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Articles by karthikeya Boyini
Page 51 of 142
Area of circle which is inscribed in an equilateral triangle?
The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa2/12, where 'a' is the side length of the triangle. Syntax area = π × a² / 12 Formula Derivation Let's see how this formula is derived − Step 1: Find the radius of the inscribed circle using the formula: Radius = Area of triangle / Semi-perimeter of triangle Step 2: For an equilateral triangle with side 'a': Area of triangle = (√3)a2/4 Semi-perimeter = 3a/2 Step 3: Calculate the radius: Radius = ...
Read MoreArea of a Circular Sector?
A circular sector (also known as a circle sector or sector of a circle) is the portion of a circle that is enclosed between two radii and an arc. To find the area of a circular sector, we need to determine the central angle between the two radii. r θ Sector Syntax Area = π × r² × (θ / 360°) Where: π (pi) ≈ 3.14159 r = radius of ...
Read MoreArea of a circle inscribed in a regular hexagon?
In C programming, calculating the area of a circle inscribed in a regular hexagon involves understanding the geometric relationship between the hexagon and its inscribed circle. A circle inscribed in a regular hexagon touches all six sides of the hexagon at their midpoints. Syntax area = (3 * π * side * side) / 4 Mathematical Formula For a regular hexagon with side length a, the radius of the inscribed circle is r = a(√3)/2. Using the circle area formula A = πr², we get − ...
Read MoreC program to find Decagonal Number?
A decagonal number is a figurate number that represents the number of dots that can be arranged in nested decagonal (10-sided) patterns. These numbers follow the formula 4n² - 3n, where n is the position in the sequence. For example, the 3rd decagonal number involves arranging dots in 3 nested decagons. Each nested layer contributes a specific number of dots, and we subtract the overlapping dots to get the final count. Decagonal Number Pattern ...
Read MoreAverage of even numbers till a given even number?
To find the average of even numbers till a given even number, we need to sum all the even numbers up to that number and divide by the count of even numbers. Syntax average = sum_of_even_numbers / count_of_even_numbers Example Average of even numbers till 10 is calculated as − Even numbers: 2, 4, 6, 8, 10 Sum: 2 + 4 + 6 + 8 + 10 = 30 Count: 5 Average: 30 ÷ 5 = 6 There are two methods for calculating the average of even numbers till n (where n is ...
Read MoreAverage of odd numbers till a given odd number?
The average of odd numbers till a given odd number is calculated by finding the sum of all odd numbers from 1 to that number, then dividing by the count of odd numbers. This is a fundamental concept that demonstrates both iterative and mathematical approaches. Syntax Average = Sum of odd numbers / Count of odd numbers Average = (n + 1) / 2 // Formula approach (where n is odd) Example: Manual Calculation For odd numbers till 9: Odd numbers: 1, 3, 5, 7, 9 Sum: 1 + 3 ...
Read More1's and 2's complement of a Binary Number?
Binary numbers are expressed in base 2, using only the digits '0' and '1'. Each digit in a binary number is called a bit. Understanding 1's and 2's complement is essential for representing signed numbers in computer systems. 1's Complement One's complement of a binary number is obtained by inverting all bits − changing every '0' to '1' and every '1' to '0'. Syntax 1's complement = invert all bits Example: 101100 → 010011 2's Complement Two's complement of a binary number is obtained by adding 1 to the 1's complement of ...
Read MoreSum of the first N Prime numbers
In C programming, finding the sum of the first N prime numbers involves identifying prime numbers sequentially and adding them together. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Syntax int isPrime(int num); int sumOfFirstNPrimes(int n); Algorithm The approach involves checking each number starting from 2 for primality, and when a prime is found, adding it to the sum until we have found N primes − Start with the first prime number (2) Check each subsequent number for primality Add ...
Read MoreAdd 1 to a given number?
Adding 1 to a given number is a fundamental operation in C programming that increments a variable's value by one. This operation is commonly used in loops, counters, and iterative processes. Syntax variable = variable + 1; // Method 1: Addition assignment variable++; // Method 2: Post-increment ++variable; // Method 3: Pre-increment There are multiple methods to add 1 to a given number in C ...
Read MoreAverage of first n even natural numbers?
The average of first n even natural numbers is the sum of the numbers divided by the count of numbers. The first n even natural numbers are 2, 4, 6, 8, ..., 2n. Syntax Average = Sum of first n even numbers / n You can calculate this using two methods − Find the sum of n even natural numbers using a loop and divide by n Use the mathematical formula for direct calculation Method 1: Using Loop This method iterates through the first n even numbers, calculates their sum, ...
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