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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Answer:
The diagonal is 421.
Step-by-step explanation:
This is a difficult question. To find the diagonal, you need to find the base and the height of the square. After that, you need to make it a triangle, by using this equation; 
(A being area, B being base, and H being height) then find the length of the hypotenuse of the triangle, which I will do for you.
The B and H = 416. Plug it into the equation now;
Now that you have done that, we know that the area of our new triangle is 86,528.
The diagonal is: 
Answer:
Mean: 49
Mode: none, since all the numbers only appear once
Median: 48
Range: 69
Step-by-step explanation:
53+64+19+25+88+48+46 = 343
343/7= 49 (mean)
19, 25, 26, 48, 53, 64, 88 (middle number is 48, so the median is 48)
Range= largest number-smallest number
88-19= 69 (range)
Answer:
87.5 inches long
Step-by-step explanation:
250 x 0.35 = 87.5
