The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A)
<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>
<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>
Now we group applying what we see above
<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>
<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>
<span>Now the given expression is: </span>
<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>
<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>
Answer: 
<u>Step-by-step explanation:</u>
a) This is an arithmetic sequence where 3 is added to the previous term.
48 + 3 = 51
51 + 3 = 54
54 + 3 = 57
The recursive formula for this sequence is: 
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b) This is a geometric sequence where 2.5 is multiplied to the previous term.
100(2.5) = 250
250 (2.5) = 625
625(2.5) = 1562.5
The recursive formula for this sequence is: 
Answer:
(x , y) ----> (-x , y)
Step-by-step explanation:
(x , y) ----> (-x , y)
Example for 1. :
(-4,2) ---> (4,2)
Answer:
0.54 ounces in each tube
Step-by-step explanation:
Add the amount she used so we can add it in. 1.35+0.27= 1.62. Then divide it by the number of tube and since it was a 3 pack you divide it by 3. 1.62/3=0.54 so there is 0.54 ounces in each tube.
