This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back — missed you this week. Step 1: Express 1470 as a product of its prime factors. 1470 = 2 × 735 735 = 3 × 245 245 = 5 × 49 49 = 7 × 7 So, the prime factorization of 1470 is: 1470 = 2 × 3 × 5 × 7^2 Step 2: Express 7056 as a product of its prime factors. 7056 = 2 × 3528 3528 = 2 × 1764 1764 = 2 × 882 882 = 2 × 441 441 = 3 × 147 147 = 3 × 49 49 = 7 × 7 So, the prime factorization of 7056 is: 7056 = 2^4 × 3^2 × 7^2 Step 3: Evaluate (1470^2)/(sqrt(7056)) in prime factor form. First, find 1470^2: 1470^2 = (2 × 3 × 5 × 7^2)^2 = 2^2 × 3^2 × 5^2 × 7^4 Next, find sqrt(7056): sqrt(7056) = sqrt(2^4 × 3^2 × 7^2) = 2^(4)/(2) × 3^(2)/(2) × 7^(2)/(2) = 2^2 × 3^1 × 7^1 Now, substitute these into the expression: (1470^2)/(sqrt(7056)) = (2^2 × 3^2 × 5^2 × 7^4)/(2^2 × 3^1 × 7^1) Simplify by subtracting the exponents of common prime factors: = 2^2-2 × 3^2-1 × 5^2 × 7^4-1 = 2^0 × 3^1 × 5^2 × 7^3 = 1 × 3 × 5^2 × 7^3 3 × 5^2 × 7^3 2) a) Step 1: Identify all prime numbers less than ten. The prime numbers less than ten are 2, 3, 5, and 7. Step 2: Arrange these prime numbers in descending order to form a number. Descending order means from largest to smallest: 7, 5, 3, 2. The number formed is 7532. 7532 2) b) Step 1: Identify the second digit of the number formed. The number formed is 7532. The digits are: • First digit: 7 • Second digit: 5 • Third digit: 3 • Fourth digit: 2 Step 2: Determine the total value of the second digit. The second digit is 5, and it is in the hundreds place. Total value = 5 × 100 = 500. 500 Send me the next one 📸