Answer:
infinite
Step-by-step explanation:
First we will convert those radian angles to degrees, since my mind works better with degrees. Let's work one at a time. First,

. If we start at the positive x-axis and measure out 315 we end up in the 4th quadrant with a reference angle of 45 with the positive x-axis. The side across from the reference angle is -1, the side adjacent to the angle is 1, and the hypotenuse is sqrt2. The cotangent of this angle, then is 1/-1 which is -1. As for the second one, converting radians to degrees gives us that

. Sweeping out that angle has us going around the origin more than once and ending up in the first quadrant with a reference angle of 30° with the positive x-axis. The side across from the angle is 1, the side adjacent to the angle is √3, and the hypotenuse is 2. Therefore, the secant of that angle is 2/√3.
Step-by-step explanation:
the answer should be 1004
Let the numbers be m and n. Then "<span>five times the quotient of two numbers" would be 5m/n.
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We can say that exchanging one couple's ticket for an individual's ticket would increase the money in the cash box from 200 to 202 and it would result in an even number of couples tickets sold.
<u>Step-by-step explanation:</u>
Let the number of tickets sold to the individuals = s
Let the number of tickets sold to the couples = c
According to the question,
s + c = 46 ( Equation 1)
Since each individual's ticket is $6, the total amount of money made by selling tickets to individuals is 6s.
Similarly, since each ticket sold to couples is $8, the total amount of money made by selling tickets to couples is 8c.
So,
6 s + 8 c = 200 ( Equation 2)
On solving both the equations, we get
c = 38 and s = 8
Therefore, 8 tickets were sold to individuals and 38 tickets were sold to the couples.