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larisa86 [58]
2 years ago
10

What is the smallest number by which 864 must be multiplied with to make the quotient a perfect cube?

Mathematics
1 answer:
In-s [12.5K]2 years ago
3 0

Answer:

Number is two

Step-by-step explanation:

First of all we find the closest factors of 864 which are 32 x 27

Simply them we have

32 x 27 = 2^5 x 3³

So

Next we know that to be aperfect cube, each exponent needs to be equally divided by divisible by 3.

So If we multiply 864 x 2 we get

Then

1728 = 2^6 x 3³

So if we finally

Take the cube root of that is 2²* 3^1 = 4 x 3= 12

So 2² x 3^1

So if we equate the powers we have the answer as 2.

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While traveling to Europe phlegm exancheged 250 US dollars he spent 150 euros on his trip after returning to the United States h
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AB has coordinates A(-5,9) and B(7,- 7). Points P, Q, and I are collinear
VMariaS [17]

Answer:

\overline{QT}

Step-by-step explanation:

We want to find the coordinates of a certain point C(x,y) such that C divides A(x_1,y_1) and B(x_2,y_2) in the ratio m:n=3:2

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x=\frac{mx_2+nx_1}{m+n}

The y-coordinate is given by:

y=\frac{my_2+ny_1}{m+n}

AB has coordinates A(-5,9) and B(7,- 7)

We substitute the values to get:

x=\frac{3*7+2*-5}{3+2}

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y=\frac{3*-7+2*9}{3+2}

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y=-\frac{3}{5}

Therefore C has coordinates  (\frac{11}{5},-\frac{3}{5})

The line segment that contains C is \overline{QT}

See attachment.

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Which description is paired with its correct expression?
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