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:
x = 2 csc(1) y - π/4
Step-by-step explanation:
Solve for x:
y = 1/2 sin(1) (x + π/4)
y = 1/2 (x + π/4) sin(1) is equivalent to 1/2 (x + π/4) sin(1) = y:
1/2 sin(1) (x + π/4) = y
Divide both sides by sin(1)/2:
x + π/4 = 2 csc(1) y
Subtract π/4 from both sides:
Answer: x = 2 csc(1) y - π/4
1 ton is 2000 pounds your answer is 7000 pounds
Hope this helps
Answer:
The answer to your question is 7:6
Step-by-step explanation:
Data
Number of red marbles = 28
Number of green marbles = 30
Number of yellow marbles = 24
Radio = ?
Process
1.- Write the ratio
Red marbles : Yellow marbles
2.- Substitution
28 : 24
3.- Simplification
-Divide both terms by 2
14 : 12
-Divide by two both terms
7 : 6
-It is not possible to simplify more.
Answer:
12* ( 4+5)
Step-by-step explanation:
48 = 12 * 4
60 = 12 * 5
48 + 60 = 12*4 + 12*5
= 12*( 4 + 5)
= 12* 9
= 108
