Concept explainers
To find: How much it takes time.
The time is equal to 1.62 seconds.
Given information:
New Age Special Effects, Inc., prepares computer software based on specifications prepared by film directors. To simulate an approaching vehicle, they begin with a computer image of a 5− cm by 7− cm by 3− box. The program increases each dimension at rate of 2 cm/sec.
Calculation:
The volume of the original box is 5×7×3=105 cm3.
Assume that it takes t time.
Since the rectangle increase at rate of 2 km/sec, so the dimensions of the new box are (5+2t),(7+2t) and (3+2t) cm.
Since the volume of the new box is 5 times its original size, so it can be expressed as below:
(5+2t)×(7+2t)×(3+2t)=5×105
Solve for t :
(5+2t)×(7+2t)×(3+2t)=5×105(35+14t+10t+4t2)×(3+2t)=525(4t2+24t+35)×(3+2t)=52512t2+72t+105+8t3+48t2+70t=5258t3+60t2+142t−420=0t≈1.62
So, the time is 1.62 seconds.
Hence, the time is 1.62 seconds.
Chapter 1 Solutions
PRECALCULUS:GRAPH...-NASTA ED.(FLORIDA)
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