When we estimate distances from velocity data, it is son times necessary to use times fo, 11, 12, 13, ... that are not equally spaced. We can still estimate distances using the time periods At, = t, -1-1. For example, on May 7, 1992, the space shuttle Endeavour was launched on mission STS-49 the purpose of which was to install a new perigee kick moto in an Intelsat communications satellite. The table, provided by NASA, gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height above the earth's surface of the Endeavour, 62 seconds after liftoff. %3D Event Time (s) Velocity (m/s) Launch Begin roll maneuver 10 56 End roll maneuver 15 97 Throttle to 89% 20 136 Throttle to 67% 32 226 Throttle to 104% 59 404 Maximum dynamic pressure 440 62 Solid rocket booster separation 125 1265

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Please help me solve question 16
expressions for the sums 81
es, even for large values of n, using
e Is> command or a For-EndFor loop,
n HP or in BASIC use a FOR-NEXT
n of the areas of approximating rect-
ntervals and right endpoints for n = 10,
15. Oil leaked from a tank at a rate of r(t) liters per hour. The rate
time intervals are shown in the table. Find lower and upper
decreased as time passed and values of the rate at two-hour
(c)
estimates? Explain.
ind estimates for the total amount of oil that leaked ou
goon oolav
uess the value of the exact area.
= x* from 0 to 1
0.
4
6.
8.
10
= cos x from 0 to 7/2
(h)
7.6
6.8
6.2
5.7
5.3
Ca bnim ni od r(1) (L/h) 8.7
gebra systems have commands that will
ng rectangles and evaluate the sums of
- if x* is a left or right endpoint. (For
= use leftbox, rightbox, left-
sum.)
x² + 1), 0 < x< 1, find the left and
En = 10, 30, and 50.
graphing the rectangles in part (a).
e exact area under f lies between 0.780
16. When we estimate distances from velocity data, it is some.
times necessary to use times fo, t1, 12, 13, ... that are not
equally spaced. We can still estimate distances using the e
periods At, = t - ti-1. For example, on May 7, 1992, the
space shuttle Endeavour was launched on mission STS-40
the purpose of which was to install a new perigee kick motor
in an Intelsat communications satellite. The table, provided
by NASA, gives the velocity data for the shuttle between
liftoff and the jettisoning of the solid rocket boosters. Use
these data to estimate the height above the earth's surface of
the Endeavour, 62 seconds after liftoff.
x, 1 < x < 4, use the commands dis-
ercise 11 to find the left and right sums
50, and 50.
graphing the rectangles in part (a).
e exact area under f lies between 2.50
Event
Time (s) Velocity (m/s)
Launch
Begin roll maneuver
56
unner increased steadily during the first
a race. Her speed at half-second intervals
Lble. Find lower and upper estimates for
she traveled during these three seconds.
10
End roll maneuver
15
97
Throttle to 89%
20
136
Throttle to 67%
32
226
0.5
1.0
1.5
2.0
2.5
3.0
always
Throttle to 104%
59
404
Maximum dynamic pressure
Solid rocket booster separation
1.9
3.3
4.5
5.5
5.9
6.2
62
440
125
1265
adings for a motorcycle at 12-second
ven in the table.
e distance traveled by the motorcycle
time period using the velocities at the
of the time intervals.
17. The velocity graph of a braking car is shown. Use it to estiia
the distance traveled by the car while the brakes are applied.
ne (s)
Velocity (m/s)
(m/s)
15
9.1
10
12
24
8.5
7.6
5
36
6.7
48
7.3
8.2
4.
6
(seconds)
60
Transcribed Image Text:expressions for the sums 81 es, even for large values of n, using e Is> command or a For-EndFor loop, n HP or in BASIC use a FOR-NEXT n of the areas of approximating rect- ntervals and right endpoints for n = 10, 15. Oil leaked from a tank at a rate of r(t) liters per hour. The rate time intervals are shown in the table. Find lower and upper decreased as time passed and values of the rate at two-hour (c) estimates? Explain. ind estimates for the total amount of oil that leaked ou goon oolav uess the value of the exact area. = x* from 0 to 1 0. 4 6. 8. 10 = cos x from 0 to 7/2 (h) 7.6 6.8 6.2 5.7 5.3 Ca bnim ni od r(1) (L/h) 8.7 gebra systems have commands that will ng rectangles and evaluate the sums of - if x* is a left or right endpoint. (For = use leftbox, rightbox, left- sum.) x² + 1), 0 < x< 1, find the left and En = 10, 30, and 50. graphing the rectangles in part (a). e exact area under f lies between 0.780 16. When we estimate distances from velocity data, it is some. times necessary to use times fo, t1, 12, 13, ... that are not equally spaced. We can still estimate distances using the e periods At, = t - ti-1. For example, on May 7, 1992, the space shuttle Endeavour was launched on mission STS-40 the purpose of which was to install a new perigee kick motor in an Intelsat communications satellite. The table, provided by NASA, gives the velocity data for the shuttle between liftoff and the jettisoning of the solid rocket boosters. Use these data to estimate the height above the earth's surface of the Endeavour, 62 seconds after liftoff. x, 1 < x < 4, use the commands dis- ercise 11 to find the left and right sums 50, and 50. graphing the rectangles in part (a). e exact area under f lies between 2.50 Event Time (s) Velocity (m/s) Launch Begin roll maneuver 56 unner increased steadily during the first a race. Her speed at half-second intervals Lble. Find lower and upper estimates for she traveled during these three seconds. 10 End roll maneuver 15 97 Throttle to 89% 20 136 Throttle to 67% 32 226 0.5 1.0 1.5 2.0 2.5 3.0 always Throttle to 104% 59 404 Maximum dynamic pressure Solid rocket booster separation 1.9 3.3 4.5 5.5 5.9 6.2 62 440 125 1265 adings for a motorcycle at 12-second ven in the table. e distance traveled by the motorcycle time period using the velocities at the of the time intervals. 17. The velocity graph of a braking car is shown. Use it to estiia the distance traveled by the car while the brakes are applied. ne (s) Velocity (m/s) (m/s) 15 9.1 10 12 24 8.5 7.6 5 36 6.7 48 7.3 8.2 4. 6 (seconds) 60
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