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2 years ago

What is the greatest prime you must consider to test whether 1471 is prime?

Mathematics

1 answer:

a_sh-v [17]2 years ago

8 0

Answer:

1471

Step-by-step explanation:

First we have to check if it is divisible with the first 15 prime numbers

1471÷2=735.5(not divisible)

1471÷3=490.33( not divisible)

1471÷5=294.2( not divisible)

1471÷7=210.14(not divisible)

1471÷11=133.73(not divisible)

1471÷13=113.15(not divisible )

1471÷17=86.53(not divisible )

1471÷19=77.42(not divisible )

1471÷23=63.96(not divisible )

1471÷29=50.72(not divisible )

1471÷31=47.45(not divisible )

1471÷37=39.76(not divisible )

1471÷41=35.88(not divisible )

1471÷43=34.20(not divisible )

1471÷47=31.39(not divisible )

1471÷53=27.75

1471÷61=24.11

1471÷67=21.85 ......

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Two numbers whose sum is 44 and whose product is a maximum

Mashcka [7]

Answer:

x = y = 22

Step-by-step explanation:

It would help to know your math course. Do you know any calculus? I'll assume not.

Equations

x + y = 44

Max = xy

Solution

y = 44 - x

Max = x (44 - x) Remove the brackets

Max = 44x - x^2 Use the distributive property to take out - 1 on the right.

Max = - (x^2 - 44x ) Complete the square inside the brackets.

Max = - (x^2 - 44x + (44/2)^2 ) + (44 / 2)^2 . You have to understand this step. What you have done is taken 1/2 the x term and squared it. You are trying to complete the square. You must compensate by adding that amount on the end of the equation. You add because of that minus sign outside the brackets. The number inside will be minus when the brackets are removed.

Max = -(x - 22)^2 + 484

The maximum occurs when x = 22. That's because - (x - 22) becomes 0.

If it is not zero it will be minus and that will subtract from 484

x + y = 44

xy = 484

When you solve this, you find that x = y = 22 If you need more detail, let me know.

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