Let's denote the three angles as x, x, and 2x, since they are in the ratio 1:1:2.
The sum of the angles in a triangle is always 180°:
x + x + 2x = 180°
Combine like terms:
4x = 180°
Divide by 4:
x = 45°
Now that we know x, we can find the other angles:
2x = 90°
A scalene triangle has no equal sides and no equal angles.
All sides and angles are of different lengths and measures.
Prime factorization:
30 = 2 × 3 × 5
24 = 2³ × 3
18 = 2 × 3²
Common factors: 2 × 3 = 6
HCF = 6
A fraction of the form P(x)/Q(x), where both P(x) and Q(x) are polynomials and Q(x) ≠ 0, is called a rational function.
This is because it represents the ratio of two polynomials, which defines a rational expression.
A set with no elements is commonly referred to as a null set, empty set, or void set.
All these terms mean the same: a set with zero elements, usually denoted by Ø or { }.
Given sets A = {1, 2, 5, 3} and B = {3, 4}, and assuming the universal set U = {1, 2, 3, 4, 5}:
Step 1: Find B'
B' = U - B
= {1, 2, 3, 4, 5} - {3, 4}
= {1, 2, 5}
Step 2: Find A ∩ B'
A ∩ B' = {1, 2, 5, 3} ∩ {1, 2, 5}
A tangent is a line that touches a circle at exactly one point.
It does not cross the circle and is perpendicular to the radius at the point of contact.
1 hour = 60 minutes, so the ratio of an hour to a minute is 60 : 1.
It compares the larger unit (hour) to the smaller unit (minute).
The lateral surface area of a right circular cone is given by the formula: πrℓ, where r is the radius and ℓ is the slant height.
This excludes the base area; the total surface area would be πr(r + ℓ).
Zakat is typically calculated as 2.5% of the total amount, which can also be expressed as 1/40.
So, Zakat on Rs. x is:
1/40x
