Sprout7430
29.05.2021 •
Mathematics
A climber is ascending the face of a 500-foot high vertical cliff at 5 feet per minute. Her climbing partner is observing from 150 feet away. Find the function that describes the amount of time climbing as a function of the angle of elevation of the observer’s line-of-sight to the climber. Does the viewing angle ever reach 75 degrees?
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Ответ:
a) t (α) = 30 * tan α
b) α = 75 ° is not possible because
Step-by-step explanation:
The vertical cliff (y), the observing partner ( 150 ft ) from the point o ( the common point for the cliff and the ground ) between the cliff, and the line of sight from the observer and the climber, shape a right triangle. Hypothenuse is the distance between the partners, the cliff, and distance of the observer to the cliff are the legs.
Then
α is the elevation angle
tan α = y / 150 (1)
y(t) = elevation of the climber
y(t) = speed * time
y(t) = 5 * t
tan α = 5 *t / 150
tan α = t / 30
t (α) = 30 * tan α
b) α = 75 ° is not possible because:
tan α = y / 150 tan 75° = 3.73
Then y = 3.73 * 150 = 559 ft and the cliff is only 500 ft
Ответ:
35% decrease
step-by-step explanation:
1) when solving for percent decrease, remember that [(original price - new price)/original price] * 100% = percent decrease:
since you are already given the difference between the original price and new price (1.26), you can simply divide it by the original price.
* 100%
2) use a calculator to solve:
= 0.34940304709 * 100%
= 34.94034709%
3) round to the nearest percent:
= 35%