Tutor profile: Kasey M.
For x = pi/6, give the coordinates of the angle, such that y = (cos(x), sin(x)).
First convert the angle from radians to degrees, in which pi/6 is equivalent to an angle of 30 degrees. Given the special angles, sin(30 degrees) = 1/2, and cos(30 degrees) = root(3)/2. Then, y = (root(3)/2, 1/2).
In an excerpt from The German Ideology, Karl Marx delineates three premises of human history in order to show that the production of society is dependent on the history of that society. Please explain the three premises and how they relate to production.
The first premise is an existence claim. Given that humans exist, they must exist of something, such that their physical makeup is derived from their existence. The second premise differentiates humans from animals by examining what it means for humans to exist. Specifically, humans produce the substance of their existence, which is dependent on their physical makeup. The third premise examines the ways in which humans produce the content of their existence. Since production is based upon one’s nature, which consists of one’s physical makeup, as well as his/her interactions with society, production is both an active and social process (McLellan, p. 127).
If the sum of the two dice equal eight, seven goldfish will be distributed for every six goldfish. If Mark risks 48 goldfish, how many goldfish will Mark have if the sum of the dice equal eight?
This problem can be set up as an equivalence of ratios. The first ratio is 6/7. The second ratio is 48/x. By setting the two ratios equal to each other, 6/7 = 48/x. You can cross multiply on the top, such that 1/7 = 8/x. Then, by cross multiplying, you get x = 56, so the answer is 56 goldfish.
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