A large weather balloon is tethered by two ropes. One rope measures 23 ft and attaches to the balloon at an angle of 32 ° from the ground. The second rope attaches to the base of the balloon at an angle of 15 ° with the ground. a. How far from the ground is the balloon floating? Round to the nearest tenth of a foot. b. Find the length of the second rope. Round to the nearest tenth of a foot c. If both ropes suddenly detach and the balloon rises straight up at a rate of 3 ft/ sec , how long will it take the balloon to reach a height of 50 ft from the ground? Round to the nearest tenth of a second.
A large weather balloon is tethered by two ropes. One rope measures 23 ft and attaches to the balloon at an angle of 32 ° from the ground. The second rope attaches to the base of the balloon at an angle of 15 ° with the ground. a. How far from the ground is the balloon floating? Round to the nearest tenth of a foot. b. Find the length of the second rope. Round to the nearest tenth of a foot c. If both ropes suddenly detach and the balloon rises straight up at a rate of 3 ft/ sec , how long will it take the balloon to reach a height of 50 ft from the ground? Round to the nearest tenth of a second.
Solution Summary: The author calculates how far from the ground a floating balloon is tethered by two ropes. One rope measures 23ft and attaches to the balloon at an angle of 32
A large weather balloon is tethered by two ropes. One rope measures
23
ft
and attaches to the balloon at an angle of
32
°
from the ground. The second rope attaches to the base of the balloon at an angle of
15
°
with the ground.
a. How far from the ground is the balloon floating? Round to the nearest tenth of a foot.
b. Find the length of the second rope. Round to the nearest tenth of a foot
c. If both ropes suddenly detach and the balloon rises straight up at a rate of
3
ft/
sec
, how long will it take the balloon to reach a height of
50
ft
from the ground? Round to the nearest tenth of a second.
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
College Algebra with Modeling & Visualization (5th Edition)
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