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1. A supermarket employee wants to construct an open-top box from a 14 by 30 in a piece four corners so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume?

1. A supermarket employee wants to construct an open-top box from a 14 by 30 in a piece four corners so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume?

Advanced Engineering Mathematics
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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1. A supermarket employee wants to construct an open-top box from a 14 by 30 in a piece four corners so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume? 2. Which point on the graph of y = square root of x is closest to the point (7,0)? 3. Two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post. If the worker wants to stake both ropes in the ground at the same point, where should the stake be placed to use the least amount of rope? 4. A particle moves along a horizontal line. Its position function is s(t) for t 0. For each problem, find the velocity function v(t) and the acceleration function a(t). Sketch the graph of s(t), v(t), and a(t). a. s(t) = t*3 - t^2 - 56t 5. A particle moves along a horizontal line. Its position function is s(t) for t2 0. For each problem, find the displacement of the particle and the distance traveled by the particle over the given interval. Sketch the graph of s(t) and v(t). a. s(t) = -t^2 + 6t + 27; 0 sts 4 b. s(t) = -t^3 + 11"2 ; 3 sts8 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the possible propagated error in the calculated volume.
Transcribed Image Text:1. A supermarket employee wants to construct an open-top box from a 14 by 30 in a piece four corners so the four sides can be bent upwards. What size should the squares be in order to create a box with the largest possible volume? 2. Which point on the graph of y = square root of x is closest to the point (7,0)? 3. Two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post. If the worker wants to stake both ropes in the ground at the same point, where should the stake be placed to use the least amount of rope? 4. A particle moves along a horizontal line. Its position function is s(t) for t 0. For each problem, find the velocity function v(t) and the acceleration function a(t). Sketch the graph of s(t), v(t), and a(t). a. s(t) = t*3 - t^2 - 56t 5. A particle moves along a horizontal line. Its position function is s(t) for t2 0. For each problem, find the displacement of the particle and the distance traveled by the particle over the given interval. Sketch the graph of s(t) and v(t). a. s(t) = -t^2 + 6t + 27; 0 sts 4 b. s(t) = -t^3 + 11"2 ; 3 sts8 6. The radius of a sphere is measured to be 7 cm, with a possible error of + (1/10) cm. Estimate the possible propagated error in the calculated volume.
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