One hundred twenty feet of fencing encloses a rectangular garden on three sides. One side of the garden is the side of a barn an
d requires no fencing. The longer side is parallel to the barn. If the length of the longer side of the rectangle is twice the width, what are the dimensions of the garden
1 answer:
Answer: The garden has dimensions 30 ft wide X 60 ft long
Step-by-step explanation:
Denote by W the width of the garden and L the length of the garden (longer side) as in the figure attached. The red sides on the figure represent the parts of the garden that require fencing.
L is also the measure of a vertical side of the garden, because a rectangle consists only of vertical and horizontal sides.
We know that the barn is parallel to the longer (vertical) side, so only one of the vertical sides L of the rectangle needs fencing. The other two parts correspond to the horizontal sides of the rectangle so they require 2W feet of fencing. Altogether, the 120 ft of fencing enclose the L+2W ft of the fence, then 120=L+2W. Because the longer side is twice the width, we have that L=2W, so 120=2W+2W=4W. From here, W=30 ft and L=2(30)= 60ft.
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Answer: The answer is 300 gallons.
Step-by-step explanation: Riemann sum is a method of calculating the total area under a curve on a graph, which is also known as Integral.
To calculate that area, we divide it into a number of rectangles with one point touching the curve. The curve has a closed interval [a,b] that can be subdivided into n subintervals, each having a width of Δ =
If a function is defined on the closed interval [a,b] and is any point in [
,
], then a Riemann Sum is defined as ∑f(
)Δ
.
For this question:
Δ =
= 1.4
Now, we have to find s(t) for each valor on the interval:
s(t) = 0.29 - t +25
s(0) = 25
s(1) = 24.29
s(2) = 24.16
s(3) = 24.61
s(4) = 25.64
s(5) = 27.25
s(6) = 29.44
s(7) = 32.21
Now, using the formula:
∑f()Δ
= 1.4(25+24.29+24.16+24.61+25.64+29.44+32.21)
∑f()Δ
= 1.4(212.6)
∑f()Δ
≅ 300
With Riemann Sum, it is estimated the total country's per capita sales of bottled water is 300 gallons.