An ????-pyramid is created with ???? blocks at the base, ???? − 1 blocks on the next level, until the peak which has 1 block.Pyr
amids are colored according to the following rules: (1) Each block can be red, gold, or black, and (2) All 3-block units composed of one block on top of two others must either all be the same color or all be different colors. Answer the following:a) How many ways are there to color a 7-pyramid?b) What is the maximum number of black blocks in a 25-pyramid that has at least one red block and at least one gold block?
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Answer:
Step-by-step explanation:
By using the cos square identity in trigonometry i.e., cos2ϴ = 1 – sin2 ϴ, we can evaluate the exact value of cos(33 ). For calculating the exact value of cos(∏/6), we have to substitute the value of sin(30°) in the same formula.
cos(30°) = √1 – sin230°
The value of sin30° is 1/2 (Trigonometric Ratios)
cos(30°) = √1 – (1/2)2
cos(30°) = √1 – (1/4)
cos(30°) = √(1 * 4 – 1)/4
cos(30°) = √(4 – 1)/4
cos(30°) = √3/4
Therefore, cos(30°) = √3/2