in a marathon race (42.195 km), the winner’s time is 2 hours, 13 minutes, and 9 seconds, while the second-place time is 2 hours, 26 minutes, and 6 seconds . The distance is 2.664 km.
D = distance of marathon = 42.195 km = 42195 m
tw = time taken by winner = 2 h 17 min = 2 (60) + 17 = 137 min = 137 (60) = 8220 sec
Vw = speed of winner
speed of winner is given as
Vw = D /tw = 42195/8220
ts = time taken by second place = 2 h 26 min 14 sec = 2 (60)(60) + (26)(60) + 14 = 8774 s
Vs = speed of second place
speed of second place is given as
Vs = D /ts = 42195/8774
distance of the second place holder from the finish line is given as
D' = Vs (ts - tw)
D' = (42195/8774 )(8774 - 8220)
D' = 2664.24 m
D'= 2.664 km
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Answer:
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Step-by-step explanation:
Answer:
1. 
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2. 
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3. 
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4. 
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Step-by-step explanation:
1.
Taking LCM of (x+3) and (x+5) which is: (x+3)(x+5)
Prove closure: The value of x≠-3 and x≠-5 because if there values are -3 and -5 then the denominator will be zero.
2.
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Factors of x^2+5x+6 = x^2+3x+2x+6 = x(x+3)+2(x+3) =(x+2)(x+3)
Putting factors
Prove closure: The value of x≠-2 and x≠4 because if there values are -2 and 4 then the denominator will be zero.
3.
Factors of x^2-9 = (x)^2-(3)^2 = (x-3)(x+3)
Factors of x^2-5x+6 = x^2-2x-3x+6 = x(x-2)+3(x-2) =(x-2)(x+3)
Putting factors
Taking LCM of (x-3)(x+3) and (x-2)(x+3) we get (x-3)(x+3)(x-2)
Prove closure: The value of x≠3 and x≠-3 and x≠2 because if there values are -3,3 and 2 then the denominator will be zero.
4.
Factors of x^2-5x+6 = x^2-3x-2x+6 = x(x-3)-2(x-3) = (x-2)(x-3)
Factors of x^2-16 = (x)^2 -(4)^2 = (x-4)(x+4)
Converting ÷ sign into multiplication we will take reciprocal of the second term
Prove Closure: The value of x≠2 and x≠4 because if there values are 2 and 4 then the denominator will be zero.
Answer:
C = 1.
Step-by-step explanation:
x^2 - 2x = (x - 1)^2 - 1 so:
x^2 - 2x + C = (x - 1)^2 - 1 + C
So to get a perfect square C must be 1 ( as -1 + 1 = 0):-
(x - 1)^2 - 1 + 1 = (x - 1)^2
Checking this:
x^2 - 2x + 1
= (x - 1)(x - 1) which is a perfect square./
Answer: The length of an arc is simply the length of its "portion" of the circumference. The circumference itself can be considered a full circle arc length. Arc Measure: In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.
Step-by-step explanation:
