An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
A device with a current of 15.0 A for 30 seconds delivers about 450 coulombs of charge. This charge corresponds to approximately 2.81 x 10^21 electrons flowing through the device. The calculation uses the formula for current and the charge of a single electron.
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To determine which of the sets is not convex, we need to understand what a convex set is. A set is convex if, for any two points within the set, the line segment connecting them is entirely contained within the set.
Let's analyze each of the given options:
(A) {( x 1 , x 2 ) : x 1 2 + x 2 2 ≤ 3 , x 1 2 + x 2 2 ≥ 1 } :
This set is the region between two circles, one with radius s q r t 3 and the other with radius 1. This forms an annular region or a ring-shaped area. In general, annular regions are not convex because there are points within the set where the line segment connecting them would pass through the region outside of the annulus.
(B) {( x 1 , x 2 ) : 9 x 1 2 + 4 x 2 2 ≤ 36 } :
This describes an ellipse. Ellipses are convex because for any two points within an ellipse, the line segment connecting them is also entirely within the ellipse.
(C) {( x 1 , x 2 ) : x 1 ≤ 5 , x 2 ≥ 3 } :
This is a half-plane formed by the intersection of the regions x 1 ≤ 5 and x 2 ≥ 3 . Half-planes are convex because any line segment connecting two points within this region will remain entirely within the half-plane.
(D) {( x 1 , x 2 ) : x 1 + 2 x 2 ≤ 5 } :
This describes a half-plane bounded by the line x 1 + 2 x 2 = 5 . Similar to option C, this set is convex.
Therefore, the set that is not convex is (A): {( x 1 , x 2 ) : x 1 2 + x 2 2 ≤ 3 , x 1 2 + x 2 2 ≥ 1 } .
