A wooden beam has a rectangular cross section of height h and width w (see figure). The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter d = 23 inches? Round your answers to two decimal places. [Hint: $S = k w h ^ { 2 },$ where $k 0$ is the proportionality constant.]
A)w = 13.28 inches and h = 18.78 inches
B)w = 7.67 inches and h = 21.68 inches
C)w = 19.92 inches and h = 11.50 inches
D)w = 16.26 inches and h = 16.27 inches
E)w = 18.78 inches and h = 13.28 inches

Question

A wooden beam has a rectangular cross section of height h and width w (see figure). The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter d = 23 inches? Round your answers to two decimal places. [Hint: $S = k w h  ^ { 2 },$ where $k > 0$ is the proportionality constant.] 
A)w = 13.28 inches and h = 18.78 inches 
B)w = 7.67 inches and h = 21.68 inches 
C)w = 19.92 inches and h = 11.50 inches 
D)w = 16.26 inches and h = 16.27 inches 
E)w = 18.78 inches and h = 13.28 inches

Quizplus · Accepted Answer

The Answer of A wooden beam has a rectangular cross section of height h and width w (see figure). The strength S of the beam is directly proportional to the width and the square of the height. What are the dimensions of the strongest beam that can be cut from a round log of diameter d = 23 inches? Round your answers to two decimal places. [Hint: $S = k w h  ^ { 2 },$ where $k > 0$ is the proportionality constant.] 
A)w = 13.28 inches and h = 18.78 inches 
B)w = 7.67 inches and h = 21.68 inches 
C)w = 19.92 inches and h = 11.50 inches 
D)w = 16.26 inches and h = 16.27 inches 
E)w = 18.78 inches and h = 13.28 inches

A Wooden Beam Has a Rectangular Cross Section of Height S=kwh2,S = k w h ^ { 2 },S=kwh2,

A Wooden Beam Has a Rectangular Cross Section of Height $S = k w h ^ { 2 },$