Answer:
Again...
Step-by-step explanation:
Answer:
The time it takes for the cannonball to hit the ground is 6.49 seconds.
Step-by-step explanation:
You know that the height of the cannonball above the ground, h, in meters, in time, t, in seconds, is found by the function h(t) = -4.9t² + 30.5t + 8.4. You want to calculate the time it takes for the cannonball to hit the ground, that is, the time it takes for the bullet to reach zero height. So, being h(t) = 0 you have:
0 = -4.9t² + 30.5t + 8.4
To solve a quadratic function 0=a*x² + b*x +c, the expression is applied:
![\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%2B-%5Csqrt%7Bb%5E%7B2%7D%20-4%2Aa%2Ac%7D%20%7D%7B2%2Aa%7D)
In this case, being a = -4.9, b =30.5 and c =8.4 you have:
![\frac{-30.5+-\sqrt{30.5^{2} -4*(-4.9)*8.4} }{2*(-4.9)}](https://tex.z-dn.net/?f=%5Cfrac%7B-30.5%2B-%5Csqrt%7B30.5%5E%7B2%7D%20-4%2A%28-4.9%29%2A8.4%7D%20%7D%7B2%2A%28-4.9%29%7D)
Solving you get:
t1= -0.26 seconds and t2=6.49 seconds
Since time does not have a negative value, then <u><em>the time it takes for the cannonball to hit the ground is 6.49 seconds.</em></u>
Answer:
The answer in the explanation
Step-by-step explanation:
The solution of the inequality is all real numbers greater than or equal to 5
so
The solution using interval notation is ------> [5,∞)
and
The solution using set notation is {x ∈ R | x ≥ 5}
The equation of the parabola in the vertex form is y = (x - 3
- 5 with ( 3, -5) is the vertex of the parabola and 1 is the multiplier
In the above question, A parabolic equation is given as follows:
Y = x^2 - 6x + 4
The equation of the parabola in the vertex form is :
y = a (x - h
+ k
Where a is a multiplier in the equation and (h,k) are the coordinates of the vertex
So, in order to obtain this form, we will use the method of completing square :
Y = x^2 - 6x + 4
y =
- 6x + (9 -9) + 4
y = (x - 3
+ ( -9 + 4)
y = (x - 3
- 5
where, ( 3, -5) is the vertex of the parabola and 1 is the multiplier
Hence, The equation of the parabola in the vertex form is y = (x - 3
- 5 with ( 3, -5) is the vertex of the parabola and 1 is the multiplier
To learn more about, parabola, here
brainly.com/question/21685473
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