The velocity of a ball thrown in the air is 72ft
Per second. The height of the ball after t seconds
Is represented by the equation
H = 72ft t - 62t^2.
Describe the dependent variable, the domain and range.
Honestly I have to say I am lost
72 x 72ft - 256 = ?
Not sure if I am heading in the right direction
the domain of all polynomials is all real numbers.
Naturally, in the real world, only positive time makes sense, so the domain here is just t >= 0
What planet is this ball on? gravity on earth wold make the function
H(t) = 72t - 16t^2
Find the vertex of that parabola. That is the maximum height. Naturally, negative height makes no sense, so the range is
0 <= H <= max-height at vertex.
No problem! Let's break it down step by step.
First, let's clarify what the dependent variable is. In this case, the dependent variable is the height of the ball, which is represented by the letter "H" in the equation.
Next, let's talk about the domain of the equation. The domain refers to the set of possible input values for the independent variable, which in this case is time (t). Since the equation represents the height of the ball after t seconds, the domain would be all real numbers that make sense in the context of the problem. This means that the domain would be all non-negative real numbers (t ≥ 0), since time cannot be negative in this scenario.
Now, let's move on to the range. The range refers to the set of possible output values for the dependent variable (H). In this case, the height of the ball can be any real number because the equation does not place any restrictions on the height. However, since the ball is thrown into the air, the height will be initially positive and eventually decrease back to the ground. So, the range would be all real numbers greater than or equal to zero (H ≥ 0).
Now, let's look at the equation you provided: H = 72t - 62t^2.
To find the value of H for a specific time t, you need to substitute that value into the equation and solve for H. Let's assume we want to find the height of the ball after 2 seconds. We would calculate it like this:
H = 72(2) - 62(2^2)
H = 144 - 62(4)
H = 144 - 248
H = -104
Therefore, the height of the ball after 2 seconds is -104ft. Keep in mind that the negative sign indicates that the ball has fallen below its initial height.
I hope this explanation helps you understand the problem better! Let me know if you have any further questions.