The smallest prime number of p for which p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
<h3>What is the smallest prime number of p for which p must have exactly 30 positive divisors?</h3>
The smallest number of p in the polynomial equation p^3 + 4p^2 + 4p for which p must have exactly 30 divisors can be determined by factoring the polynomial expression, then equating it to the value of 30.
i.e.
By factorization, we have:
Now, to get exactly 30 divisor.
- (p+2)² requires to give us 15 factors.
Therefore, we can have an equation p + 2 = p₁ × p₂²
where:
- p₁ and p₂ relate to different values of odd prime numbers.
So, for the least values of p + 2, Let us assume that:
p + 2 = 5 × 3²
p + 2 = 5 × 9
p + 2 = 45
p = 45 - 2
p = 43
Therefore, we can conclude that the smallest prime number p such that
p^3 + 4p^2 + 4p has exactly 30 positive divisors is 43.
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To solve this we would do 30×365
We would do this because each day the dog 30lbs
So we have the equation y=30x
Where y= total amount of dog food
And x= number of days
In a year there are 365 days typically, so we do 30×365
30×365=10,950
In one year 10,950 lbs of dog food are used
Answer: 9,600
Step-by-step explanation:
I could possibly did wrong but I shall explain this none the less. I first knew that 10% of 16,000 was 1,600. So then I just timed that by four getting 6,400. I then did 16,000-6,400 getting $9,600. Sorry if I’m wrong
Step-by-step explanation:
Area for a right angle triangle = 1/2 bh
b = Base
h = Height
A = 1/2×bh
= 1/2 × 2c^3d^2 × 4c
= (2c^3d^2 × 4c) / 2
= c^3d^2 × 2c
= 2c^4 × d^2
1/2 it's a fifty fifty unless the guys are complete idiots
