In a classroom, there are 7 male students and 11 female students that are taking a test. If each student is equally likely to tu
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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
Answer: There are 3 strips that can be cut from the roll of ribbon.
Step-by-step explanation:
since we have given that
Length of a ribbon is given by
Length of pieces of ribbon cut into strips is given by
So, we need to find the number of strips that can be cut is given by
Hence, there are 3 strips that can be cut from the roll of ribbon.