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)
Answer:
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Step-by-step explanation:
Point slope:
y-y1= m(x-x1) <- we will plug all the given information into this formula.
We have the slope, which equals m. m= 5
y-y1= 5(x-x1)
-4= x1 and 0= y1
y-0=5(x-(-4)
Two negatives equal a positive.
y-0=5(x+4)
Combine like terms.
y= 5x + 20
We could talk this one step further and convert it to standard form.
Ax+By= C
y=5x+20
Subtract 5x on both sides.
-5x+y= 20 <- this is standard form.
Here's a simple way to check to see if this is correct. Plug in x and y.
-5(-4)+0= 20
20+0= 20; 20=20
I hope this helps!
~kaikers
Answer:
The answer is letter A
Step-by-step explanation:
Area of a circle in terms of radius:
A circle of radius = 6.996 or 7, or diameter = 13.99 or circumference = 43.96 meters
Area = π · r^2 = 3.14 * 7^2 = 153.86 square meters
Considering the volume of the cylinder, it is found that the height must be decreased by 18.51%.
<h3>What is the volume of a cylinder?</h3>
The volume of a cylinder of diameter d is given by:
![V = 0.25\pi d^2h](https://tex.z-dn.net/?f=V%20%3D%200.25%5Cpi%20d%5E2h)
In this problem, the diameter will be increased by 25%, hence d = 1.25d, and the volume will be of:
![V = 0.25\pi d^2h](https://tex.z-dn.net/?f=V%20%3D%200.25%5Cpi%20d%5E2h)
![V = 0.25\pi (1.25d)^2h](https://tex.z-dn.net/?f=V%20%3D%200.25%5Cpi%20%281.25d%29%5E2h)
V = 0.390625 πd²h
Solving for the height, we have that:
h = V/0.390625 πd²
h = 0.8149 of the original, hence the height must be decreased by 18.51%.
More can be learned about the volume of a cylinder at brainly.com/question/9408912
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