Since a maximum area is desired, the dimensions of the larger, outer rectangle would be equal to 96 ft and 96 ft.
<h3>How to calculate the area of a rectangle?</h3>
Mathematically, the area of a rectangle is calculated by using this formula:
A = LW
<u>Where:</u>
Since the perimeter shouldn't be larger than the available fencing, we have:
384 = 2L + 2W
2W = 384 - 2L
W = 192 - L
Now, the area becomes:
A = L × (192 - L)
A = 192L - L²
By using completing the square to find the roots, we have:
A = 192L - L²
0 = 192L - L² + 96² - 96²
0 = 96² - (L² - 192L + 96²)
0 = 9216 - (L - 96)²
L = 96 ft.
W = 192 - 96
W = 96 ft.
<h3>The dimensions of the smaller holding pens.</h3>
For the width of the smaller holding pens, we have:
Width = 96/3
Width = 31 ft.
However, the length of the smaller holding pens would remain the same as 96 feet.
Read more on rectangle here: brainly.com/question/25292087
What speech? you never attached a file.
By applying Pythagorean' theorem, the value of tanP is equal to 3/4.
<h3>How to determine the value of tan P?</h3>
Since triangle PQR has right-angle Q and sinR = 4/5, we have:
sinR = Opp/hyp = 4/5
tanP = Opp/Adj = QR/4
Next, we would determine the length of QR by applying Pythagorean' theorem:
PR² = QR² + PQ²
5² = QR² + 4²
25 = QR² + 16
QR² = 25 - 18
QR = √9
QR = 3 units.
For the value of tanP, we have:
tanP = 3/4.
Read more on Pythagorean theorem here: brainly.com/question/23200848
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Bromine has stronger inter molecular force than Fluorine.
<h3> Inter molecular forces and relationship with physical states of matter</h3>
The intermolecular forces of a substance tells the physical state of that substance , We can therefore say that the Solid, liquid and gas states of substances depends on the intermolecular forces surrounding them.
- For solids,the inte molecular forces will be so strong as they draw the molecules together giving them a compact structure.
- For liquids, the the inter molecular forces will be just strong enough to keep the molecules together in a confined space.
- For gases, the the inter molecular forces are weakest as the molecules move about.
We can then conclude that At stp, fluorine is a gas and bromine is a liquid because, compared to fluorine, bromine has a stronger intermoleclar force.
See more of intermolecular forces here: brainly.com/question/492113
