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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9u-9t=18
original no. is 10t+u
reversed no. is 10u+t
so its (10u+t)-(10t+u)=18
which gives 9u-9t=18
Answer:
80 pages
Step-by-step explanation:
Given:
Number of pages printed = 5493
Number of booklets made = 68
Let each booklet use 'x' pages.
So, pages used by 68 booklets is given by unitary method and is equal to:
Now, total number of pages are 5493.
Therefore, the pages used by the 68 booklets should be less than or equal to the total number of pages available. So,
Therefore, the number of pages in each booklet is 80.
I can't think of what the form is called, but the slope is in that equation.
y=mx+b
m is the slope and in that equation, m=-4/3
Answer:
Step-by-step explanation:
Indicates leg lengths of 1 and√3 and hypotenuse 2, the desired ratio is √3/2
