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Pachacha [2.7K]
3 years ago
6

Prove that there are no positive perfect cubes less than 1000 that are the sum of the cubes of two positive integers?

Mathematics
1 answer:
valentina_108 [34]3 years ago
6 0

The perfect cubes less than 1000 are: 

<span>1^3 = 1 </span>
<span>2^3 = 8 </span>
<span>3^3 = 27 </span>
<span>4^3 = 64 </span>
<span>5^3 = 125 </span>
<span>6^3 = 216 </span>
<span>7^3 = 343 </span>
<span>8^3 = 512 </span>
<span>9^3 = 729 
</span>
so 
<span>2^3 = 8 could only be 1 + 1, but this is 2, not 8. </span>
<span>3^3 = 27 could be 1 + 1, 1 + 8 or 8 + 8, but all of these are too small </span>
4^3 = 64 could be 1 + 1, 1 + 8, 1 + 27, 8 + 8, 8 + 27, 27 + 27.
<span> general proof that a^3 + b^3 = c^3 holds for no positive integers 
</span>hope it helps
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almond37 [142]

Answer:

Range of the function → {24, 375}

Step-by-step explanation:

Domain of the function f(x) = 3x³ is {2, 5}

we have to find the range when its domain is {2, 5}

Since x-values of any function define the domain and y-values define the range.

For x = 2,

f(2) = 3(2)³ = 24

For x = 5,

f(5) = 3(5)³ = 375

Therefore, range of the given function for the given domain will be {24, 375}.

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4 years ago
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Maksim231197 [3]

Answer:

The angle is of 600º.

Step-by-step explanation:

Angle of -60:

An anle of -60 is the same as an angle of -60 + 360 = 300º, which is in the fourth quadrant. In the fourth quadrant, just like in the third, the sine is negative.

Equivalent of an angle of 300º in the third quadrant:

The equivalent of an angle of 300º in the third quadrant(between 180 and 270) is given by: 270 - (300 - 270) = 270 - 30 = 240º. That is, they have the same sine.

Angle between 450 and 630:

This is on the second lap of the trigonometric circle, that is, we take the original measures and add 360º(length of a lap). So

240 + 360 = 600º

The angle is of 600º.

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Likurg_2 [28]
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The athletic director needs to pay $112.5 to buy 15 more sun visors.
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Answer:

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Step-by-step explanation:

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