Answer:
P(x) = x^4 -16x^3 +76x^2 -72x -100
Step-by-step explanation:
The two roots 1-√3 and 1+√3 give rise to the quadratic factor ...
... (x -(1-√3))(x -(1+√3)) = (x-1)^2 -(√3)^2 = x^2 -2x -2
The complex root 7-i has a conjugate that is also a root. These two roots give rise to the quadratic factor ...
... (x -(7 -i))(x -(7 +i)) = (x-7)^2 -(i)^2 = x^2 -14x +50
The product of these two quadratic factors is ...
... P(x) = (x^2 -2x -2)(x^2 -14x +50) = x^4 +x^3(-14 -2) +x^2(50 +28 -2) +x(-100+28) -100
... P(x) = x^4 -16x^3 +76x^2 -72x -100
Answer:
A = 72°
B = 108°
Step-by-step explanation:
5y - 3 = 3y + 27
5y - 3y = 27 + 3
2y = 30
y = 30/2
y = 15
A = 5y - 3
A = 5(15) - 3
A = 75 - 3
A = 72°
A + B = 180°
72° + B = 180°
B = 180° - 72°
B = 108°
<span>1) Equation for the parabola y = - x² + 36.
</span>
<span>2) A drone is in the distance, flying upward in a
straight line. It intersects the rainbow at two points. Choose the
points where your drone intersects the parabola and create a table of at
least four values for the function.
</span>
<span>The points of intersection will be: (0,36) and (4, 20)
</span><span>
</span>
T<span>able of values
for a linear function and the parabola
</span>
<span>x linear function parabola y = - x² + 36
</span>
<span>0 36 (0)² + 36 = 36
</span>
<span>1 32 - (1)² + 36 = 35
</span>
<span>2 28 - (2)² + 36 = 32
</span>
<span>3 24 -3² + 36 = 27
</span>
<span>4 20 -4² + 36 = 20
</span>
It
is a linear function because the rate of change is constant: for each
increase of 1 unit in x, there is a decrease of 4 units in y: ⇒ slope = - 4
Remember to include the two points
of intersection in your table. Analyze the two functions; they are there (0,36) and (4, 20)
Answer the
following reflection questions in complete sentences. What is the domain
and range of the rainbow?
Explain what the domain and range represent.
Do all of the values make sense in this situation? Why or why not? What
are the x- and y-intercepts of the rainbow? Explain what each intercept
represents.
The domain is all the real values of x between - 6 and 6: - 6 ≤ x ≤ 6
The range is all the values between 0 and 36: 0 ≤ y ≤ 36
The domain represents the horizontal distance between the extremes of the rainbow at the ground.
The range represents: the altitude of the rainbow from the ground (y = 0). The height is at x = 0, y = 36.
The x-intercepts are - 6 and 6, that is the opening of the rainbow at the ground level.
The y-intercept is when x = 0, it is y = 36, and is the height of the rainbow.
Is the linear function you created positive or negative?
Explain. What are the solutions or solution to the system of equations
created? Explain what it or they represent.
The linear function is positive and decreasing. It is positive because it goes above the x-axis, this is y ≥ 0.
The solutions where already signaled: (0,6) and (4, 20). They are the points at which the drone intercepts the rainbow.
Answer:
34°
Step-by-step explanation:
∠A = arccos(b^2 + c^2 - a^2)/2bc
= 34.016°
