The Latin word for the digit 9 is nove. In the context of Latin numerals, it is often written as ‘IX’, which is derived from the combination of ‘I’ (1) placed before ‘X’ (10), indicating one less than ten. The word ‘nove’ has roots in the Proto-Indo-European language, where it is connected to other numeral … Read more
To make the number 100 using exactly six 9s, you can utilize mathematical operations in a clever way. Here’s how you can do it: One common method is to express the six 9s as follows: 99 + (9 / 9) = 100 Here’s the breakdown: The first two 9s are combined to form 99. The … Read more
To determine the value of f(3) for the quadratic function graphed with the points (9, 3) and (0, 9), we first need to derive the equation of the quadratic function. A quadratic function can be expressed in the standard form as: f(x) = ax² + bx + c Given the points (9, 3) and (0, … Read more
The sequence defined by the formula an = 3n + 1 is quite straightforward to compute. Each term is generated by substituting successive integer values of n into the formula. Let’s break it down step by step: For n = 1: a1 = 3(1) + 1 = 3 + 1 = 4 For n = … Read more
The question of whether 0 is a rational or irrational number is an interesting one in the field of mathematics. Let’s break it down: A rational number is defined as any number that can be expressed as the quotient of two integers, where the denominator is not zero. In simpler terms, a rational number can … Read more
To convert the mixed number 6 7 into a fraction with a denominator of 42, we first need to understand how to represent this mixed number as an improper fraction. The mixed number 6 7 consists of the whole number 6 and the fraction 7/1. To convert it into an improper fraction: Multiply the whole … Read more
The sequence provided is 8, 16, 32, and 64. We can observe that this is a geometric progression where each term is multiplied by 2 to get the next term. To express this mathematically, we can identify the first term (a) and the common ratio (r). The first term in this sequence, a, is 8. … Read more
The Indian numbering system formats numbers using lakhs and crores. In this system, commas are placed after every two digits, except for the first three digits. For the number 27597 219, the formatting would look like this: 2,75,97,219. Now, to express this number in words: The number 2,75,97,219 is written in words as: Two Crore … Read more
The volume of a sphere can be calculated using a simple mathematical formula: Volume (V) = (4/3) × π × r³ In this formula: V represents the volume of the sphere. π (pi) is a constant approximately equal to 3.14159. r is the radius of the sphere, which is the distance from the center of … Read more
To find sin(2x), cos(2x), and tan(2x) given that sin(x) = 0.35 and x is in the first quadrant, we can use some trigonometric identities and properties. Step 1: Find cos(x) Since we know sin(x), we can find cos(x) using the Pythagorean identity: sin²(x) + cos²(x) = 1 Substituting the value of sin(x): 0.35² + cos²(x) … Read more