The shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
<h3>What dimensions would guarantee that the garden has the greatest possible area?</h3>
The given parameter is
Perimeter, P = 520 feet
Represent the shorter side with x and the longer side with y
One side of the garden is bordered by a river:
So the perimeter is:
P = 2x + y
Substitute P = 520
2x + y = 520
Make y the subject
y = 520 - 2x
The area is
A = xy
Substitute y = 520 - 2x in A = xy
A = x(520 - 2x)
Expand
A = 520x - 2x^2
Differentiate
A' = 520 - 4x
Set to 0
520 - 4x = 0
Rewrite as:
4x= 520
Divide by 4
x= 130
Substitute x= 130 in y = 520 - 2x
y = 520 - 2 *130
Evaluate
y = 260
The area is then calculated as:
A = xy
This gives
A = 130 * 260
Evaluate
A = 33800
Hence, the shortest side is 130 feet, the longest side is 260 feet and the greatest possible area is 33800 square feet
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First you would need to Simplify <span>{3}^{2}<span>3<span>2</span></span></span> to <span>99
Next you would need to : </span>Use Negative Power Rule =9÷31
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then you would need to use a ÷ b/c = a * c/b and get 9*3
And you will lastly get 27</span>
Since it starts at 12 and is increasing by 5 each time, the 70th term will be;
12 + 5(70)
12 + 350
362
362 is the 70th term of the sequence.
X=-1/3 and x=4 are the positive and negative x intercepts