Carrying a Ladder around a Corner Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the illustration. It can be shown that the length L of the ladder as a function of θ is L ( θ ) = 4 csc θ + 3 sec θ . a. In calculus, you will be asked to find the length of the longest ladder that can turn the comer by solving the equation 3 sec θ tan θ − 4 csc θ cot θ = 0 0 ∘ < θ < 90 ∘ Solve this equation for θ . b. What is the length of the longest ladder that can be carried around the corner? c. Graph L = L ( θ ) , 0 ∘ ≤ θ ≤ 90 ∘ , and find the angle θ that minimizes the length L . d. Compare the result with the one found in part (a). Explain why the two answers are the same.
Carrying a Ladder around a Corner Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the illustration. It can be shown that the length L of the ladder as a function of θ is L ( θ ) = 4 csc θ + 3 sec θ . a. In calculus, you will be asked to find the length of the longest ladder that can turn the comer by solving the equation 3 sec θ tan θ − 4 csc θ cot θ = 0 0 ∘ < θ < 90 ∘ Solve this equation for θ . b. What is the length of the longest ladder that can be carried around the corner? c. Graph L = L ( θ ) , 0 ∘ ≤ θ ≤ 90 ∘ , and find the angle θ that minimizes the length L . d. Compare the result with the one found in part (a). Explain why the two answers are the same.
Carrying a Ladder around a Corner Two hallways, one of width 3 feet, the other of width 4 feet, meet at a right angle. See the illustration. It can be shown that the length
of the ladder as a function of
is
.
a. In calculus, you will be asked to find the length of the longest ladder that can turn the comer by solving the equation
Solve this equation for
.
b. What is the length of the longest ladder that can be carried around the corner?
c. Graph
,
, and find the angle
that minimizes the length
.
d. Compare the result with the one found in part (a). Explain why the two answers are the same.
Only 100% sure experts solve it correct complete solutions ok
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
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