I kinda need help With this
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X=2
You have to first distribute the two and then you have to move the variable to one side of the equation and the number to the other. The work is attached below
You have to first distribute the two and then you have to move the variable to one side of the equation and the number to the other. The work is attached below
Refer to the figure shown below.
x = the width of the rectangle (meters)
y = the height of the rectangle (meters(
The fencing for the perimeter of the rectangle costs $30 per meter.
The two inner partitions cost $25 per meter.
The total cost of the fencing is
C = 2(x+y)*$30 + 2y*$25
= 60(x+y) + 50y
= 60x + 110y
Because the amount available to spend is $600, therefore
60x + 110y = 6000
or
6x + 11y = 600
That is,
y = (600 - 6x)/11 (1)
The area is
A = x*y (2)
Substitute (1) into (2).
A = (x/11)*(600 - 6x) = (1/11)*(600x - 6x²)
To maximize A, the derivative of A with respect to x is zero.
That is,
600 - 12x = 0
x = 600/12 = 50
From (1), obtain
y = (1/11)*(600 - 6*50) = 300/11 = 27.273
Because the second derivative of A with respect to x is negative, x=50, y = 27.273 will yield the maximum area.
The maximum area is
50*27.273 = 1363.64 m² = 1364 m² (nearest integer)
Answer: 1364 m² (nearest integer)
x = the width of the rectangle (meters)
y = the height of the rectangle (meters(
The fencing for the perimeter of the rectangle costs $30 per meter.
The two inner partitions cost $25 per meter.
The total cost of the fencing is
C = 2(x+y)*$30 + 2y*$25
= 60(x+y) + 50y
= 60x + 110y
Because the amount available to spend is $600, therefore
60x + 110y = 6000
or
6x + 11y = 600
That is,
y = (600 - 6x)/11 (1)
The area is
A = x*y (2)
Substitute (1) into (2).
A = (x/11)*(600 - 6x) = (1/11)*(600x - 6x²)
To maximize A, the derivative of A with respect to x is zero.
That is,
600 - 12x = 0
x = 600/12 = 50
From (1), obtain
y = (1/11)*(600 - 6*50) = 300/11 = 27.273
Because the second derivative of A with respect to x is negative, x=50, y = 27.273 will yield the maximum area.
The maximum area is
50*27.273 = 1363.64 m² = 1364 m² (nearest integer)
Answer: 1364 m² (nearest integer)