Solve for y: 2x + 4y = 6

A building manager

My name is Ann [436]

42 I think it’s the right one if not am sorry

3 0

3 years ago

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The length of the diagonal of a wooden cube is 24 cm. The cube is cut into the cylinder of the

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.
The formula for the volume of a cylinder is $V=\pi r^2h$ , where $r$ is the radius and $h$ is the height of the cylinder. If $d$ is the diameter, then $r=\frac{d}{2}$ .

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 $2089.497\hspace{1mm}\text{cm}^3$ .

To know more about volume, refer: brainly.com/question/1972490

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4 0

2 years ago

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What elements in domain has the image 5 under function f(x)= 3x+ 2?

bekas [8.4K]

Answer:

Step-by-step explanation:

hello

calculate x : 3x+2 =5

means : 3x+2-2 =5-2

3x = 3

so : x = 3/3 =1

1 is the element in domain has the image 5 under function f(x)= 3x+ 2

7 0

2 years ago

Find sin3A, cos<br> 3A and tan 3A when sin=1/2<br>

Slav-nsk [51]

Answer:

Sin 3A = 1

cos 3A = 0

tan 3 A = undefined

Step-by-step explanation:

$\sin A = \frac{1}{2} \\ \therefore \: \sin A = \sin \: 30 \degree.. \bigg( \because \: \sin \: 30 \degree = \frac{1}{2} \bigg) \\ \therefore \: A = 30 \degree \\ \\ now \\ \sin 3A =\sin (3 \times 30 \degree)= \sin \: 90 \degree = 1 \\ \\ \cos 3A =\cos (3 \times 30 \degree)= \cos \: 90 \degree = 0\\\\ \tan 3A =\tan (3 \times 30 \degree)= \tan \: 90 \degree = \infty$

4 0

4 years ago

Which equation has solution x = -3?

Tema [17]

Hello there.

<span>Which equation has solution x = -3?

</span> $\frac{1}{2} (2x - 6) = -6?$

3 0

3 years ago