A contractor building eight ocean-front condominiums wants to maximize the view of the ocean for each unit. The side of the building facing the ocean is not built in a straight line parallel to the ocean, but instead is built in a zigzag pattern as shown in the figure. Each condo has a window of length x facing the ocean at an angle of 70 ° from a line perpendicular to the ocean. a. Find the length x of each window. Round to the nearest foot. b. The windows facing the ocean are 8 ft high and x feet wide. By using the zigzag pattern how much more ocean-front viewing area does each window provide than if the windows were parallel to the ocean? Round to the nearest square foot.
A contractor building eight ocean-front condominiums wants to maximize the view of the ocean for each unit. The side of the building facing the ocean is not built in a straight line parallel to the ocean, but instead is built in a zigzag pattern as shown in the figure. Each condo has a window of length x facing the ocean at an angle of 70 ° from a line perpendicular to the ocean. a. Find the length x of each window. Round to the nearest foot. b. The windows facing the ocean are 8 ft high and x feet wide. By using the zigzag pattern how much more ocean-front viewing area does each window provide than if the windows were parallel to the ocean? Round to the nearest square foot.
Solution Summary: The author calculates the length of each window to the nearest foot for a contractor building eight ocean front condominiums.
A contractor building eight ocean-front condominiums wants to maximize the view of the ocean for each unit. The side of the building facing the ocean is not built in a straight line parallel to the ocean, but instead is built in a zigzag pattern as shown in the figure. Each condo has a window of length
x
facing the ocean at an angle of
70
°
from a line perpendicular to the ocean.
a. Find the length
x
of each window. Round to the nearest foot.
b. The windows facing the ocean are
8
ft
high and x feet wide. By using the zigzag pattern how much more ocean-front viewing area does each window provide than if the windows were parallel to the ocean? Round to the nearest square foot.
Consider the following system of equations, Ax=b :
x+2y+3z - w = 2
2x4z2w = 3
-x+6y+17z7w = 0
-9x-2y+13z7w = -14
a. Find the solution to the system. Write it as a parametric equation. You can use a
computer to do the row reduction.
b. What is a geometric description of the solution? Explain how you know.
c. Write the solution in vector form?
d. What is the solution to the homogeneous system, Ax=0?
2. Find a matrix A with the following qualities
a. A is 3 x 3.
b. The matrix A is not lower triangular and is not upper triangular.
c. At least one value in each row is not a 1, 2,-1, -2, or 0
d. A is invertible.
Find the exact area inside r=2sin(2\theta ) and outside r=\sqrt(3)
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