Answer:
n = π/6, π/4, 3π/4, 5π/6
Step-by-step explanation:
sin(3n) − sin n = cos(2n)
Use double and triple angle formulas:
(3 sin n − 4 sin³ n) − sin n = 1 − 2 sin² n
2 sin n − 4 sin³ n = 1 − 2 sin² n
4 sin³ n − 2 sin² n − 2 sin n + 1 = 0
Factor by grouping:
2 sin² n (2 sin n − 1) − (2 sin n − 1) = 0
(2 sin² n − 1) (2 sin n − 1) = 0
Solve:
2 sin² n − 1 = 0
2 sin² n = 1
sin² n = 1/2
sin n = √2/2
n = π/4, 3π/4
2 sin n − 1 = 0
2 sin n = 1
sin n = 1/2
n = π/6, 5π/6
Answer:
Step-by-step explanation:
The total number of apples produced at the apple harvest is 2,350kg.
1 kg = 1000 grams. Therefore,
2350 kg = 2350 × 1000 = 2350000kg
A farmer packs 36 apples in the box. If one apple weighs approximately 250 grams, the total weight of 36 apples would be
36 × 250 = 9000 grams
Therefore, the number of boxes that are needed to pack the apples would be
2350000/9000 = 261.11
It means that 262 boxes would be needed.
Answer:
4 7/8 or 4.875
Step-by-step explanation:
1 1/4 + 3 5/8 = 4 7/8 or 4.875
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Answer:
Step-by-step explanation:
Similar figures have the same shape but the same size.
Moving from left to right:
The first figure is similar because it is rotated
The second figure is not similar because of shape
The third figure is not similar because of different ratio the ratio for the figure above is 3/5 or 0.6, while this figure is 12/15 or 0.8
The fourth figure is not similar because of ratio, but it is still a rectangle
The fifth figure is not similar because of shape
The last figure is similar because the ratio is the same with 6/10 or 0.6
