a soccer-ball was kicked off the top of the building and its height was monitored.regression equation is h= -4t^2+24.5t+146. what is the height of the building?
well, what is h when t=0?
i don't understand
the ball is at the top of the building to start with. At t=0, the ball is kicked. So, the last term, 146, is the height of the building.
To find the height of the building, we need to look at the equation provided: h = -4t^2 + 24.5t + 146.
In this equation, 'h' represents the height of the soccer ball above the ground at a given time (t), measured in seconds. The equation is a quadratic equation in the form of y = ax^2 + bx + c, where 'a' represents the coefficient of the squared term, 'b' represents the coefficient of the linear term, and 'c' represents the constant term.
Comparing the given equation with the quadratic equation form, we can determine the following values:
- 'a' = -4 (coefficient of the squared term)
- 'b' = 24.5 (coefficient of the linear term)
- 'c' = 146 (constant term)
To find the height of the building, we need to determine the value of 'h' when the soccer ball hits the ground. When the ball hits the ground, its height will be zero. Therefore, we set the equation equal to zero and solve for 't':
0 = -4t^2 + 24.5t + 146
To solve this quadratic equation, we can use different methods such as factoring, completing the square, or the quadratic formula. In this case, let's use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values of 'a', 'b', and 'c' into the formula:
t = (-24.5 ± √(24.5^2 - 4(-4)(146))) / (2(-4))
Simplifying the equation further:
t = (-24.5 ± √(600.25 + 2336)) / (-8)
t = (-24.5 ± √2936.25) / -8
Now, we have two possible values for 't', which correspond to the two points in time when the ball reaches the ground. Let's calculate both:
t₁ = (-24.5 + √2936.25) / -8
t₂ = (-24.5 - √2936.25) / -8
Solving these equations using a calculator or by hand:
t₁ ≈ 8.1 seconds
t₂ ≈ -4 seconds (we can disregard this negative value since time cannot be negative in this context)
Now that we have the time when the ball hits the ground, we can find the height of the building by substituting the obtained value of 't' into the original equation:
h = -4(8.1)^2 + 24.5(8.1) + 146
h ≈ 193.04
Therefore, the height of the building is approximately 193.04 units.