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2 years ago

The height of

Mathematics

1 answer:

Amiraneli [1.4K]2 years ago

4 0

Hey there! I'm happy to help!

This glass is most likely a cylinder. To find the volume of a cylinder you take the area of the circle base and multiply it by the height.

To find the area of a circle, you square the radius and multiply it by pi (we will use 3.14 for pi).

Our radius is 3cm.

We square it.

3²=9

Multiply by 3.14.

9×3.14=28.26

Now that we have our circle base area, we multiply it by the height (7 cm).

28.26×7= 197.82

This is how many cubic centimeters the glass can hold if it is completely full. However, we want half full, so we can just divide by 2.

197.82/2=98.91

We can also multiply our circle base by 3.5, which will give us half of the full height.

So, the height of the water is 3.5 cm and the volume of the water is 98.1 cm³.

Have a wonderful day and keep on learning! :D

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|-------------------|-----------------|

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3 years ago

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kodGreya [7K]

Answer:

(1) $g[f(x)]=\frac{8x-1}{12x-4}$

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Step-by-step explanation:

Given functions f(x) = (4x-1)

are $g(x)=\frac{2x+1}{3x-1}$

(1) $g[f(x)]=\frac{2(4x-1)+1}{3(4x-1)-1}$

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$=\frac{8x-1}{12x-4}$

(2) for $g^{-1}(x)$ , rewrite the function g(x) in terms of an equation

$y=\frac{2x+1}{3x-1}$

Substitute y in place of x and x in place of y, then solve for y.

$x=\frac{2y+1}{3y-1}$

(3y-1)x = 2y+1

3xy - x = 2y + 1

3xy - 2y = x + 1

y(3x-2) = x + 1

$y=(\frac{x+1}{3x-2} )$

⇒ $g^{-1}(x)=\frac{x+1}{(3x-2)}$

(3) $f[g(x)]=(x-1)$

$f[g(x)]=4[\frac{2x+1}{3x-1}] =(x-1)$

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⇒ $\frac{8x-3x+4+1}{3x-1}=(x-1)$

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⇒ $5x+5=(3x-1)(x-1)$

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$x=\frac{9\pm\sqrt{81+48} }{6}$

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$x=\frac{9+\sqrt{129} }{6}, \frac{9-\sqrt{129} }{6}$

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