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3 years ago

Simplify 1/4 (1-2/3)^2+1/3

Mathematics

2 answers:

tiny-mole [99]3 years ago

7 0

In exact form: 13/36

in decimal form: 0.36111111...

muminat3 years ago

5 0

$\frac{1}{4} * (1-2/3)^{2} + \frac{1}{3}$

= $\frac{1}{4} * ( 1 - \frac{4}{3} + \frac{4}{9} ) + \frac{1}{3}$

= $\frac{1}{4} - \frac{1}{3} + \frac{1}{9} + \frac{1}{3}$

= $\frac{1}{4} + \frac{1}{9}$

= $\frac{9 + 4}{9 * 4}$

= $\frac{13}{36}$

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jek_recluse [69]

The biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

<h3>What will be the diameter and height of the cylinder obtained from a cube and what are the formulas for the diagonal of a cube and the volume of a cylinder?</h3>

If a cylinder with the biggest possible volume is cut inside the cube, the height of the cylinder and the diameter of the cylinder will be equal to the side length of the cube.
For example, consider the following figure in which the cylinder is cut inside of the cube and since the side length of the cube is $x$ , the diameter and the height of the cylinder are also $x$
If the side length of a cube is $x$ unit, then its diagonal will be $x\sqrt{3}$ unit.
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Now, given that the diagonal of the cube is $24$ cm. So, if the side length of the cube is $x$ cm, then we must have

$x\sqrt{3}=24\\\Longrightarrow x=\frac{24}{\sqrt{3}}\\\Longrightarrow x=8\sqrt{3}$

Thus, the side length of the cube is $8\sqrt{3}$ cm.

So, the height of the cylinder with maximum volume will be $h=8\sqrt{3}$ cm and the diameter will be $d=8\sqrt{3}$ cm i.e. the radius will be $r=\frac{d}{2}=\frac{8\sqrt{3}}{2}=4\sqrt{3}$ cm.

So, using the above formula for the volume of a cylinder, we get

$V=\pi r^{2}h=\pi\times (4\sqrt{3})^2\times 8\sqrt{3}=2089.497\hspace{1mm}\text{cm}^3$ .

Therefore, the biggest possible volume of the cylinder will be $2089.497\hspace{1mm}\text{cm}^3$ .

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3 years ago

Line AB contains points A(4, 5) and B(9, 7). What is the slope of AB? 5 2 2 5 N/ur un in ni 2 5 o 2

IRINA_888 [86]

Answer:

The answer is

$\frac{2}{5} \\$

Step-by-step explanation:

The slope of a line given two points can be found by using the formula

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4 years ago

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<span> Remember that what you must do for this case is to calculate the area of the parallelogram and add it to the area of the rectangle.
</span> Palelogram area:
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A1 = b * h
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