Find all polar coordinates of point p = (6, 31°).

( show step by step i do not understand the full process) : ))

P = 5.143 + i 3.090

Step-by-step explanation:

∵ Z = a + i b = (r , Ф)

∵ a = r cosФ and b = r sinФ

∵ r =

∵ P = (6 , 31°)

∴ P = 6(cos31 + i sin31)

      = 6cos31 + i (6sin31) = 5.143 + i 3.090

OR

∵ a² + b² = (6)² ⇒ a² + b² = 36 ⇒ (1)

∵ b/a = tanФ ⇒ b/a = tan31

∴ b = a tan31 ⇒ (2)

Substitute (2) in (1)

∴ a² + a² tan²31 = 36 ⇒ a²(1 + tan²31) = 36

∴ a² = 36/(1 + tan²31) = 26.45

∴ a = 5.143

∴ b = 5.143 × tan31 = 3.090

∴ P = 5.14 + i 3.090

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870