Answer:
8
Step-by-step explanation:
Answer:
detailed one
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Answer:
x = -2, x = 3 − i√8, and x = 3 + i√8
Step-by-step explanation:
g(x) = x³ − 4x² − x + 22
This is a cubic equation, so it must have either 1 or 3 real roots.
Using rational root theorem, we can check if any of those real roots are rational. Possible rational roots are ±1, ±2, ±11, and ±22.
g(-1) = 18
g(1) = 18
g(-2) = 0
g(2) = 12
g(-11) = 1782
g(11) = 858
g(-22) = -12540
g(22) = 8712
We know -2 is a root. The other two roots are irrational. To find them, we must find the other factor of g(x). We can do this using long division, or we can factor using grouping.
g(x) = x³ − 4x² − 12x + 11x + 22
g(x) = x (x² − 4x − 12) + 11 (x + 2)
g(x) = x (x − 6) (x + 2) + 11 (x + 2)
g(x) = (x (x − 6) + 11) (x + 2)
g(x) = (x² − 6x + 11) (x + 2)
x² − 6x + 11 = 0
Quadratic formula:
x = [ 6 ± √(36 − 4(1)(11)) ] / 2
x = (6 ± 2i√8) / 2
x = 3 ± i√8
The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.
Answer:
angle 4
Step-by-step explanation:
Angle 4 is the opposite of angle 5, if you flip the paper upside down, you'll see that it is the same
According to the given information, the equation represents a line that is tangent to the circle and goes through the point W is given by:
y = -x + 6.
<h3>What is the equation of the circle?</h3>
The equation of a circle of center 
and radius r is given by:
In this problem, we have that the center is at point (0,2), hence:
It goes through point (3,3), hence:
Hence, the equation is:
<h3>What is the equation of the tangent line at point W?</h3>
It is given by:
Applying implicit differentiation, we have that:
Point W(3,3), hence:
Hence the equation is:
y - 3 = -(x - 3).
y = -x + 6.
More can be learned about the equation of a tangent line at brainly.com/question/8174665
