Write the recursive definition for the geometric sequence. Then write the exponential equation using regression
1 answer:
The geometric sequence 128,32,8,2 has a common ratio
The recursive definition of the geometric sequence is where a1 = 128
The geometric sequence is given as:
128,32,8,2
Start by calculating the common ratio (r)
Substitute 2 for n
Substitute known values
Evaluate the quotient
Substitute 4 for r in
Cross multiply
Hence, the recursive definition of the geometric sequence is where a1 = 128
Read more about geometric sequence at:
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Answer:
Maximum added area will be 60,000 ft²
Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.
Step-by-step explanation:
Consider the provided information.
There is sufficient funding to rent 1200 feet of temporary chain-link fencing.
The plan is to form two paddocks with one shared fence running down the middle.
The total length of fencing is 1200 feet that is same as the total perimeter including that shared line down the middle.
Therefore, the perimeter is
Solve for L
As we know the area of rectangle is A=L×W
Substitute the value of L in above formula.
The above equation makes a downward parabola.
In order to find the maximum, find the vertex of parabola as shown:
Hence, the width should be 200 ft in order to get maximum area,
Therefore, the length will be:
Now substitute the value of L and W in area formula.
A=300×200=60,000
Hence, maximum added area will be 60,000 ft²
Hence, the length should be 300 ft, and each paddock should then be 150 feet long.
Each paddock measure 200 ft by 150 ft, and the paddocks share a 200-ft long side.
