A ball was thrown into the air with an initial velocity of 72ft per second. The height of the ball after t seconds is represented by the equation h=72t-16². The graph of the function is shown to the right.
It says to describe the dependent variable for this problem and describe the domain and range using appropriate notation.
Honestly I have to say I am lost
72x72-32=?
height h is the dependent variable, time domain is on your graph. I have no idea what the graph shows for time.
First, let's break down the given equation: h = 72t - 16t².
In this equation:
- h represents the height of the ball after t seconds (the dependent variable).
- t represents the time in seconds (the independent variable).
So, the dependent variable for this problem is the height of the ball (h), as it depends on the independent variable, time (t).
Now, let's discuss the domain and range:
Domain: The domain of a function represents all possible values of the independent variable. In this case, t represents time, so the domain would include all possible values of time. Since time cannot be negative, we can assume that the ball was thrown at t = 0 and that the ball will eventually hit the ground. Therefore, the domain would typically include all non-negative real numbers, or in interval notation, this can be written as [0, ∞).
Range: The range of a function represents all possible values of the dependent variable. For this problem, the range would represent all possible heights that the ball can reach. Since the ball was thrown into the air, it can go up to a certain maximum height and then fall back down. The maximum height can be determined by finding the vertex of the quadratic equation. The vertex is given by the formula t = -b/2a, where a, b, and c are the coefficients in the quadratic equation. In this case, a = -16. Plugging the values into the formula, we get t = -72/(2*(-16)) = 2.25 seconds. So, for t = 2.25 seconds, the ball reaches its maximum height. Therefore, the range would include all heights from 0 (when the ball is at the ground) up to the maximum height reached by the ball. In interval notation, this can be written as [0, h_max], where h_max is the maximum height reached by the ball.
Now, onto the question you asked: 72 x 72 - 32. To solve this arithmetic expression, we follow the order of operations, which is known as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right)).
Using PEMDAS, we calculate the expression step by step:
72 x 72 - 32
= 5184 - 32
= 5152
So, the value of 72 x 72 - 32 is 5152.