The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:
<h3>How to write the polynomial?</h3>
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:
Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:
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Answer:
Step-by-step explanation:
We can break down this problem by first realizing different parts of the circle.
With this, we can find out if we find the radius of the circle, we have our answer.
We should also note that the angle formed by the 3.6 units long line and the chord is a right angle.
<em>What we need is a way to find the radius of the circle</em><em>. This will get us x</em>. The radius of a circle will be the length of any line that starts from point O and ends at the circle edge.
If we draw a line connecting the end of the 3.6 line at point O to the end of the 8 unit long chord, we get a triangle! (Image attached for reference).
We can solve for the hypotenuse using the Pythagorean Theorem. This theorem states that:
Since we know one side is 3.6, we can use that as A. The second side will be 4 since the 3.6 line lies directly in the center of the chord = 8/2 = 4!
Therefore, since this is the radius of the circle (also the hypotenuse), this can be said for any line that comes from point O onto the edge of the circle.
The line X does just that. Therefore, the value of x is also 5.4.
Hope this helped!
The function exists in a parabola.
The axis of symmetry of a parabola exists at the midpoint between the two real roots.
The roots exist the solutions of H(t) = 0
To estimate the roots equation exists
Factor t(-16t + 64) = 0
t = 0 and -16t + 64 =0
-16t + 64 = 0
t = 64 / 16 = 4
t = 4
Then the two roots are t = 0 and t = 4, and the axis of symmetry exists
t = (0+4)/2 = 4/2 = 2
<h3>How to estimate the axis of symmetry?</h3>The axis of symmetry exists at t = 2.
It represents the time at which the ball is at the higher point, the maximum height.
You can find the maximum height replacing t = 2 in the function H(t)
= 64 feet.
And you can also deduce that the second part of the flight will take 2 seconds, for a total flight time of 4 seconds.
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