Answer:
Step-by-step explanation:
We are given the position function and need to find the value of t when h<17.
Create an inequality that represents this situation:
The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.
The simplest way to solve this is to subtract 81 from both sides:
then divide both sides by -16:
Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is
t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.
Answer:
4 right angles.
Step-by-step explanation:
1 right angle: 90 degrees
360/90= 4
We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is 
. The graph of the function does not show a phase shift. We are asked to write the equation of our function.
We know that general form a cosine function is 
, where,
A = Amplitude,
= Period,
c = Horizontal shift,
d = Vertical shift.
The equation of parent cosine function is 
. Since function is reflected about x-axis, so our function will be 
.
Let us find the value of b.
Upon substituting our given values in general cosine function, we will get:
Therefore, our required function would be .
F(g(x)) = f(3x+2) = h(x)=9x^2+12x + 6
Note that (3x+2)^2 = 9x^2 + 12x + 4, which is almost, but not quite, equal to h(x).
Let's experiment. What if f(x) = x^2 + 2?
Then f(3x+2) = (3x+2)^2 + 2 = 9x^2 + 12x + 4 + 2 = 9x^2 + 12x + 6, which is the same as the given h(x).
Thus, f(x) is x^2 + 2.
