Question

CAN SOMEONE help me with my assignment pls

Find the volume of the largest box that can be made by cutting equal squares out of the corners of a cardboard of dimension 15 inches and 24 inches and then turning up the sides

Answer 1

Answer:

54 in2

Step-by-step explanation:

V=(9−2x)2xV=(9−2x)2x

V=81x−36x2+4x3V=81x−36x2+4x3

dVdx=81−72x+12x2=0dVdx=81−72x+12x2=0

4x2−24x+27=04x2−24x+27=0

 

Using quadratic formula

a=4;b=−24;c=27a=4;b=−24;c=27

x=−b±b2−4ac−−−−−−−√2ax=−b±b2−4ac2a

x=−(−24)±(−24)2−4(4)(27)−−−−−−−−−−−−−−√2(4)x=−(−24)±(−24)2−4(4)(27)2(4)

x=24±128x=24±128

x=4.5 and 1.5x=4.5 and 1.5

 

Use x = 1.5 inches

 

Maximum volume:

V=[9−2(1.5)]2(1.5)V=[9−2(1.5)]2(1.5)

V=54 in2V=54 in2         answer

Answer 2

Answer:

54 in2

Step-by-step explanation:

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