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kramer
3 years ago
5

Going against the current, a boat takes 7 hours to make a 120 mile trip. When the boat travels with the current on the return tr

ip, it takes 4.5 hours. If x is the speed of the boat is still water and y is the speed of the current, which of the following system of equations could be used to solve the problem?
Mathematics
1 answer:
mel-nik [20]3 years ago
3 0
You would divide the miles by the hours  to solve the porblem.
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What is the smallest prime number p such that
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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.

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By factorization, we have:

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Now, to get exactly 30 divisor.

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Therefore, we can have an equation p + 2 = p₁ × p₂²

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So, for the least values of p + 2, Let us assume that:

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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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2 years ago
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