Question

-Al multiplicar por 33 al numeral: A=21.〖11〗^n, se duplica su cantidad de división .hallar n+1

Answer 1

A = 21 × 11ⁿ = 3 × 7 × 11ⁿ

Cantidad de divisores de A = (1 + 1)(1 + 1)(n + 1) = (2)(2)(n + 1) = 4(n + 1)

33A = 33 × 21 × 11ⁿ = 3 × 11 × 3 × 7 × 11ⁿ = 3² × 7 × 11ⁿ⁺¹

Cantidad de divisores de 33A = (2 + 1)(1 + 1)(n + 1 + 1) = (3)(2)(n + 2) = 6(n + 2)

6(n + 2) = 2(4(n + 1))

6(n + 2) = 8(n + 1)

6n + 12 = 8n + 8

12 - 8 = 8n - 6n

4 = 2n

2 = n

n + 1 = 2 + 1

n + 1 = 3

Answer 2

Respuesta:

Explicación paso a paso:

A = 21 × 11ⁿ = 3 × 7 × 11ⁿ

Cantidad de divisores de A = (1 + 1)(1 + 1)(n + 1) = (2)(2)(n + 1) = 4(n + 1)

33A = 33 × 21 × 11ⁿ = 3 × 11 × 3 × 7 × 11ⁿ = 3² × 7 × 11ⁿ⁺¹

 

Cantidad de divisores de 33A = (2 + 1)(1 + 1)(n + 1 + 1) = (3)(2)(n + 2) = 6(n + 2)

6(n + 2) = 2(4(n + 1))

6(n + 2) = 8(n + 1)

6n + 12 = 8n + 8

12 - 8 = 8n - 6n

4 = 2n

2 = n

n + 1 = 2 + 1

n + 1 = 3

por favor una coronita