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alexgriva
21 hour ago
10

A park ranger has 32 feet of fencing to fence four sides of a rectangular recycling site. What is the greatest area of recycling

site that the ranger can fence? Explain how you know.
Mathematics
2 answers:
Inessa [9K]20 hours ago
8 0
The maximum area that can be enclosed is 64 ft². To achieve the largest area while minimizing the perimeter, the dimensions should be as equal as possible. Allocating 32 feet of fencing for four sides gives us 8 feet per side, resulting in a square with a side length of 8; thus, the area equals 8*8 = 64.
Svet_ta [9.5K]20 hours ago
5 0
The equations representing the perimeter and area of the rectangle are respectively: After manipulating the equations, we derive the area formula in a simplified way. The highest area is calculated using the First and Second Derivative Tests. Based on the second derivative analysis, the critical point consistently indicates an absolute maximum, which is found. The other side's length is computed as follows: The greatest area of the recycling site amounts to:
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1 month ago
1-i need to mix 25% mineral spirits to the varnish i am using what ratio of spirit to varnish am i using? 2-if i use 240 ml of v
Svet_ta [9500]

Answer:

(1) The necessary proportion of spirit to varnish stands at 1:3.

(2) A total of 80 ml of mineral spirit is required.

(3) The ratio of the heights to the widths of the tapestries is 3:2.

Step-by-step explanation:

(1) To achieve a mixture containing 25% mineral spirit, the blend consists of 25% spirit and 75% varnish.

Therefore, \frac{spirit}{varnish}=\frac{25}{75}

=\frac{1}{3}

Consequently, the proportion of spirit to varnish is 1:3.

(2) Using 240ml of varnish indicates this is 75% of the entire solution, which means the ratio of varnish to the total solution is 3:4.

Let the total solution quantity be x.

Thus, 240:x=3:4.

⇒\frac{240}{x}=\frac{3}{4}

⇒3x=240*4

⇒x=\frac{240*4}{3}

⇒x=320

This means the total solution amounts to 320 ml.

Now, calculating Spirit = Total solution - Varnish

⇒Spirit = 320ml-240ml

⇒Spirit = 80ml

Therefore, when using 240 ml of varnish, you will require 80 ml of mineral spirit.

(3) The dimensions of Robison's tapestries are uniform at 1.5m in length and 1m in width. Initially, to obtain whole numbers, we multiply these dimensions by 10.

Thus, the dimensions become 15m long and 10m wide.

Now, the proportion of Height to Width is 15:10

⇒\frac{Height}{Width} =\frac{15}{10}

⇒\frac{Height}{Width} =\frac{3}{2}

Thus, the proportion of the heights of the tapestries to their widths is 3:2.

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1 day ago
Anya found the slope of the line that passes through the points (–7, 4) and (2, –3). Her work is shown below. Let (x2, y2) be (–
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A pile of sand has a weight of 90kg the sand is put into a small bag and a medium bag and a large bag in the ratio 2:3:7
tester [8842]
90kg of sand was divided into 3 bags, constituting a total of 2+3+7=12 sections.
90kg/12=7.5kg
The smaller bag comprises 2 sections, hence it weighs 7.5kg*2=15kg
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