Base case: if <em>n</em> = 1, then
1² - 1 = 0
which is even.
Induction hypothesis: assume the statement is true for <em>n</em> = <em>k</em>, namely that <em>k</em> ² - <em>k</em> is even. This means that <em>k</em> ² - <em>k</em> = 2<em>m</em> for some integer <em>m</em>.
Induction step: show that the assumption implies (<em>k</em> + 1)² - (<em>k</em> + 1) is also even. We have
(<em>k</em> + 1)² - (<em>k</em> + 1) = <em>k</em> ² + 2<em>k</em> + 1 - <em>k</em> - 1
… = (<em>k</em> ² - <em>k</em>) + 2<em>k</em>
… = 2<em>m</em> + 2<em>k</em>
… = 2 (<em>m</em> + <em>k</em>)
which is clearly even. QED
<h3>
Answer: B) real number</h3>
Explanation:
Something like 3.5 = 7/2 is a rational number because its a fraction of two integers.
While on the other hand, the constant pi = 3.14159... is irrational because we cannot write pi as a fraction of two integers. We can get approximations like 22/7, but not a perfect exact match.
Both types of numbers, rational and irrational, are under the umbrella of the real number system. Any real number is a string of decimal digits. Sometimes it might be a whole number, but fractional values can be included as well. The decimal number may terminate, or it may repeat, or it may go on forever without a pattern.
In short, any number you can think of is a real number assuming your teacher hasn't covered complex numbers (or imaginary numbers) just yet.
Divide total km by the km in the scale:
112 / 16 = 7
The answer is A. 7 cm
Answer:
A. -[ln(0.5)/6,300]
Step-by-step explanation:
Done on apex, it is correct.
Answer:
I think its 2 hours 30 minutes
Step-by-step explanation:
