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: 10.8
Step-by-step explanation: the pythagorean theorem is A sqaured or A^2 + B^2 or B squared equals C^2 or C squared so 10 squared as is the first number is 100 and 4 squared as is the second number is 16 add the two to get 116 but since your answer is squared you need to take the square root which means your answer is 10.7703296143 but since your rounding to the tenths place your answer is 10.8
Answer:
Step-by-step explanation:
we are given a exponential function
where x represents the number and f(x) represents the amount
we are also given that when x is 3 then f(x) is 59 likewise when x is 6 then f(x) is 2165
to figure out the average rate of change between 3 and 6 we can consider the average rate of change formula given by
substitute what we have:
simplify substitution:
simplify division:
hence, the average rate of change between 3 and 6 is <u>7</u><u>0</u><u>2</u>
Ill say, C) Place the compass' point on the other end of the segment.
Step-by-step explanation:
75×1=75
75×2=150
75×3=225
75×4=300
75×5=375
75×6=450
75×7=525
75×8=600
75×9=675
75×10=750