To determine the missing angle of P, which measures 30 degrees, angle P and C are congruent since they are identical. The longest side, the hypotenuse, is PC, corresponding to angle T. Utilizing the Pythagorean Theorem, a² + b² = c², we find (PT)² + (CT)² = (PC)². Knowing that PT equals 4 and since PT and CT are congruent, we can restate it as (4)² + (4)² = (PC)², leading to PC being equal to rad(32). Could someone please confirm?
96 soldiers will remain unassigned and the arrangement will consist of 52 rows.
Part a) When a page is scaled down to 80%, how much enlargement is necessary to bring it back to its original size?
Let
x---------> the percent enlargement
Given the original size is 100%
This means:
x*80%=100%
x=(100%/80%)
x=1.25--------> 1.25=(125/100)=125%
Thus,
The answer to Part a) is
The percent enlargement required is 125%
Part b) Estimate how many successive copies of a page are needed to make the final copy less than 15% of its original size.
Since the photocopy machine reduces sizes to 80% of the original
Therefore:
Copy N 1
0.80*100%=80%
Copy N 2
0.80*80%=64%
Copy N 3
0.80*64%=51.2%
Copy N 4
0.80*51.2%=40.96%
Copy N 5
0.80*40.96%=32.77%
Copy N 6
0.80*32.77%=26.21%
Copy N 7
0.80*26.21%=20.97%
Copy N 8
0.80*20.97%=16.78%
Copy N 9
0.80*16.78%=13.42%-------------> 13.42% < 15%
Therefore,
The answer to Part b) is
The necessary number of copies to achieve this is 9
