Answer:
lol
Step-by-step explanation:
lollololol
llllllllllllllllllllllllooooooooooooooooooooooooooooooooooooooooollllllllllllllllllllll
<span>we have that
the cube roots of 27(cos 330° + i sin 330°) will be
</span>∛[27(cos 330° + i sin 330°)]
we know that
e<span>^(ix)=cos x + isinx
therefore
</span>∛[27(cos 330° + i sin 330°)]------> ∛[27(e^(i330°))]-----> 3∛[(e^(i110°)³)]
3∛[(e^(i110°)³)]--------> 3e^(i110°)-------------> 3[cos 110° + i sin 110°]
z1=3[cos 110° + i sin 110°]
cube root in complex number, divide angle by 3
360nº/3 = 120nº --> add 120º for z2 angle, again for z3
<span>therefore
</span>
z2=3[cos ((110°+120°) + i sin (110°+120°)]------ > 3[cos 230° + i sin 230°]
z3=3[cos (230°+120°) + i sin (230°+120°)]--------> 3[cos 350° + i sin 350°]
<span>
the answer is
</span>z1=3[cos 110° + i sin 110°]<span>
</span>z2=3[cos 230° + i sin 230°]
z3=3[cos 350° + i sin 350°]<span>
</span>
Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
------------------------------------
2*(1) - (2)
------------------------------------
4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
------------------------------------
9B+6C = 1,140 --- (4)
------------------------------------
3(2) -4(3)
-----------------------------------
12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
-----------------------------------
-15B-6C = -1,620 --- (5)
------------------------------------
(4) + (5)
------------------------------------
9B+6C = 1140
-15B-6C = -1620 +
-------------------------------------
-6B = -480 => 6B = 480 => B = 480/6 = 80
-------------------------------------------------------
Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
------------------------------------------------------------------------------
Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
----------------------------------------------------------------------------------------------
The rates are:
A = $100
B = $80
C = $70
--------------------------------
On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090
Percentage increase = (increase) x 100 / original
Percentage increase = (5,800,000 - 5,000,000) x 100 / (5,000,000)
Percentage increase = 16%
