Answer:
Part I: cot(15 degrees) = cot(45 - 30)
Part II: Evaluation is below
Step-by-step explanation:
<em>Everything is done in degrees</em>
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Two angles that differ by 15 degrees that is easy to evaluate is 30 degrees and 45 degrees. The cot(15 degrees) = cot(45 - 30) = 1/tan(45-30) = (1+tan45tan30)/(tan30 - tan45) = (1+ sqrt(3))/(sqrt(3) - 1)
We rationalize this by multiplying 1+ sqrt(3) in the top and bottom, getting:
(4 + 2sqrt(3))/2 = 2 + sqrt(3)
I hope this helps! :)
Answer:
5 years
Step-by-step explanation:
1. if able's age is x, then his sister's is x-4, and his brother's is 2x
2. if these sum to 32, then we can formulate the equation x+(x-4)+2x=32
3. now solve for x, 4x-4=32, 4x=36, x=9
4. if able's sister is x-4 years old, she is 9-4, or 5 years old
10x=1
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2x(x+3)
is the answer ,hope its corect and help