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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-2w + 20 = -17 - 17 + 4w
Combine like terms on the right side of the equation.
-2w + 20 = -34 + 4w
Add 2w to both sides.
20 = -34 + 6w
Add 34 to both sides.
54 = 6w
Divide both sides by 6.
w = 9 is your answer.
Answer:
A book about a mass of 1 kilogram, but that isn't the only answer.
Explanation:
There's many objects with a mass of one kilogram like one liter of water, a pineapple, bag of sugar etc.
Mary worked 22 hours.
To solve first you would subtract the amount she made in tips from her total earnings (317-185)
= 132
Then you divide that answer by her hourly salary of $6 (132/6)
=22
Answer:
0.+.20.=.40Step-by-step explanation:
