula value for the x-coordinate of the vertex. (And, yes, they're right about this formula.) Plug-n-chug.