In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
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Area of a sector is x over 360 * pi r squares so in this case x would be 210 so it would be 210 over 360 and the pi r squared would be 24 pi and when we times that our answer is 14 pi
Answer:14 pi
Subtract corresponding x and y components
- u - v = - <- 8, 4> - <2, 7> = <8, - 4> - <2, 7> = <8 - 2, - 4 - 7> = <6, - 11>
u - v = <- 8, 4> - <2, 7> = <- 8 - 2, 4 - 7> = <- 10, - 3>
v - u = <2, 7> - <- 8, 4> = <2 + 8, 7 - 4> = <10, 3>
There is a typo in the available options for this problem. BOTH options B and E are 3/25+4/25i. One of those options should be 3/25-4/25i. So check your problem carefully and be sure to select the correct answer.
1. D. 1 + 0i
2. A. -7/25 + 24/25i
3. B or E, 3/25 + 4/25i
4. F. 3-4i
5. B or E, 3/25 - 4/25i
6. C. -7/25 -24/25i
For this problem, you need to perform complex division, then select the matching answer from the available options. In order to perform a complex division, simply multiply the numerator and denominator by the conjugate of the denominator. The conjugate of the denominator is simply the denominator with the sign of the complex term inverted. So:
1. i/i
Let's rewrite as (0 + i)/(0 + i)
(0 + i)/(0+i) * (0 - i)/(0 - i)
= (0*0 + 0*i - 0*i - i^2)/(0*0 + 0*i - 0*i - i^2)
= (0 - -1)/(0 - -1)
= 1/1
= 1 + 0i which is option "D"
2. 3+4i/3-4i
3+4i/3-4i * 3+4i/3+4i
= (9 + 12i + 12i + 16i^2) / (9 - 12i + 12i - 16i^2)
= (-7 + 24i) / 25
= -7/25 + 24/25i, which matches option "A"
3. 1/3-4i
1/3-4i * 3+4i/3+4i
= (3 + 4i)/(9 + 12i - 12i - 16i^2)
= (3 + 4i)/(9 - -16)
= (3 + 4i)/25
= 3/25 + 4/25i, which matches option "B" or "E". BE SURE TO SELECT THE
CORRECT OPTION. You want 3/24 PLUS 4/25i.
4. 3-4i/1
3-4i/1 * 1/1 = 3-4i, which matches option "F"
5. 1/3+4i
1/3+4i * 3-4i/3-4i
= 3-4i/(9 + 12i - 12i - 16i^2)
= 3-4i/25
= 3/25 - 4/25i, which matches option "B" or "E". BE SURE TO SELECT THE
CORRECT OPTION. You want 3/24 MINUS 4/25i.
6. 3-4i/3+4i
3-4i/3+4i * 3-4i/3-4i
= (9 - 12i - 12i + 16i^2) / (9 - 12i + 12i - 16i^2)
= (9 - 12i - 12i + -16) / (9 - 12i + 12i - -16)
= (-7 - 24i) / 25
= -7/25 -24/25i, which matches option "C"
