9514 1404 393
Answer:
a) 14√5 feet
b) about 31.3 feet
Step-by-step explanation:
a) The 42-ft hose is the hypotenuse of a right triangle with one leg 28 ft. We are asked to find the other leg. The Pythagorean theorem is useful.
h² +(28 ft)² = (42 ft)²
h² = (1764 -784) ft² = 980 ft²
h = √(196·5) ft
h = 14√5 ft
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b) The approximate height is ...
14√5 ≈ 31.305, about 31.3 feet
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Explanation:
Start with the point (-2,-4). Let's try to move it to (2, -9)
To do so, we need to shift down and to the right (in either order).
Specifically we shift 4 units to the right to go from x=-2 to x=4
Note how x=-2 moves to x+4 = -2+4 = 2
Also, we shift 5 units down. We have y = -4 turn into y = -9 as shown below
y ---> y-5 = -4-5 = -9
So the translation rule is
Let's see what happens when we apply the translation rule to (2,4)
which is the other endpoint of the blue segment. This shows that the translation rule works for (2,4) to move to (6,-1)
We do not apply any dilations. The red and blue segments are the same length because translations preserve distance. All we're effectively doing is moving the red segment to land on the blue segment. This means no vertical or horizontal stretches are done. The same can be said about compressions as well.