Constructing a Rain Gutter A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, the builder bends this length up at an angle θ . See the illustration. The area A of the opening as a function of θ is given by A ( θ ) = 16sin θ ( cos θ + 1 ) , 0 ∘ < θ < 90 ∘ (a) In calculus, you will be asked to find the angle that maximizes A by solving the equation cos ( 2 θ ) + cos θ = 0, 0 ∘ < θ < 90 ∘ Solve this equation for θ . (b) What is the maximum area A of the opening? (c) Graph A = A ( θ ) , 0 ∘ ≤ θ ≤ 90 ∘ and find the angle θ that maximizes the area A . Also find the maximum area.
Constructing a Rain Gutter A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, the builder bends this length up at an angle θ . See the illustration. The area A of the opening as a function of θ is given by A ( θ ) = 16sin θ ( cos θ + 1 ) , 0 ∘ < θ < 90 ∘ (a) In calculus, you will be asked to find the angle that maximizes A by solving the equation cos ( 2 θ ) + cos θ = 0, 0 ∘ < θ < 90 ∘ Solve this equation for θ . (b) What is the maximum area A of the opening? (c) Graph A = A ( θ ) , 0 ∘ ≤ θ ≤ 90 ∘ and find the angle θ that maximizes the area A . Also find the maximum area.
Constructing a Rain Gutter A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, the builder bends this length up at an angle
. See the illustration. The area
of the opening as a function of
is given by
,
(a) In calculus, you will be asked to find the angle that maximizes A by solving the equation
Solve this equation for
.
(b) What is the maximum area
of the opening?
(c) Graph
and find the angle
that maximizes the area
. Also find the maximum area.
Exercise 1
Given are the following planes:
plane 1:
3x4y+z = 1
0
plane 2:
(s, t) =
( 2 ) + (
-2
5 s+
0
(
3 t
2
-2
a) Find for both planes the Hessian normal form and for plane 1 in addition the parameter form.
b) Use the cross product of the two normal vectors to show that the planes intersect in a line.
c) Calculate the intersection line.
d) Calculate the intersection angle of the planes. Make a sketch to indicate which angle you are
calculating.
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
Chapter 7 Solutions
Precalculus Enhanced with Graphing Utilities (7th Edition)
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