The profit-sharing ratio between Hyder and Ahsan is 3:5.
The total parts are 3 + 5 = 8.
Ahsan's share is 5/8 of the total profit.
Given the total profit is 32,000:
Ahsan's share = (5/8) × 32,000
= 5 × 4000
= 20,000
To find the intersection (C ∩ D) of sets C and D, we need to find the elements that are common to both sets.
C = {a, b, e, f}
D = {2, 4, 8, 10}
Since there are no common elements between C and D, the intersection is an empty set.
Let's break it down step by step:
1. (√9²+12²) = √(81+144) = √225 = 15
2. (-3)² = 9
3. 15 + 9 = 24
4. (-1 + 2 + 3) = 4, and 4³ = 64
5. 24 - 64 = -40
6. ³√-125 = -5 (since (-5)³ = -125)
7. -40 - (-5) = -40 + 5 = -35
Let's simplify the expression:
√3 × √5 × √15
= √(3 × 5 × 15)
= √(225)
= 15
First, find the LCM of 3 and 5, which is 15.
Now, convert both fractions:
5/3 = 25/15
2/5 = 6/15
Subtract:
25/15 - 6/15 = 19/15
Let Soomal's age be x.
Saira's age = x + 6
Five years later:
x + 5 + x + 11 = 40
2x + 16 = 40
2x = 24
x = 12
Saira's age = 12 + 6 = 18
Let's say the original number is x.
Given:
1/3 of x + 16 = 2 1/3 of x
1/3x + 16 = 7/3x
Multiply both sides by 3:
x + 48 = 7x
48 = 6x
x = 48/6
x = 8
Valid Methods for Linear Equations:
Substitution: Solve one equation for a variable and substitute into the other.
Elimination: Add/subtract equations to eliminate a variable.
Cramer’s Rule: Uses determinants for systems with unique solutions.
If a, b, c ∈ R (real numbers), then:
a < b ⟹ a + c < b + c
This is a fundamental property of inequalities, which states that adding the same value to both sides of an inequality preserves the inequality.
Terminating Decimal Definition:
A decimal that ends after a finite number of digits (e.g., 0.5, 0.75).
0.125: Terminates after 3 digits.