Answer:
36cm
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
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Answer:
A. (2+4)² +(5-8)²
Step-by-step explanation:
To find then distance between two points, we will follow the steps below;
write down the formula
D = √(x₂-x₁)²+(y₂-y₁)²
(-4, 8)
x₁=-4
y₁ = 8
(2,5)
x₂=2
y₂=5
we can now proceed to insert the values into the formula
D = √(x₂-x₁)²+(y₂-y₁)²
= √(2+4)²+(5-8)²
=√(6)² + (-3)²
=√36+9
=√45
Therefore the expression which gives the distance between two the two points is (2+4)² +(5-8)²
Yesss they are parallel lines:)
(2/3) / (1/18) =
2/3 * 18/1 =
36/3 =
12 cups <===
