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3 years ago

Evaluate the expression 9/225

Mathematics

1 answer:

SVEN [57.7K]3 years ago

3 0

Step-by-step explanation:

3/15

the square root of 9 is 3 and the square root of 225 is 15

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A container manufacturing company was contracted to design and manufacture cylindrical cans for fruit juice. The volume of each

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The volume of the cylinder is the amount of fruit juice it can contain.

The relationship between the volume and the surface area is:

$\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}$

The given parameter is:

$\mathbf{V = 0.946}$

The volume of a cylinder is calculated as:

$\mathbf{V = \pi r^2 h}$

Make h the subject

$\mathbf{h = \frac{V}{ \pi r^2}}$

The surface area (A) of a cylinder is:

$\mathbf{A = \pi r^2 + \pi rh}$

Substitute $\mathbf{h = \frac{V}{ \pi r^2}}$

$\mathbf{A = \pi r^2 + \pi r \times \frac{V}{\pi r^2}}$

$\mathbf{A = \pi r^2 + \frac{V}{r}}$

Differentiate

$\mathbf{A' = 2\pi r - Vr^{-2}}$

Set to 0

$\mathbf{2\pi r - Vr^{-2} = 0}$

Rewrite as:

$\mathbf{ 2\pi r = Vr^{-2}}$

Multiply through by r^2

$\mathbf{ 2\pi r^3 = V}$

Solve for r

$\mathbf{r = \sqrt[3]{\frac{V}{2\pi}}}$

$\mathbf{A = \pi r^2 + \frac{0.946}{r}}$

So, we have:

$\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}$

Hence, the relationship between the volume and the surface area is:

$\mathbf{A = \pi (\sqrt[3]{\frac{V}{2\pi}})^2 + \frac{0.946}{(\sqrt[3]{\frac{V}{2\pi}})}}$

Read more about surface areas and volumes at:

brainly.com/question/3628550

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Answer:

Step-by-step explanation:

$a,\ b,\ c-\text{sides of a triangle}\\\\\text{If}\ a\leq b< c\ \text{and}\ a^2+b^2=c^2,\ \text{then it's the lengths of the sides of a right triangle}\\\\\text{If}\ a\leq b\leq c\ \text{and}\ a^2+b^2>c^2,\ \text{then it's the lengths of the sides of a acute triangle}\\\\\text{If}\ a\leq b< c\ \text{and}\ a^2+b^2$

$\text{Triangle condition:}\\\text{That each side has to be shorter than the sum of the other two sides}\\\text{and longer than their difference.}\\\\\text{If}\ a\leq b\leq c,\ \text{then}\ a+b>c.$

$--------------------------\\a.\\a=1,\ b=2,\ c=3\\\\a+b=1+2=3=c\\\\\text{These are not the lengths of the sides of the triangle.}\\----------------------------\\b.\\a=6,\ b=8,\ c=10\\\\a+b=6+8=14>10=c\qquad OK\\\\a^2+b^2=6^2+8^2=36+64=100\\\\c^2=10^2=100\\\\a^2+b^2=c^2\\\\\text{It's the right triangle.}\\----------------------------$

$c.\\a=6,\ b=7,\ c=8\\\\a+b=6+7=13>8\qquad OK\\\\a^2+b^2=6^2+7^2=36+49=85\\\\c^2=8^2=64\\\\a^2+b^2>c^2\\\\\text{It's the acute triangle.}\\----------------------------\\d.\\a=4,\ b=6,\ c=10\\\\a+b=4+6=10=c\\\\\text{These are not the lengths of the sides of the triangle.}$

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