(a) The accompanying figure shows a sector of radius r and central angle 2 α . Assuming that the angle α is small, use the local quadratic approximation of cos α at α = 0 to show that x ≈ r α 2 / 2. (b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part(a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.
(a) The accompanying figure shows a sector of radius r and central angle 2 α . Assuming that the angle α is small, use the local quadratic approximation of cos α at α = 0 to show that x ≈ r α 2 / 2. (b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part(a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.
(a) The accompanying figure shows a sector of radius
r
and central angle
2
α
.
Assuming that the angle
α
is small, use the local quadratic approximation of
cos
α
at
α
=
0
to show that
x
≈
r
α
2
/
2.
(b) Assuming that the Earth is a sphere of radius 4000 mi, use the result in part(a) to approximate the maximum amount by which a 100 mi arc along the equator will diverge from its chord.
find the length of the part of the c=2(1+cosa)
curve that remaîns în the r =2(1+sind) curve
sina)
and
on the pole axis.
3)
S] Another Ferris wheel at a local fair has a radius of 13m, and is 1 m above the ground at its lowest
point. The Ferris wheel makes one full rotation every 45 seconds.
Determine a sine function model for the vertical position, h, in metres, of a rider on the wheel after a time, t, in
seconds.
Assume that at t =
Determine a:
Determine c:
(a)
Os, the rider is at the highest point. Show your work to determine each parameter
Determine k:
Equation: h(t) =
Determine d:
Chapter 9 Solutions
Calculus Early Transcendentals, Binder Ready Version
Precalculus: Mathematics for Calculus - 6th Edition
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