When x is 2, y is 4, p is 0.5, and m is 2. If x varies directly with the product of p and m and inversely with y, which equation
2 answers:
Answer:
Step-by-step explanation:
You have that x varies directly with p*m (which means that if the result of m*p increase, x increase)
And you have too that x is inversely with y (which means that if y increase, x decrease).
Then you must get:
If the problem says that x is 2, y is 4, p is 0.5, and m is 2
the constant value should be 8, in this way:
If you replace:
The result is x=2
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Answer:
(i) Debemos apilar 5 dados para construir el cubo de mayor tamaño.
(ii) Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.
Step-by-step explanation:
(i) Sabemos por la Geometría Euclídea del Espacio que un cubo es un sólido regular con 6 caras cuadradas y longitudes iguales. Cada dado tiene un volumen de 1 dado cúbico y 125 dados dan un volumen total de 125 dados cúbicos.
El volumen de un cubo está dado por la siguiente fórmula:
Donde:
- Longitud de la arista, medida en dados.
- Volumen del cubo, medido en dados cúbicos.
Ahora, necesitamos despejar la longitud de la arista para calcular la altura máxima posible:
Dado que , encontramos que la altura del cubo de mayor tamaño sería:
Debemos apilar 5 dados para construir el cubo de mayor tamaño.
(ii) El área cuadrada formada por cubos está determinada por la siguiente fórmula:
Donde:
- Longitud de arista, medida en dados.
- Área, medida en dados cuadrados.
Puesto que la longitud de arista se basa en un conjunto discreto, esto es, el número de dados disponibles, debemos encontrar el valor máximo de tal que no supere 125 y de un área entera. Es decir:
Si cada cubo tiene un área de 1 dado cuadrado, entonces un cuadrado conformado por 125 dados tiene un área total de 125 dados cuadrados. Entonces:
Esto nos lleva a decir que:
Entonces, la longitud máxima del cuadrado con la mayor cantidad de cubos posible es de 11 dados. El número total requerido de cubos es el cuadrado de esa cifra, es decir:
Se necesita 121 dados cuadrados para formar el cuadrado con la mayor cantidad de dados posibles, quedando 4 dados sobrantes.
Given:
Paco's cell phone carrier charges him $0.20 for each text message he sends or receives, $0.15 per minute for calls, and a $15 monthly service fee. Paco is trying to keep his bill for the month below $30.
To Find:
The number of texts 't' Paco can send/receive in a month.
Answer:
best describes the number of texts he can send or receive to keep his bill less than $30 in a month.
Step-by-step explanation:
Paco wants to keep is monthly bill below $30.
We see that he has to pay a foxed monthly service fee of $15. This means he is only left with a limit of $30 - $15 = $15 for his monthly calls and texts.
That is, the amount he has to pay for texting and calling has to be less than $15.
For texts, the cell phone carrier charges $0.20 for sending/receiving texts.
For calls, he is charged $0.15 per minute.
Let the number of text messages Paco can send or receive in a month be denoted by 't'.
Let the number of minutes Paco can call in a month be denoted by 'c'.
Then, the total cost of text messages he can send or receive per month would be 0.20t and the total cost of the minutes he spends on calls would be 0.15c. Together, the sum of these has to be less than $15 if his monthly bill has to be kept less than $30 (accounting for the monthly service fee).
So,
The number of texts he can send will dpend on the number of minutes he spends on his calls. For Paco to spend maximum number of texts, he has to spend 0 minutes on calls.
So, putting c = 0, the aboce equation can be written as
That is, Paco has to send and receive less than 75 texts.
So,
best describes the number of texts he can send or receive to keep his bill less than $30 in a month.