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vagabundo [1.1K]

3 years ago

11

Two spheres, one of radius 15 and the other of radius 33, have the same center. Find the side length of the largest cube that fi

ts between them.

1 answer:

Sophie [7]3 years ago

6 0

Answer: 18

Step-by-step explanation:

The detailed explanation is in the attached picture.

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Which expression is a sum of cubes?

erik [133]

we know that

A polynomial in the form $a^{3} +b^{3}$ is called a sum of cubes

so

Let's verify each case to determine the solution

<u>case A)</u> $-64x^{6} y^{12} +125x^{16} y^{3}$

we know that

$-64=-4^{3}$

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{16}=x^{15} *x=x*(x^{5})^{3}$ -------> is not a perfect cube

$y^{3}= (y)^{3}$

therefore

the case A) is not a sum of cubes

<u>case B)</u> $-32x^{6} y^{12} +125x^{16} y^{3}$

we know that

$-32=-2^{5}$ -------> is not a perfect cube

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{16}=x^{15} *x=x*(x^{5})^{3}$ -------> is not a perfect cube

$y^{3}= (y)^{3}$

therefore

the case B) is not a sum of cubes

<u>case C)</u> $32x^{6} y^{12} +125x^{9} y^{3}$

we know that

$32=2^{5}$ -------> is not a perfect cube

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{9}=(x^{3})^{3}$

$y^{3}= (y)^{3}$

therefore

the case C) is not a sum of cubes

<u>case A)</u> $64x^{6} y^{12} +125x^{9} y^{3}$

we know that

$64=4^{3}$

$x^{6}= (x^{2})^{3}$

$y^{12}= (y^{4})^{3}$

$125=5^{3}$

$x^{9}=(x^{3})^{3}$

$y^{3}= (y)^{3}$

Substitute

$4^{3}(x^{2})^{3}(y^{4})^{3} +5^{3}(x^{3})^{3}(y)^{3}$

$(4x^{2}y^{4})^{3} +(5x^{3}y)^{3}$

therefore

<u>the answer is</u>

$64x^{6} y^{12} +125x^{9} y^{3}$ is a sum of cubes

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3 years ago

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Find the mean of the following data set : 0.5 , 0.7 , 1.0 , 1.7 , 0.6 , 1.0 , 0.8

pychu [463]

I got the answer to be 0.9. To get the mean, you add up all the data and then divide it by the number of numbers in you data, so I did 0.5+0.7+1.0+1.7+0.6+1.0=0.8 and then divided by 7, giving me 0.9.

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3 years ago

A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at (3

Elenna [48]

Answer:

a

Step-by-step explanation:

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3 years ago

Which of these rational numbers is also an integer?

dexar [7]

Answer:

6/3

Step-by-step explanation:

An integer is a whole number, that is not a fraction. All of the numbers are fractions, but if you simplify them, you see that 6/3=2. 2 is a whole number, and therefore an integer.

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3 years ago

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En la expresión algebraica: a (y+2) + n (y+2),el factor común es

sveta [45]

Answer:

2

Step-by-step explanation:

vjibnonlml

number cycle g vjuvgulnojhi

3 0

3 years ago