Find all positive integers n such that n^4- 1 is divisible by 5.
1 answer:
Answer:
All positive integers except multiple of 5.
Step-by-step explanation:
From the rule of divisibility, a number's last digit should be either 0 or 5 for it to be divisible by 5.
For to be a multiple of 5, the last digit of
should be 0 or 5. In other words, the last digit of
should be 1 or 6.
The last digit of is 1 if
is an odd number except those that are multiples of 5.
The last digit of is 6 if
is an even number except those that are multiples of 5.
Therefore, the possible values of are all positive integers except those that are multiples of 5.
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Answer:
The population will reach 34,200 in February of 2146.
Step-by-step explanation:
Population in t years after 2012 is given by:
In what month and year will the population reach 34,200?
We have to find t for which P(t) = 34200. So
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that
, given by the following formulas:
In this question:
So
Then
We only take the positive value.
134 years after 2012.
.14 of an year is 0.14*365 = 51.1. The 51st day of a year happens in February.
So the population will reach 34,200 in February of 2146.
Answer:
Sample Response: To write a two-variable equation, I would first need to know how much Maya’s allowance was. Then, I would need the cost of playing the arcade game and of riding the Ferris wheel. I could let the equation be cost of playing the arcade games plus cost of riding the Ferris wheel equals the total allowance. My variables would represent the number of times Maya played the arcade game and the number of times she rode the Ferris wheel. With this equation I could solve for how many times she rode the Ferris wheel given the number of times she played the arcade game.
