[No Calculator]An open-top box is to be made by cutting congruent squares of side length x from the corners of a 5- by 8-inch sheet of tin and bending up the sides (see figure below). a) Write an equation for the Volume of the box. b) What is the domain of this function? c) How large should the squares be to maximize the volume? d) What are the dimensions of the box with maximum volume? What is the maximum volume?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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OrCalculator Allowed] Wile E. is after Road Runner again! This time he's got it
figured out. Sitting on his ACME rocket he hides behind a hill anxiously awaiting
the arrival that "beeping" bird. In his excitement to light the rocket he tips the rocket
up. Instead of thrusting himself parallel to the ground where he can catch the Road
Runner, he sends himself widely into the air following a path given by function
h(t) = .1r -1.3 + 4.21 +2,
where h is the height of the rocket after t seconds. The rocket fuel lasts for 10
seconds. At that point, Wile E. Coyote stops suddenly and falls straight down to the
ground.
a) What is the domain of this function?
b) What is the highest point reached by Wile E. Coyote? [Use Calculus!]
Transcribed Image Text:OrCalculator Allowed] Wile E. is after Road Runner again! This time he's got it figured out. Sitting on his ACME rocket he hides behind a hill anxiously awaiting the arrival that "beeping" bird. In his excitement to light the rocket he tips the rocket up. Instead of thrusting himself parallel to the ground where he can catch the Road Runner, he sends himself widely into the air following a path given by function h(t) = .1r -1.3 + 4.21 +2, where h is the height of the rocket after t seconds. The rocket fuel lasts for 10 seconds. At that point, Wile E. Coyote stops suddenly and falls straight down to the ground. a) What is the domain of this function? b) What is the highest point reached by Wile E. Coyote? [Use Calculus!]
* Show appropriate work ☺
2)
[No Calculator]An open-top box is to be made by cutting congruent squares of side length x from the corners of a 5-
by 8-inch sheet of tin and bending up the sides (see figure below).
a) Write an equation for the Volume of the box.
b) What is the domain of this function?
5"
c) How large should the squares be to maximize the volume?
d) What are the dimensions of the box with maximum volume? What is the maximum volume?
Transcribed Image Text:* Show appropriate work ☺ 2) [No Calculator]An open-top box is to be made by cutting congruent squares of side length x from the corners of a 5- by 8-inch sheet of tin and bending up the sides (see figure below). a) Write an equation for the Volume of the box. b) What is the domain of this function? 5" c) How large should the squares be to maximize the volume? d) What are the dimensions of the box with maximum volume? What is the maximum volume?
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