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

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.

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

step-by-step explanation:

formula

x = x1 + p/w(x2 - x1)

let the line segment ab with a(x1,y1) and b(x2,y2)

a point(x,y) divide ab in the ratio, 2: 3 the x coordinate can be written as

x = x1 + p/w(x2 - x1)

here p=2 and w = 2+3

therefore,

x coordinate can be written by using the formula, x= x1 + 2/5(x2 - x1)

similarly y coordinate y = y1 + 2/5(y2 - y1)