Step 1: Analyzing the sentence.
The sentence is discussing the effect of an electro-magnet in the context of inductive action. The phrase following the conjunction "and" should logically expand on the first part of the sentence, with appropriate structure and clarity.
Step 2: Analyzing the options.
- (A) "and that an electro-magnet would affect the space about it practically inversely as the square of the distance" creates unnecessary repetition of the word "and," which disrupts the sentence flow.
- (B) "and an electro-magnet would affect the space about it practically inversely as the square of the distance" is clear and grammatically correct, providing the intended expansion of the idea in a succinct manner.
- (C) "and also that an electro-magnet would affect the space about it practically inversely like the square of the distance" introduces the word "like," which weakens the comparison and makes the sentence awkward.
- (D) "and that an electro-magnet would affect the space about them practically inversely as the square of the distance" introduces an error by switching "it" to "them," which causes confusion regarding the subject.
- (E) "and also known that an electro-magnet would affect the space about it practically inversely as the square of the distance" introduces an awkward phrasing with the use of "also known" that weakens the sentence structure.
Step 3: Conclusion.
Option (B) is the most natural, clear, and grammatically correct choice to complete the sentence.
If \(8x + 5x + 2x + 4x = 114\), then, \(5x + 3 = ?\)
If \(r = 5 z\) then \(15 z = 3 y,\) then \(r =\)