Let the width of the rectangle be W in.
Therefore, length = 2W in
Area of the rectangle, Ar = L*W = 2W*W = 2W^2
Also, perimeter of the rectangle, Pr = 2(L+W) = 2(2W+W) = 2(3W) = 6W
Then, perimeter of square, Ps = 52-6W
And, area of the square, As = [(52-6W)/4]^2 = [13-1.5W]^2 = (13-1.5W)(13-1.5W) = 169-19.5W-19.5W+2.25W^2 = 2.25W^2-39W+169
Therefore,
Total area, At = Ar+As = 2W^2+2.25W^2-39W+169 = 4.25W^2 -39W+169
For maximum area, the first derivative of the total area expression should be zero. Therefore;
dAt/dW = 8.5W - 39 = 0 => 8.5W = 39 => W = 39/8.5 = 4.588 in
Therefore, for maximum area, width (W) should be 4.588 in
Answer:
The intervals do not have the same range
For this case we have the following expression:
![(\sqrt {12} +6) (- \sqrt {8} - \sqrt {2})](https://tex.z-dn.net/?f=%28%5Csqrt%20%7B12%7D%20%2B6%29%20%28-%20%5Csqrt%20%7B8%7D%20-%20%5Csqrt%20%7B2%7D%29)
We apply distributive property:
![(\sqrt {12} * - \sqrt {8}) + (\sqrt {12} * - \sqrt {2}) + (6 * - \sqrt {8}) + (6 * - \sqrt {2} ) =\\- \sqrt {96} - \sqrt {24} -6 \sqrt {8} -6 \sqrt {2} =](https://tex.z-dn.net/?f=%28%5Csqrt%20%7B12%7D%20%2A%20-%20%5Csqrt%20%7B8%7D%29%20%2B%20%28%5Csqrt%20%7B12%7D%20%2A%20-%20%5Csqrt%20%7B2%7D%29%20%2B%20%286%20%2A%20-%20%5Csqrt%20%7B8%7D%29%20%2B%20%286%20%2A%20-%20%5Csqrt%20%7B2%7D%20%29%20%3D%5C%5C-%20%5Csqrt%20%7B96%7D%20-%20%5Csqrt%20%7B24%7D%20-6%20%5Csqrt%20%7B8%7D%20-6%20%5Csqrt%20%7B2%7D%20%3D)
We rewrite in equivalent form:
![- \sqrt {4 ^ 2 * 6} - \sqrt {2 ^ 2 * 6} -6 \sqrt {2 ^ 2 * 2} -6 \sqrt {2} =\\-4 \sqrt {6} -2 \sqrt {6} -6 * 2 \sqrt {2} -6 \sqrt {2} =](https://tex.z-dn.net/?f=-%20%5Csqrt%20%7B4%20%5E%202%20%2A%206%7D%20-%20%5Csqrt%20%7B2%20%5E%202%20%2A%206%7D%20-6%20%5Csqrt%20%7B2%20%5E%202%20%2A%202%7D%20-6%20%5Csqrt%20%7B2%7D%20%3D%5C%5C-4%20%5Csqrt%20%7B6%7D%20-2%20%5Csqrt%20%7B6%7D%20-6%20%2A%202%20%5Csqrt%20%7B2%7D%20-6%20%5Csqrt%20%7B2%7D%20%3D)
![-4 \sqrt {6} -2 \sqrt {6} -12 \sqrt {2} -6 \sqrt {2} =\\-6 \sqrt {6} -18 \sqrt {2}](https://tex.z-dn.net/?f=-4%20%5Csqrt%20%7B6%7D%20-2%20%5Csqrt%20%7B6%7D%20-12%20%5Csqrt%20%7B2%7D%20-6%20%5Csqrt%20%7B2%7D%20%3D%5C%5C-6%20%5Csqrt%20%7B6%7D%20-18%20%5Csqrt%20%7B2%7D)
Answer:
![-6 \sqrt {6} -18 \sqrt {2}](https://tex.z-dn.net/?f=-6%20%5Csqrt%20%7B6%7D%20-18%20%5Csqrt%20%7B2%7D)
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Answer:
<em>(BEFORE YOU SUBMIT IT, PLEASE READ THE WARNING)</em>
QUESTION EIGHT: 2690
QUESTION NINE: 120
QUESTION ELEVEN: 12.5
QUESTION FOURTEEN: 24
Step-by-step explanation:
<u>WARNING!! FOR QUESTIONS WITH INTEREST: I do not know if interest is good or bad (if you get money, or if you lose money. I counted interest as making money, but if you are sure it's not, contact me in the comments and I will solve it again! :)</u>
<u />
8.
may 3rd -> july 15th = 73 days
500*0.06 = 30
30 = how much he makes in one day (so he has 530 after 1 day)
30*73 = 2190
500 + 2190 = 2690
9.
210/7 = 30
1% for 3 years = 30
1% for 1 year = 10
100% for 1 year = 1000
2000*0.06 = 120
11.
54,000*0.08 = 4320
54,000/4320 = 12.5
14.
5000*6.26% = 312.5
7500/312.5 = 24
Hope this helps... T-T