Which of the following shows the correct order? 5497,0.75,
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° 0,75–1.2
(23<3<0,75

The last one, (1/2)^2 < 2/3 < 0.75

Step-by-step explanation:

So lets try to put each number in the same form, and see what their values are.

Lets start with (1/2)^2

This is squaring the 1 and 2 in 1/2. 1^2 is 1. 2^2 is 4. So its now:

1/4

Lets look at the others:

2/3

Lets just give it a common denominator. To do this, lets find the lowest number that both 3(from 2/3) and 4(from 1/4) go into. This is also known as the LCM.

This will be 12.

Since 3(from 2/3) goes into 12 4 times, we multipy both numerator and denominator of 2/3 by 4:

4*2=8, 3*4=12:

8/12

Since 4(from 1/4) goes into 12 3 times, we multiply both the numerator and denominator by 3:

1*3=3, 4*3=12:

3/12

So lets just go over what we know so far:

(1/2)^2 = 3/12

2/3 = 8/12

Now lets find our last value:

0.75

When converted into fraction form, we will get:

3/4

We already have a LCM, which is 12, that goes into this.

The denominator goes into 12 3 times, so again, we multiply numerator and denominator in this:

3*3=9, 4*3=12:

9/12

So:

(1/2)^2 = 3/12, 2/3 = 8/12, and 0.75 = 9/12

3/12 is smaller than 8/12, and 8/12 is smaller than 9/12. This can be written as:

3/12 < 8/12 < 9/12

And this basically means that:

(1/2)^2 < 2/3 < 0.75

This is the last answer in your answer list.

Hope this helps!

answer: ok

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.