Eight children sit together at story time. Seven children sit in a circle and one child sits in the middle to tell the story. In
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Answer:
a) t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
b) x = 0,97 miles
c) t (min) = 1,24 hours
Step-by-step explanation: See Annex
Figure in annex shows a clear description of the situation
Let x be distance in miles between point P and where boat lands
A woman has to row a distance L
L = √ (4)² + (x)²
and the part to get to the town (which she has to walk)
d = ( 7 - x)
But we are required to give time as a function of x
distance = speed * time ⇒ t = distance / speed
Therefore
t(x) = [ √ (4)² + (x)²]/ 4 + ( 7 - x ) / 5
t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
Taking derivatives both sides of the equation
t¨(x) = ( 2x)*4 / 16√ (4)² + (x)²] - 5/25
t¨(x) = x/ 2√ (4)² + (x)²] - 1/5
t¨(x) = 0 x/ 2√ (4)² + (x)²] - 1/5 = 0
[ 5 x - 2√ (4)² + (x)²] = 0 ⇒ 5x = 2√ (4)² + (x)²] or
25 x² = 4 ( 4 + x²)
25 x² = 16 + 8x²
17x² = 16
x² = 16/17
x² = 0,941
x = 0,97 miles
And the distance walking to get to town
d = 7 - x d = 7 - 0,97
d = 6,03 miles
The least travel time is t(x) = [ √ (4)² + (x)²]/ 4 + 7/5 - x/5
t (min) = √ 16 + 0,94) /4 + 1,4 - 0,97/5
t (min) = 1,03 + 1,4 - 0,194
t (min) = 1,24 hours
Option C: –10, –7.5, –5, –2.5, … is the sequence that could be partially defined by the recursive formula
Explanation:
The given recursive formula is for
and
We need to determine the sequence.
The sequence can be determined by substituting n = 1, 2, 3, 4,....
<u>2nd term of the sequence:</u>
Substituting n = 1 in the formula , we get,
Simplifying, we have,
Thus, the 2nd term of the sequence is -7.5
<u>3rd term of the sequence:</u>
Substituting n = 2 in the formula , we get,
Simplifying, we have,
Thus, the 3rd term of the sequence is -5
<u>4th term of the sequence:</u>
Substituting n = 3 in the formula , we get,
Simplifying, we have,
Thus, the 4th term of the sequence is -2.5
Therefore, the sequence is –10, –7.5, –5, –2.5, …
Hence, Option C is the correct answer.