Tutor profile: Dustin T.
Triangles ABC and DEF are congruent. If AB = 3, AC = 5, and DE = 6, what is the length of DF?
We know that corresponding parts of congruent triangles are congruent, so DF is going to be some multiple of 5. Since the ratios of corresponding sides of congruent triangles are equal, we can set up a proportion to find out. AB/DE = AC/DF 3/6 = 5/DF By now, we should be able to intuitively see the answer, but just in case we can cross multiply. 30 = 3DF 10 = DF
According to Aristotle, how is it that we can act akratically?
Aristotle argues that there are two types of knowledge: active and passive. When we act against our better judgement, it is because we "cease attending to the fact" that we know our action is wrong or bad for us. In short, we can have a universal judgement about a certain thing (broccoli is good for you) that conflicts with a particular opinion we hold about that thing (broccoli tastes gross). When we act on our particular opinion, we temporarily forget our universal judgement, hence we act akratically.
Bob rolls a ball off a cliff 35 feet high. The trajectory of the ball can be measured by this equation: h(t) = -t^2 + 2t + 35. How long does it take the ball to hit the ground?
This is a classic quadratic equation. By using the quadratic formula, we'll be able to solve this pretty easily. We know that when the ball hits the ground, the height of the ball will be zero. So, we can say that 0 = -t^2 + 2t + 35. To solve for t, we'll use the quadratic formula t = [-2 - sqrt(4 - (4)(-1)(35))] / (-2) This turns out to be (-2 - 12) / (-2) = -14/-2 = 7 so, it will take 7 seconds for the ball to hit the ground. *note, normally, we would do negative b plus OR minus the square root, but since we are talking about time, we can ignore a negative answer (since we can't travel back in time), and since -2 + the sqrt will give us a negative answer, we can ignore it.
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