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Andreas93 [3]
2 years ago
14

What is the smallest prime number p such that

Mathematics
1 answer:
Ne4ueva [31]2 years ago
8 0

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.

  • p^3 + 4p^2 + 4p

By factorization, we have:

  • = p(p+2)²

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:

  • p₁ = 5 and p₂ = 3

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

#SPJ1

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2.145 is divisible by which numbers<br> 2<br> 6<br> 5<br> 3​
mariarad [96]

Answer:

  • 3 and 5 if "." marks thousands
  • 2, 3, 5, 6 if "." is a decimal point

Step-by-step explanation:

The number 2145 is not even, so will not be divisible by 2 or 6. It ends in 5 so is divisible by 5. Its sum of digits is 12, which is divisible by 3, so the number is divisible by 3.

2145 is divisible by 3 and 5.

2.145 is divisible by all of these numbers:

  2.145/2 = 1.0725

  2.145/6 = 0.3575

  2.145/5 = 0.429

  2.145/3 = 0.715

_____

Here, we take the mixed number to be divisible if the decimal representation of the quotient is a terminating decimal fraction.

6 0
3 years ago
100 pts!!!! PLEASE HELP!!!!!
natka813 [3]

Answer:

1)3/4

2)3

3)12 MILES

4)2.5 pounds

5)5/8 pounds

am not sure but hopefully it helps you!!!!!!

5 0
3 years ago
Read 2 more answers
Is the following statement true or false:
saw5 [17]
<span>True, Every diameter is a chord

but not every chord is a diameter 

hope this helped :)</span>
6 0
3 years ago
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5/10 × 3 explain how you got the answer then when finish do 4/10 × 4 and explain.
barxatty [35]

Hello from MrBillDoesMath!

Answer:

1.5,   1.6


Discussion:

The question is how to interpret 5/10 * 3.   Both multiplication and division have the same precedence but we proceed from left to right (doing the divison first)

5/10 * 3 = (5/10) * 3 = (1/2)* 3 = 3/2 = 1.5                  

Same approach for the second equation:

4/10 * 4 = (4/10) * 4 = 16/10 = 8/5 = 1.6


Thank you,

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6 0
3 years ago
I need to find the volume of a sphere
Feliz [49]

Answer:

523.6

Step-by-step explanation:

Following the calculation, and 3.14 for pi, the answer would be 523.6

8 0
3 years ago
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