The back of jake's property is a creek. Jake would like to enclose a rectangular area, using the creek as one side and fencing f
1 answer:
Answer:
The maximum possible area of the pasture is 26,450 feet square.
Step-by-step explanation:
Let us assume the width of the rectangular area = m ft
and the length of the area = k ft
Also assume: ( one side with k units IS NOT FENCED)
So, the total perimeter of the fencing is:
2 m + k = 460
or, k = 460 - 2m ........ (1)
Now, AREA OF THE RECTANGULAR PORTION = Length x Width = k x m
Put k = 460 - 2m
We get: A = m (460 - 2m)
or, A = 460 m - 2m²
We need to find the maximum for the parabolic function A = 460 m - 2m²
The function has a maximum value as the quotient in front of x^2 is negative: -2 < 0
A (max) = where a = -2, b = 460, c = 0
=
A max = 26,450 sq ft.
The maximum possible area of the pasture is 26,450 feet square.
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Answer
a) C
b) B
c) C, E
d) 15.5
e) 0.7
f) 67.7
Step-by-step explanation
a) A linear equation can be written as where
is the slope and
is the intercept on the
-axis. The slope describes how
changes when
changes. A negative value means the it is a decreasing change. In our case,
is
and
is
. Thus, the slope of the equation is
. This means that the area of glacier is decreasing by
every year since 2000.
b) The -intercept (= 16.2
) represents the area covered when
. But
starting from year 2000. This intercept then represents the area covered by glacier in the year 2000. Therefore, the area covered by glacier in 2000 was 16.2
.
c) means the area covered after year 2000. Setting it to 12 means the area covered after
years is 12
).
is therefore the number of years since 2000 that the total area covered will be 12
).
d) to 1 decimal place.
e) The term involving represents the disappearing area. In 12 years, the disappeared area is
to 1 decimal place.
f)
years to 1 decimal place.