What happens to the graph of f(x) when it is multiplied by a number between 0 and 1?
2 answers:
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A) The length of the longer leg is x-1
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
b) Based on the area, the other leg is 2*30/(x -1). Based on the Pythagorean theorem, the other leg is √(x^2 -(x -1)^2).
c) Equating the two expressions for the shorter leg, we have
.. 60/(x -1) = √(2x -1)
.. 3600/(x -1)^2 = (2x -1)
.. (2x -1)(x^2 -2x +1) = 3600
.. 2x^3 -5x^2 +4x -3601 = 0
d) There is one positive real root, at x=13. A graphical solution works well.
The three sides of the triangle are 5 in, 12 in, 13 in.
_____
5-12-13 is a well-known Pythagorean triple. It is the next smallest one after 3-4-5.
Answer:
The probability that they will teach different courses is .
Step-by-step explanation:
Sample space is a set of all possible outcomes of an experiment.
In this case we will write the sample space in the form (x, y).
Here <em>x</em> represents the course taught by the first part-time instructor and <em>y</em> represents the course taught by the second part-time instructor.
Denote every course by their first letter.
The sample space is as follows:
S = {(P, P), (P, I), (P, S), (I, P), (I, I), (I, S), (S, P), (S, I) and (S, S)}
The outcomes where the the instructors will teach different courses are:
s = {(P, I), (P, S), (I, P),(I, S), (S, P) and (S, I)}
The probability of an events <em>E</em> is the ratio of the number of favorable outcomes to the total number of outcomes.
Compute the probability that they will teach different courses as follows:
Thus, the probability that they will teach different courses is .