+3693 A box is to be formed by cutting square pieces out of the corner of a rectangular piece of a 3" x 5" notecard as shown below. The sides are then folded up to form a box.
a)Write the function that expresses the area of the bottom of the box as a function of the length of the side of one of the square pieces. (6 points)
b)How large should x be in order for the area of the bottom of the box to equal 10 in2? Round your answer to the nearest hundredth.
Thank you!!!
+130466
a)......Since we're cutting two "x"s" off each side, the area of the bottom of the box is just W * L = (5 - 2x) * (3-2x)
b) So we have
(5 - 2x)(3 -2x) = 10 simplify
15 - 16x + 4x^2 = 10 rearrange
4x^2 - 16x + 5 = 0
Using the onsite solver (since this doesn't factor), we have
4×x2−16×x+5=0⇒{x=−(√11−4)2x=(√11+4)2}⇒{x=0.3416876048223001x=3.6583123951776999}
Reject the larger answer...(it would make the length of both sides negative).....
.34 (rounded) "works"
+130466
a)......Since we're cutting two "x"s" off each side, the area of the bottom of the box is just W * L = (5 - 2x) * (3-2x)
b) So we have
(5 - 2x)(3 -2x) = 10 simplify
15 - 16x + 4x^2 = 10 rearrange
4x^2 - 16x + 5 = 0
Using the onsite solver (since this doesn't factor), we have
4×x2−16×x+5=0⇒{x=−(√11−4)2x=(√11+4)2}⇒{x=0.3416876048223001x=3.6583123951776999}
Reject the larger answer...(it would make the length of both sides negative).....
.34 (rounded) "works"
