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.
3. We'd like to know the first time when the population reaches 7000 people. First, graph the
function from part (a) on your calculator or Desmos. In the same window, graph the line y =
7000. Notice that you will need to adjust your window so that you can see values as big as
7000! Investigate the intersection of the two graphs. (This video shows you how to find the
intersection on your calculator, or in Desmos just hover the cursor over the point.) At what
value t> 0 does the line intersect with your exponential function? Round your answer to two
decimal places. (You don't need to show work for this part.) (2 points)
Suppose the planet of Tattooine currently has a population of 6500 people and an annual growth rate of
0.35%. Use this information for all the problems below.
1. Find an exponential function f(t) that gives the population of Tattooine t years from now. (3
points)
A house was valued at $95,000 in the year 1988. The value appreciated to $170,000 by the year 2007.
A) If the value is growing exponentially, what was the annual growth rate between 1988 and 2007?
Round the growth rate to 4 decimal places.
r =
B) What is the correct answer to part A written in percentage form?
r = 3
%.
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