The cost of a newsletter subscription is $20 per year. The cost is expected to increase 10% each year. Which expression can be u
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Answer:
<em>Thus, the values of x are 70° and 250°</em>
Step-by-step explanation:
<u>Trigonometric Functions</u>
The tangent is defined as:
Given a value for the tangent, there are two angles with the same tangent, one of them being and the other
+180°.
We are given:
The angle is the inverse tangent:
Using a scientific calculator, we find the first angle:
x=70°
The second angle is found adding 180°:
x=70°+180°=250°
Thus, the values of x are 70° and 250°
So for this, since the rate is linear we will be using the slope-intercept form, which is y=mx+b (m = slope/rate of change, b = y-intercept)
Since the rate of change "descends 150 ft per min", the m variable is -150.
The y-intercept is, in this case, the height of the balloon at 0 mins, or the starting height. Since the balloon "is at a height of 2250 ft", the b variable is 2250.
Putting our equation together, its y = -150x + 2250.
Since time is our independent variable, plug in 6, 8, and 10 mins into the x variable to solve for their heights:
In context, after 6 minutes the balloon is at 1,350 ft, after 8 minutes the balloon is at 1,050 ft, and after 10 minutes the balloon is at 750 ft.