find the greatest common factor and factored form of monomials
1. 6a³+15ab²
2. 6y³+15y²-6y
3. 18xy-9xy²-36xy³+27x²y
Answers
Answer:
The chocolate crumb mystery. Explosions ignited by electrostatic discharges (sparks) constitute a serious danger in facilities handling grain or powder. Such an explosion occurred in chocolate crumb powder at a biscuit factory in the 1970s. Workers usually emptied newly delivered sacks of the powder into a loading bin, from which it was blown through electrically grounded plastic pipes to a silo for storage. Somewhere along this route, two conditions for an explosion were met: (1) The magnitude of an electric field became 3.0×10
6
N/C or greater so that electrical breakdown and thus sparking could occur. (2) The energy of a spark was 150mJ or greater so that it could ignite the powder explosively. Let us check for the first condition in the powder flow through the plastic pipes.Suppose a stream of negatively charged powder was blown through a cylindrical pipe of radius R=5.0cm. Assume that the powder and its charge were spread uniformly through the pipe with a volume charge density r. (a) Using Gauss’ law, find an expression for the magnitude of the electric field in the pipe as a function of radial distance r from the pipe center. (b) Does E increase or decrease with increasing r? (c) Is directed radially inward or outward? (d) For ρ=1.1×10
−3
C/m
3
(a typical value at the factory), find the maximum E, and determine where that maximum field occurs. (e) Could sparking occur, and if so, where?