The cube roots of unity are 1, ω, and ω², where ω = -1 + √3i / 2 and ω² = -1 - √3i / 2. Their product is 1 × ω × ω² = 1.
Step 1: Find A'
A' = I - A = {a, b, c, e, f, g} - {b, e, f} = {a, c, g}.
Step 2: Find B'
B' = I - B = {a, b, c, e, f, g} - {a, b, c} = {e, f, g}.
Step 3: Find A' ∩ B'
A' ∩ B' = {a, c, g} ∩ {e, f, g} = {g}.
Let's denote the cost of a geometry box as x. Since the cost of a bag is three times the cost of a geometry box, the cost of a bag is 3x.
Given that the cost of 2 bags and 3 geometry boxes is Rs.3,960, we can set up the equation:
2(3x) + 3(x) = 3960
6x + 3x = 3960
9x = 3960
Divide both sides by 9:
x = 3960 / 9
x = 440
The set { 0, +, - } contains three distinct elements:
0, +, and −
40% of 45 = (40 ÷ 100) × 45 = 18.
So, 18 is 40 percent of 45.
Given a + b + c = 9 and ab + bc + ca = 20
We know that (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
Substituting the given values:
(9)² = a² + b² + c² + 2(20)
81 = a² + b² + c² + 40
Now, find a² + b² + c²:
a² + b² + c² = 81 - 40
= 41
Work done is constant.
If 6 workers take 5 hours, total work = 6 × 5 = 30 worker-hours.
For 3 workers, time = 30 ÷ 3 = 10 hours.
Let's denote the length of the tangent as l.
We know that the radius is perpendicular to the tangent at the point of contact.
Using the Pythagorean theorem:
l² = 10² - 6²
= 100 - 36
= 64
l = √64
= 8 cm
Multiplying by 100 shifts the decimal 2 places to the right.
Example: 3.45 × 100 = 345.