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.
Joseph earns $15 for every lawn he mows. Is the amount of money he earns proportional to the number of lawns he mows? Make a tab
le to help you identify the relationships
2 answers:
Given that Joseph earns $15 for every lawn he mows.
so if he mows lown 1 time then his earning = $15
if he mows lown 2 time then his earning = $15*2= $30
if he mows lown 3 time then his earning = $15*3= $45
if he mows lown 4 time then his earning = $15*4= $60
if he mows lown 5 time then his earning = $15*5= $75
So the required table will be:
From the table we can see that Joseph's earning increases by $15 each time so we can say that YES, the amount of money he earns proportional to the number of lawns he mows.
<h2>Answer with explanation:</h2>
It is given that:
Joseph earns $15 for every lawn he mows.
If x denotes the number of lawns he mow.
and y denotes his earnings.
Then the equation which is obtained on the basis of this information is:
Also, the table of values is given as follows:
Number of lawn mowed 1 2 3 4
Earnings($) 15 30 45 60
Yes, the amount of money he earns is proportional to the number of lawns he mows.
Since, with each increase in the number of lawns he mowed, his earnings are also increasing by a constant rate.
Hence, the relationship is a direct variation.
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