Adding 0 to the right of a decimal (after the last digit) does not change its value.
For example, 3.5 = 3.50 = 3.500 — all represent the same number.
To complete the square for x⁴ + 64, recognize that:
(x²)² + 2(x²)(8) + 8² = (x² + 8)²
So, the missing term to complete the square is:
2(x²)(8) = 16x²
Factor the numerator:
(a² - b²) = (a + b)(a - b)
Now, divide by (a + b):
[(a + b)(a - b)] ÷ (a + b)
= (a - b)
The square root of 256 is 16, which has 2 digits.
Counting the digits in 16 confirms that the answer is 2.
Total amount = Rs. 5,376
Ratio = Ayesha : Sadia : Madiha = 8 : 7 : 6
Step-by-step:
Total parts = 8 + 7 + 6 = 21 parts
Sadia's share = (7 / 21) × 5376 = 1792
A straight angle is equal to 180 degrees.
A complete rotation is 360 degrees, so it contains 2 straight angles (180° + 180° = 360°).
The sum of the first n natural numbers can be calculated using the formula:
n(n + 1)/2
Here, n = 200:
Sum = 200(200 + 1)/2
= 200 * 201 / 2
= 20100
Given ratio:
Sand : Cement = 4.8 : 2
Let's find the factor by which 4.8 is multiplied to get 6 kg of sand:
6 kg / 4.8 = 1.25
Now, multiply the cement ratio by this factor:
Cement needed = 2 × 1.25
= 2.5 kg
The discriminant (D) of a quadratic equation ax^2 + bx + c = 0 is given by:
D = b^2 - 4ac
Given:
a = 1, b = 9, c = 2
D = 9^2 - 4(1)(2)
= 81 - 8
= 73
Total marks of 5 students = 5 × 18 = 90
Total marks of 6 students = 6 × 19 = 114
Marks of the sixth student = 114 - 90 = 24