A trough with a rectangular base and rectangular sides has vertical trapezoidal ends and is 200 cm long, as shown in the adjacent diagram. The slant sides and the base of the trapez- ium are 30 cm long. 30 cm 200 cm 30 cm 30 cm How wide is the top of the trapezium, given that the trough has maximum volume?

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6. A trough with a rectangular base and rectangular sides has
vertical trapezoidal ends and is 200 cm long, as shown in the
adjacent diagram. The slant sides and the base of the trapez-
ium are 30 cm long.
30 cm
200 cm
30 cm
30 cm
How wide is the top of the trapezium, given that the trough
has maximum volume?
Use the First Derivative Test to justify that the volume is a maximum.
Transcribed Image Text:6. A trough with a rectangular base and rectangular sides has vertical trapezoidal ends and is 200 cm long, as shown in the adjacent diagram. The slant sides and the base of the trapez- ium are 30 cm long. 30 cm 200 cm 30 cm 30 cm How wide is the top of the trapezium, given that the trough has maximum volume? Use the First Derivative Test to justify that the volume is a maximum.
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