Answer:
2
Step-by-step explanation:
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.
Learn more about prime numbers here:
brainly.com/question/145452
#SPJ1
Well first of all, let's define what an integer is...
Integers are numbers such as -2, -1, 0, 1, 2 etc etc.
------
If f(5)=12,
f(6)=0.3*f(6-1)
= 0.3*f(5)
= 0.3*12
= 3/10 * 12
= 36/10
= 3.6
We now know that f(6)=3.6
Now:
f(7)=0.3*f(7-1)
= 0.3*f(6)
= 0.3*3.6
= (3/10) * (36/10)
= 108/100
= 1.08
Answer:
f(7)=1.08
Answer:
25% .
Step-by-step explanation:
D.
Because 4 divided by 2 is 2
