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3 years ago

How would the expression x^2+27 be rewritten using sum of cubes?

1 answer:

6 0

Assuming the square is not a typo, one can write

$x^2+27=(x^{2/3})^3+3^3=(x^{2/3}+3)\bigg((x^{2/3})^2-3x^{2/3}+9\bigg)$

$=(x^{2/3}+3)\bigg(x^{4/3}-3x^{2/3}+9\bigg)$

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3 years ago

4) Find the sum of 6\12 and 1\2 .

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2 years ago

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3 years ago

How many yards are in 33 feet

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A custom rectangular tabletop has a length that is twice it’s width, and the tabletop measures 76 inches on its diagonal. What a

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Answer:

<em>The dimensions of the tabletop: Length= 67.976... inches and Width= 33.988... inches and the perimeter will be 203.929... inches.</em>

Step-by-step explanation:

Suppose, the width of the rectangular tabletop is $x$ inch.

As the tabletop has a length that is twice it’s width, so the length will be: $2x$ inch.

The tabletop measures 76 inches on its diagonal.

<u>Formula for length of diagonal of rectangle</u>: $d=\sqrt{l^2+w^2}$

So, the equation will be..........

$76=\sqrt{(2x)^2+ x^2}\\ \\ 76=\sqrt{4x^2+x^2} \\ \\ 76=\sqrt{5x^2} \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= \frac{5776}{5}=1155.2 \\ \\ x= \sqrt{1155.2} =33.988...$

Thus, the width of the tabletop is 33.988... inches and the length will be: (2×33.988...) = 67.976... inches.

The perimeter will be: 2(33.988...+ 67.976...) inches = 203.929... inches.

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2 years ago