Answer:
see explanation
Step-by-step explanation:
given x² - 6x - 21 = 0 ( add 21 to both sides )
x² - 6x = 21
to complete the square
• add ( half the coefficient of the x-term)² to both sides
x² + 2 (- 3)x +9 = 21 + 9
(x - 3)² = 30 ( take the square root of both sides )
x - 3 = ± ( add 3 to both sides )
x = 3 ±
x = 3 - = - 2.48 ( to 2 dec. places ) or
x = 3 + = 8.48 ( to 2 dec. places )
9514 1404 393
Answer:
3.694∠127.8°
Step-by-step explanation:
A suitable calculator makes short work of this.
(8; 240°) +(10; 80°) ≈ (3.694; 127.8°)
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If you like, you can add the components of the vectors and figure the magnitude and direction of the result.
a = 8(cos(240°), sin(240°)) ≈ (-4.0000, -6.9282)
b = 10(cos(80°), sin(80°)) ≈ (-1.7365, 9.8481)
r = a + b ≈ (-2.2635, 2.9199)
|r| = √(2.2635² +2.9199²) ≈ 3.69448
∠r = arctan(2.9199/-2.2635) ≈ 127.783°
The resultant is approximately 3.694∠127.78°.
