Déjà Vu At 8:00 a.m. on Saturday, a nun 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 only10 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 the Intermediate Value Theorem to the function f ( t ) = s ( t ) − r ( t ) .]
Déjà Vu At 8:00 a.m. on Saturday, a nun 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 only10 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 the Intermediate Value Theorem to the function f ( t ) = s ( t ) − r ( t ) .]
Déjà Vu At 8:00
a.m.
on Saturday, a nun 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 only10 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 the Intermediate Value Theorem to the function
f
(
t
)
=
s
(
t
)
−
r
(
t
)
.]
Use the information to find and compare Δy and dy. (Round your answers to four decimal places.)
y = x4 + 7 x = −3 Δx = dx = 0.01
Δy =
dy =
4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown
in the table. For each problem, approximate the distance the car traveled (in miles) using the given method,
on the provided interval, and with the given number of rectangles or trapezoids, n.
Time (min) 0 6 12 18|24|30|36|42|48|54|60
Speed (mph) 0 10 20 40 60 50 40 30 40 40 65
a.) Left Rectangles, [0, 30] n=5
b.) Right Rectangles, [24, 42] n=3
c.) Midpoint Rectangles, [24, 60] n=3
d.) Trapezoids, [0, 24] n=4
The bracket BCD is hinged at C and attached to a control cable at B. Let F₁ = 275 N and F2 = 275 N.
F1
B
a=0.18 m
C
A
0.4 m
-0.4 m-
0.24 m
Determine the reaction at C.
The reaction at C
N Z
F2
D
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.