A box contains 6 blue pens and 10 red pens. What is the ratio of red pens to total pens as a fraction
2 answers:
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Answer:
682,000 miles
Step-by-step explanation:
Using the ratio of 186,000 miles per second:
we can set up a proportion (equivalent ratios) to find the distance, in miles, from the earth to the moon
where 'x' is the number of miles between the earth and the moon
Cross-multiply: x = 186,000*
Solve for x = 682,000 miles
Recall the angle sum identities:
cos(a + b) = cos(a) cos(b) - sin(a) sin(b)
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
sin(a + b) = sin(a) cos(b) + sin(b) cos(a)
sin(a - b) = sin(a) cos(b) - sin(b) cos(a)
Notice that adding the first two together, and subtract the last from the third, we get two more identities:
cos(a + b) + cos(a - b) = 2 cos(a) cos(b)
sin(a + b) + sin(a - b) = 2 sin(b) cos(a)
Let a = 4x and b = x. Then
cos(5x) + cos(3x) = 2 cos(4x) cos(x)
sin(5x) - sin(3x) = 2 sin(x) cos(4x)
Now,
as required.