————————————-The answer is 3.78
Roots with imaginary parts always occur in conjugate pairs. Three of the four roots are known and they are all real, which means the fourth root must also be real.
Because we know 3 and -1 (multiplicity 2) are both roots, the last root is such that we can write
There are a few ways we can go about finding , but the easiest way would be to consider only the constant term in the expansion of the right hand side. We don't have to actually compute the expansion, because we know by properties of multiplication that the constant term will be .
Meanwhile, on the left hand side, we see the constant term is supposed to be 9, which means we have
so the missing root is 3.
Other things we could have tried that spring to mind:
- three rounds of division, dividing the quartic polynomial by , then by twice, and noting that the remainder upon each division should be 0
- rational root theorem
9514 1404 393
Answer:
90° CCW
Step-by-step explanation:
The slope of BA is -1/3. The slope of BA' is 3, so the slopes are opposite reciprocals of one another. These segments are perpendicular, meaning the angle between them is 90°.
Point A' has been rotated 90° CCW about point B.
Answer:
Step-by-step explanation:
a). Total surface area of cylinder is defined by sum of curved surface area and surface area of the top and bottom.
Total surface area = 2πrh + 2πr²
Skateboarders use a half pipe structure which are not closed at the ends.
Therefore, curved surface of the half pipe =
= πrh
b). If r = 2.5 m and h = 9 m,
Curved surface area of the half pipe = π(2.5)(9)
= 70.69 m²
≈ 71 m²
62 multiplied by 3 is 186
Add on 31 for the half hour
and you get 217