Déjà Vu At 8:00 a.m. on Saturday, a man begins running up the side of a mountain to his weekend campsite (see figure). On Sunday morning at 8:00 a.m., he runs back down the mountain. It takes him 20 minutes to run up but only 10 minutes to run down. At some point on the way down, he realizes that he passed the same place at exactly the same time on Saturday. Prove that he is correct, [ Hint : Let s ( t ) and r ( t ) be the position functions for the runs up and down, and apply die Intermediate Value Theorem to die function f ( t ) = s ( t ) − r ( t ) . ]
Déjà Vu At 8:00 a.m. on Saturday, a man begins running up the side of a mountain to his weekend campsite (see figure). On Sunday morning at 8:00 a.m., he runs back down the mountain. It takes him 20 minutes to run up but only 10 minutes to run down. At some point on the way down, he realizes that he passed the same place at exactly the same time on Saturday. Prove that he is correct, [ Hint : Let s ( t ) and r ( t ) be the position functions for the runs up and down, and apply die Intermediate Value Theorem to die function f ( t ) = s ( t ) − r ( t ) . ]
Solution Summary: The author explains that the condition is correct by applying intermediate value theorem.
Déjà Vu At 8:00 a.m. on Saturday, a man begins running up the side of a mountain to his weekend campsite (see figure). On Sunday morning at 8:00 a.m., he runs back down the mountain. It takes him 20 minutes to run up but only 10 minutes to run down. At some point on the way down, he realizes that he passed the same place at exactly the same time on Saturday. Prove that he is correct, [Hint: Let
s
(
t
)
and
r
(
t
)
be the position functions for the runs up and down, and apply die Intermediate Value Theorem to die function
Use the properties of logarithms, given that In(2) = 0.6931 and In(3) = 1.0986, to approximate the logarithm. Use a calculator to confirm your approximations. (Round your answers to four decimal places.)
(a) In(0.75)
(b) In(24)
(c) In(18)
1
(d) In
≈
2
72
Find the indefinite integral. (Remember the constant of integration.)
√tan(8x)
tan(8x) sec²(8x) dx
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