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
Read more about area at:
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Answer: 61.16 ft
Step-by-step explanation:
We can think in this situation as a triangle rectangle.
where:
The height of the tree is one cathetus
The shadow of the tree is the other cathetus.
We know that the angle of elevation of the sun is 78°, an angle of elevation is measured from the ground, then the adjacent cathetus to this angle is the shadow of the tree. And the opposite cathetus will be the height of the tree.
Now we can remember the relationship:
Tg(A) = (opposite cathetus)/(adjacent cathetus)
Where:
A = 78°
Adjacent cathetus = 13ft
opposite cathetus = height of the tree = H
Then we have the equation:
Tg(78°) = H/13ft
Tg(78°)*13ft = H = 61.16 ft
Answer:
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the 3rd vertex is on the x axis line which means Y =0
since the longer leg is twice as long as the shorter leg and the length of the shorter leg is a, then twice the length would be 2a ( 2 times a)
so the 3rd vertex is (2a,0)
question 19
equal to: 3's
less than: 2's, 1's
greater than: 0's
question 20
40 gallons, 12 concentrate, 28 water
this is a fraction of 12/28
simplification: (12) divided by 12 / (28) divided by 12
1/2
1 part concentrate 2 parts water per each of the 40 total gallons.
so color in 33% for concentrate and 66% water
I am totally not wrong :D:D:D:D