Answer:
See below.
Step-by-step explanation:
Fifth root of 243 = 3,
Suppose r( cos Ф + i sinФ) is the fifth root of 243(cos 240 + i sin 240),
then r^5( cos Ф + i sin Ф )^5 = 243(cos 240 + i sin 240).
Equating equal parts and using de Moivre's theorem:
r^5 =243 and cos 5Ф + i sin 5Ф = cos 240 + i sin 240
r = 3 and 5Ф = 240 +360p so Ф = 48 + 72p
So Ф = 48, 120, 192, 264, 336 for 48 ≤ Ф < 360
So there are 5 distinct solutions given by:
3(cos 48 + i sin 48),
3(cos 120 + i sin 120),
3(cos 192 + i sin 192),
3(cos 264 + i sin 264),
3(cos 336 + i sin 336).. (Answer).
Answer:
26.4 is what i came up with if you divide im probably wrong sorry if i am
Answer:
1100 square inches
Step-by-step explanation:
Formula: LxW
<u>Smallest rectangles</u> area: 5*20=100= 1 rectangle
there are 2 smal rectangles so= 100*2=200
<u>Medium rectangles</u> area: 5*30=150
There are 2 so= 150*2= 300
<u>Biggest rectangle:</u> 30*20= 600
Total Area: 200+300+600= 1100 square inches
Answer:
n = 60.22
Step-by-step explanation:
Hello
To find Sn, we need to draw out equations for each a₇ and a₁₉
In an arithmetic progression,
Sn = a + (n-1)d
Where Sn = sum of the A.P
a = first term
d = common difference
a₇ = 32
32 = a + (7-1)d
32 = a + 6d ........equation (i)
a₁₉ = 140
140 = a + (19-1)d
140 = a + 18d .........equation (ii)
Solve equation (i) and (ii) simultaneously
From equation (i)
32 = a + 6d
Make a the subject of formula
a = 32 - 6d .....equation (iii)
Put equation (iii) into equation (ii)
140 = (32 - 6d) + 18d
140 = 32 - 6d + 18d
Collect like terms
140 - 32 = 12d
12d = 108
d = 108 / 12
d = 9
Put d = 9 in equation (i)
32 = a + 6(9)
32 = a + 54
a = 32 - 54
a = -22
When Sn = 511
Sn = a + (n - 1)d
Substitute and solve for n
511 = -22 + (n-1) × 9
511 = -22 + 9n - 9
511 = -31 + 9n
511 + 31 = 9n
542 = 9n
n = 542 / 9
n = 60.22
Answer:
Part a)
We need to find the equation of a straight line passing through two given points in slope-intercept form
Part b)
The information given; we are given two points where the line passes through; (0, -4) and (-2, 2)
Part c)
We shall first determine the slope of the line using the formula;
change in y/change in x. Next, we determine the value of the y-intercept using the general form of the equation of a straight line in slope-intercept form; y = mx+c
Part d)
The slope of the line is calculated as;
(2--4)/(-2-0) =6/-2 = -3
The equation of the line in slope-intercept form becomes;
y = -3x +c
We use the point (0, -4) to determine the value of c;
-4 = -3(0)+c
c = -4
Part e)
Final solution thus becomes;
y=-3x-4
