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.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
College Algebra with Modeling & Visualization (5th Edition)
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