How many integers are there between m and n, including m and n
1 answer:
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Answer:
Step-by-step explanation:
Let us assume that we have n different dots on a paper. We are to connect pairwise by a line. We have to find out how many lines can be formed.
Let us prove by induction.
If there is one dot then we have no line = 1(1-1) =0
Thus n(n-1) is true for 1 dot
Let us assume that for n dots we have n(n-1) lines
Add one more point now total points are n+1.
Already the existing n points are connected by a line.
So the extra point has to be connected to each of n point
i.e. n lines should be added from the new point to the n points and again n lines from the points to the new point(Assuming lines are different if initial and final point are different)
So 2n lines would be added
So total number of lines for n+1 points
Thus true for n+1 if true for n. Already true for n =1
So proved by induction for all natural numbers n.
Answer:
The length of the candle (in inches) 3.6 hours after it was lit is 0.95 inches
Step-by-step explanation:
Given
---- candle length
--- rate (it is negative because the candle length reduces)
Solving (a): The function, f(t)
This is calculated as:
So, we have:
Solving (b): The domain
The domain, in this case, represents time from 0 till the candle burns out.
Set to calculate the time the candle burns out
Collect like terms.
Solve for t
Hence, the domain is:
Solving (c): The range
The domain, in this case, represents the candle height from 15 till the candle burns out (0 inches)
Hence, the range is:
Solving (d):
Recall that:
Sp, we have
Collect like terms
Divide by 12