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S_A_V [24]
3 years ago
9

A+B-C=3pi then find sinA+sinB-sinC

Mathematics
1 answer:
steposvetlana [31]3 years ago
7 0
The answer:
the full question is as follow:

if A+B-C=3pi, then find sinA+sinB-sinC

first, the main formula of sine and cosine are:
sinC = 2sin(C/2)cos(C/2)
sinA +sinB = 2sin[(A+B)/2]cos[(A-B)/2]

therefore: 
 sinA+sinB-sinC = 2sin[(A+B)/2]cos[(A-B)/2] - 2sin(C/2)cos(C/2)

sin[(A+B)/2] = cos(C/2)
2sin(C/2)cos(C/2) = cos[(A+B)/2
and 
A+B-C=3 pi implies A+B =3 pi + C, so 
cos[(A+B)/2] = cos [3 pi/2  + C/2]
and  with the equivalence cos (3Pi/2  + X) = sinX

sinA+sinB-sinC =  cos(C/2)+ sin(C/2) 
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225.78 grams

Step-by-step explanation:

To solve this question, we would be using the formula

P(t) = Po × 2^t/n

Where P(t) = Remaining amount after r hours

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t = Time

In the question,

Where P(t) = Remaining amount after r hours = unknown

Po = Initial amount = 537

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Dustin decides to try selling whole-wheat muffins and bagels at his farm stand. He has $60 to spend on ingredients and 8 hours t
vaieri [72.5K]

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The correct answer is D.

Step-by-step explanation:

Option A establishes that 4 dozen bagels and 3 dozen muffins will be prepared, thus spending $ 30 and 3 hours on muffins and $ 60 and 12 hours on bagels. In total, $ 90 and 15 hours will be spent, so this option is not correct.

Option B establishes that 2 dozen bagels and 6 dozen muffins will be prepared, thus spending $ 60 and 6 hours on muffins and $ 30 and 6 hours on bagels. In total, $ 90 and 12 hours will be spent, so this option is not correct either.

Option C states that 3 dozen bagels and 1 dozen muffins will be prepared, which will spend $ 10 and 1 hour on muffins and $ 45 and 9 hours on bagels. In total, $ 55 and 10 hours will be spent, so this option is not correct.

Finally, option D establishes that 1 dozen bagels and 3 dozen muffins will be prepared, thus spending $ 30 and 3 hours on muffins and $ 15 and 3 hours on bagels. In total, $ 45 and 6 hours will be spent, with which this option is within the predetermined parameters, that is, the expense is less than $ 60 and the time is less than 8 hours.

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