To find the height of a pole, a surveyor uses a theodolite. The theodolite is 4 ft tall. The surveyor stands 140 feet away from
the base of the pole. Then she measures the angle of elevation to the top of the pole to be 44°. What is the height of the pole? Round the answer to the nearest foot.
2 answers:
Answer:
Step-by-step explanation:
Alright, lets get started.
Please refer the diagram I have attached.
The height of pole will be in two parts, upper part is x and second will be the height of theodolite which is already given as 4 feet.
Using SOH CAH TOA in triangle ABC
So the total length of pole is =
Rounding to the nearest feet, the height of pole is 139 feet. : Answer
Hope it will help :)
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Answer:
D = L/k
Step-by-step explanation:
Since A represents the amount of litter present in grams per square meter as a function of time in years, the net rate of litter present is
dA/dt = in flow - out flow
Since litter falls at a constant rate of L grams per square meter per year, in flow = L
Since litter decays at a constant proportional rate of k per year, the total amount of litter decay per square meter per year is A × k = Ak = out flow
So,
dA/dt = in flow - out flow
dA/dt = L - Ak
Separating the variables, we have
dA/(L - Ak) = dt
Integrating, we have
∫-kdA/-k(L - Ak) = ∫dt
1/k∫-kdA/(L - Ak) = ∫dt
1/k㏑(L - Ak) = t + C
㏑(L - Ak) = kt + kC
㏑(L - Ak) = kt + C' (C' = kC)
taking exponents of both sides, we have
When t = 0, A(0) = 0 (since the forest floor is initially clear)
So, D = R - A =
when t = 0(at initial time), the initial value of D =