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3 years ago

Find the surface area of the cube shown.

Mathematics

2 answers:

Alja [10]3 years ago

8 0

A=6a^2

A=6(5.5)^2

A=181.5

Hopefully I answered correctly.

ozzi3 years ago

4 0

As we know that surface area of the cube is given by the formula

Surface Area (SA)= $6a^2$

where a is the side length of the cube .

As we can see in the diagram the side length of the cube is $a=5.5cm$

Hence the surface area of the cube will be

$SA=6*(5.5)^2\\\\SA=6*30.25 cm^2=181.5 cm^2\\$

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zhuklara [117]

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3 years ago

Let L be a tangent line to the hyperbola x y = 2 at x = 9 . Find the area of the triangle bounded by L and the coordinate axes.

mafiozo [28]

Answer:

$A = 4$

Step-by-step explanation:

The equation of the slope of the tangent line L is obtained by deriving the equation of the hyperbola:

$y = \frac{2}{x}$

$y'=-2\cdot x^{-2}$

The numerical value of the slope is:

$y' = -2 \cdot (9)^{-2}\\y' = -\frac{2}{81}$

The component of the y-axis is:

$y = \frac{2}{9}$

Now, the tangent line has the following mathematical model:

$y = m \cdot x + b$

The value of the intercept is found by isolating it within the equation and replacing all known variables:

$b = y - m \cdot x$

$b = \frac{2}{9}-(-\frac{2}{81} )\cdot (9)\\b = \frac{4}{9}$

Thus, the tangent line is:

$y = -\frac{2}{81}\cdot x + \frac{4}{9}$

The vertical distance between a point of the tangent line and the origin is given by the intercept.

$d_{y} = \frac{4}{9}$

In order to find horizontal distance between a point of the tangent line and the origin, let equalize y to zero and clear x:

$-\frac{2}{81}\cdot x + \frac{4}{9}=0$

$-\frac{2}{9}\cdot x + 4 = 0$

$x = 18$

$d_{x} = 18$

The area of the triangle is computed by this formula:

$A = \frac{1}{2}\cdot d_{x}\cdot d_{y}$

$A = \frac{1}{2}\cdot (18)\cdot (\frac{4}{9} )$

$A = 4$

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3 years ago

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erica [24]

Answer:

Step-by-step explanation:

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Multiply through by 2

That's

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<u>Expand</u>

That's

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9x = 58 - 4

9x = 54

Divide both sides by 9

That's

$\frac{9x}{9} = \frac{54}{9}$

We have the final answer as

Hope this helps you

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