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Rasek [7]
3 years ago
5

Hola, alguien me puede resolver esta operación? a. Múltiplo de 5 y de 6 mayor que 95.000 ( _ 8 9 1 _ ) b. Divisible por 3, 4 y 5

, menor que 4.675. ( 4 6 _ _ )
Mathematics
1 answer:
bezimeni [28]3 years ago
5 0

Answer:

a) 98,910

b) 4,620

Step-by-step explanation:

Recordar que un numero N es multiplo de A si N es divisible por A.

Entonces, decir:

Buscar N, tal que sea multiplo de A

es lo mismo que decir:

Buscar N, tal que sea divisible por A.

a) Queremos un múltiplo de 5 y de 6 mayor que 95.000

( _ 8 9 1 _ )

Sabemos que los múltiplos de 5 terminan en 0 o 5.

Y un número de 5 dígitos mayor que 95,000 requiere que el quinto digito en este caso sea 9, entonces tendremos:

98,91_

Para encontrar el dígito de las unidades, podemos probar remplazarlo por 0 y por 5, y luego dividirlo por 6.

Si el resultado es un número entero, entonces el número será un múltiplo de 6.

Probemos con 0, vamos a tener el número:

98,910

dividiéndolo por 6 obtenemos:

98,910/6 = 16,485

Entonces:

98,910 es más grande que 95,000

es múltiplo de 5 (porque termina en cero)

Y es múltiplo de 6, como acabamos de comprobar.

b) Ahora queremos un número divisible por 3, 4 y 5, que sea menor que 4,675

4,6__  

De vuelta, como tiene que ser divisible por 5, sabemos que termina en 5 o 0.

Y como también tiene que ser divisible por 4, sabemos que tiene que terminar si o si en número par, entonces podemos concluir que solo puede terminar en 0.

Así, sabemos que el número va a ser algo como:

4,6_0

Ahora podemos probar con el dígito de las decenas, de tal forma que el número sea divisible por 3, 4 y 5.

Recordar que este número tiene que ser menor que 4,675

Entonces el número faltante puede ser:

0, 1, 2, 3, 4, 5, 6, 7

Ahora también podemos recordar que un número es solo divisible por 3 si la suma de todos sus dígitos es divisible por 3.

Entonces tenemos que tener que:

4 + 6 + x + 0 = múltiplo de 3

10 + x = múltiplo de 3

Los posibles valores de x van a ser:

x = 2   (porque 12 es múltiplo de 3)

x = 5   (porque 15 es múltiplo de 3)

Ok, ahora sabemos que el número restante solo puede ser 2 o 3.

Entonces tenemos que remplazar esos valores en el número y ver si este es divisible por 4 o no.

Comenzamos con el 2.

Tendremos el número:

4,620

Probamos dividiendo esto por 4:

4,620/4 = 1,155

El resultado es entero, entonces 4,620 es divisible por 4 (y por como lo creamos, también sabemos que es divisible por 3 y por 5, y además es menor que 4,675, como queríamos)

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3 years ago
Some of the students three scores is 231. If the first is 20 points more than the second, and the sum of the first two is 6 more
Aleks [24]

Answer:

The first score is 109

Step-by-step explanation:

I am assuming that in the first sentence of the question, you meant:

Sum of the students three scores is 231...

First, let the scores of the first second and third student be a, b and c respectively. We are told that:

a + b + c = 231 . . . . . . . .(1)         (sum of students three scores is 231)

a = b + 20 . . . . . . . . . . . (2)        (the first is 20 points more than the second)

a + b = 6c . . . . . . . . . . . .(3)        (sum of the first two is 6 more times the third)

required, find a.

substituting the value of (a + b) in equation (3) into equation (1), we will have the following:

since a + b = 6c . . . (3)

a + b + c = 231 . . . . . (1), becomes,

(a + b) + c = 231

(6c)  + c = 231

7c = 231 (divide both sides by 7)

c = 231 ÷ 7 = 33

∴ c = 33

Next, from equation (2), we know that a = b + 20; this can also be written as:

a - 20 = b

∴ b = a - 20 . . . . . . . (4)

Finally, putting the value of b in equation (4) and the value of c calculated above into equation 1, ( a + b + c = 231), we have the following:

a + (a - 20) + 33 = 231

(a + a) - 20 + 33 = 231

2a + 13 = 231

2a = 231 - 13 = 218

a = 218 ÷ 2 = 109

∴ a = 109

we can also calculate for 'b' by substituting for the value of 'a' in equation 4

b = a - 20 = 109 - 20 = 89.

and to test if the values of a, b and c are correct:

a + b + c = 231

109 + 89 + 33 = 231

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An alternating series \sum\limits_n(-1)^na_n converges if |(-1)^na_n|=|a_n| is monotonic and a_n\to0 as n\to\infty. Here a_n=\dfrac1{\ln(n+1)}.

Let f(x)=\ln(x+1). Then f'(x)=\dfrac1{x+1}, which is positive for all x>-1, so \ln(x+1) is monotonically increasing for x>-1. This would mean \dfrac1{\ln(x+1)} must be a monotonically decreasing sequence over the same interval, and so must a_n.

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from a window 24 feet above the ground, the angle of elevation to the top of another building is 38 degrees. The distance betwee
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Answer:

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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

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Answer:

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