Find a number such that 12% if the number is 60
1 answer:
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Answer:
73.25 m
Step-by-step explanation:
In the right triangle formed by the pole, the ground, and the cable, the pole is the side opposite the angle of elevation, and the cable is the hypotenuse of the triangle. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
Solving for the Hypotenuse, we find ...
Hypotenuse = Opposite/Sin
cable length = (20 m)/sin(55°) ≈ 24.4155 m
The total length of the 3 cables is ...
3 × (24.4155 m) ≈ 73.25 m
The total length of the cables is about 73.25 meters.
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In the attached, we computed the length of a single cable for a pole 3 times as high. That will be the same length as the total we seek here.
Answer:
(-∞, -2) and (2, ∞)
Step-by-step explanation:
ƒ(x) = x³ -12x + 10
f'(x) = 3x² - 12
Set 3x² - 12 = 0
x² - 4 = 0
x² = 4
x = ±2
The points x = -2 and x = + 2 divide the number line into three intervals:
(-∞, -2), (-2, +2), and (+2, ∞).
a. Interval (-∞, -2)
x < -2, so f'(x) > 0 when -∞ < x < -2
The function is increasing in (-∞, -2).
b. Interval (-2, 2)
|x| < 2, so f'(x) <0
The function is decreasing in (-2, 2).
c. Interval (2, ∞)
x > 2, so f'(x) > 0 when 2 < x < ∞
The function is increasing in (2, ∞).
Thus, the function is increasing in the intervals (-∞, -2) and (2, ∞).
