b) x 2 + x -2 Find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coefficients;
1 answer:
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Answer:
Equation of Sphere = +
+
- 18x - 4/3y +10z + 142/3 = 0
Step-by-step explanation:
Data Given:
P = (x,y,z)
Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)
Solution:
Find the equation of the sphere:
It is given that:
PA = 2PB
Squaring both sides:
+
+
= 4 x
+
+
Solving the above equation:
+
+
= 4 x {
+
+
}
+ 9 + 6x +
+ 36 - 12y +
+ 9 - 6z = 4 {
+ 36 - 12x +
+ 4 - 4y +
+ 9 + 6z}
+ 9 + 6x +
+ 36 - 12y +
+ 9 - 6z = 4
+ 144 - 48x +4
+ 16 - 16y + 4
+ 36 + 24z
Putting the right hand side = 0 and solving the equation:
- 4
+
- 4
+
- 4
+ 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0
-3 - 3
-3
+ 54x + 4y -30z -142 = 0
Taking (-) common
- ( 3 + 3
+ 3
- 54x - 4y +30z + 142) = 0
3 + 3
+ 3
- 54x - 4y +30z + 142 = 0
dividing the whole equation by 3
+
+
- 54/3x - 4/3y +30/3z + 142/3 = 0
+
+
- 54/3x - 4/3y +30/3z + 142/3 = 0
+
+
- 18x - 4/3y +10z + 142/3 = 0
Answer:
3003
Step-by-step explanation:
We want to find out how many ways we can choose 10 players among 15 players (since the goalie is not interchangeable)
The number of different lineups you can have can be found by using combination:
There are 3003 different lineups that can be chosen.