19 trees should be planted to maximize the total
<h3>How many trees should be planted to maximize the total</h3>
From the question, we have the following parameters:
Number of apples, x = 18
Yield, f(x) = 80 per tree
When the number of apple trees is increased (say by x).
We have:
Trees = 18 + x
The yield decreases by four apples per tree.
So, we have
Yield = 80 - 4x
So, the profit function is
P(x) = Apples * Yield
This gives
P(x) = (18 + x) *(80 - 4x)
Expand the bracket
P(x) = 1440 - 72x + 80x - 4x^2
Differentiate the function
P'(x) = 0 - 72 + 80 - 8x
Evaluate the like terms
P'(x) = 8 - 8x
Set P'(x) to 0
8 - 8x = 0
Divide through by 8
1 - x = 0
Solve for x
x = 1
Recall that:
Trees = 18 + x
So, we have
Trees = 18 + 1
Evaluate
Trees = 19
Hence, 19 trees should be planted to maximize the total
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If we refer to the longest side as x and the shortest side as y and the medium side as z then we come up with this formation:
x+y+z= 22
y is shorter than x by 5 inches so y= x-5
z is longer than y by 2 inches therefore z= x-5 +2
therefore:
x+(x-5)+(x-5+2)=22
x+x-5+x-5+2=22
3x-8=22
3x= 22-8
3x=14
x=
replace x in y and z in previous formations
Answer:
11 hours
Step-by-step explanation:
let he works at first store x hours and at car wash y hours. Then
x+y=25
multiply by 4
4x+4y=100 ...(1)
12x+15y=333
divide by 3
4x+5y=111 ... (2)
(2)-(1) gives
y=111-100=11
The values of a and b if the coordinate is rotated 90° clockwise is -1 and -1
<h3>Rotation of coordinates</h3>
The rotation is a transformation technique that changes the position of an object in an xy plane. If the coordinate (x, y) is rotated 90° clockwise, the resulting coordinate will be at (-y, x)
If the coordinate (-1, 1) is therefore rotated 90° clockwise about the origin, the resulting coordinate will be (-1, -1).
Comparing
a = -1 and b = -1
Hence the values of a and b if the coordinate is rotated 90° clockwise is -1 and -1
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Answer: r≈17.84
Step-by-step explanation:
