A fish tank holds 180 gallons of water and is leaking at a rate of 8 gallons per day. A second fish tank holds 160 gallons of wa
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Answer:
Step-by-step explanation:
An ellipse with vertices (-8, 0) and (8, 0)
Distance between two vertices = 2a
Distance between (-8,0) and (8,0) = 16
2a= 16
so a= 8
Vertex is (h+a,k)
we know a=8, so vertex is (h+8,k)
Now compare (h+8,k) with vertex (8,0) and find out h and k
h+8 =8, h=0
k =0
a minor axis of length 10.
Length of minor axis = 2b
2b = 10
so b = 5
General formula for the equation of horizontal ellipse is
a= 8 , b=5 , h=0,k=0. equation becomes
ANSWER
3200 m²
EXPLANATION
Peter wants to build a fence around a rectangular field, except for one side because the river is there,
So, the total perimeter of the fence is,
And this is equal to 160 m. Solving for L,
The area of this field is,
Replace L with the expression we found from the perimeter,
The area is given by a quadratic function whose leading coefficient is negative, which means that the graph is a downward parabola and, therefore, the vertex is the maximum value of the area.
The x-coordinate of the vertex is given by,
In this case, x is W, a = -2, and b = 160, so the width of the field for the maximum area is,
And the length when W = 40 is,
And the area is,
Hence, the largest area of Peter's farm that can be fenced is 3200 square meters.
