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kolezko [41]
3 years ago
5

Michael has a fish tank that has a length of 7 inches, a width 6 inches and and height of 8 inches. What is the total surface ar

ea of the fish tank ?
Mathematics
2 answers:
Ainat [17]3 years ago
5 0

Answer:

I think the answer is 292 inches.

bazaltina [42]3 years ago
5 0

Answer: 250in².

Step-by-step explanation:

Total surface area of the fish tank wil be, listen we can can derive a formula for the surface area.

The fish tanks has five surfaces since the top will be opened. For fnd the total surface area now, find the area of each of the surfaces and add together. If it is 6 surfaces, the formula would have been.

2(lb) + 2(lb) + 2(lb)

2( lb + lb + lb )

Now , first (lb) = 7 × 6in²= 42in² ie. the top and the bottom,

Second surfaces, the sides

7 × 8 = 56in²

The third is the other sides

6 × 8 = 48in². Now applying the formula now, bearing in mind that the top is open, we now have

42in² + 2( lb + lb )in²

= 42 + 2( 56 + 48 )

= 42 + 2(104)

= 42 + 208

= 250in².

Note, if the tank or box is closed, then the above derived formula could be suitable.

The height is also regarded as the depth.

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3 years ago
Which is equivalent to V180x11 after it has been simplified completely?
inna [77]

Question:

Which is equivalent to \sqrt{180x^{11}} after it has been simplified completely?

Answer:

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

Step-by-step explanation:

Given

\sqrt{180x^{11}}

Required

Simplify

We start by splitting the square root

\sqrt{180x^{11}} = \sqrt{180} * \sqrt{x^{11}}

Replace 180 with 36 * 5

\sqrt{180x^{11}} = \sqrt{36 * 5} *  \sqrt{x^{11}}

Further split the square roots

\sqrt{180x^{11}} = \sqrt{36} *\sqrt{5} *  \sqrt{x^{11}}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{11}}

Replace power of x; 11 with 10 + 1

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10 + 1}}

From laws of indices; a^{m+n} = a^m * a^n

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x^1}

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10} * x}

Further split the square roots

\sqrt{180x^{11}} = 6*\sqrt{5} *  \sqrt{x^{10}} * \sqrt{x}

From laws of indices; \sqrt{a} = a^{\frac{1}{2}}

So, we have

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{10*\frac{1}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{\frac{10}{2}} * \sqrt{x}

\sqrt{180x^{11}} = 6*\sqrt{5} *  x^{5} * \sqrt{x}

Rearrange Expression

\sqrt{180x^{11}} = 6 *  x^{5} * \sqrt{5} * \sqrt{x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5} * \sqrt{x}

From laws of indices; \sqrt{a} *\sqrt{b} = \sqrt{a*b} = \sqrt{ab}

So, we have

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5*x}

\sqrt{180x^{11}} = 6x^{5} * \sqrt{5x}

\sqrt{180x^{11}} = 6x^{5}\sqrt{5x}

<em>The expression can no longer be simplified</em>

Hence, \sqrt{180x^{11}} is equivalent to 6x^{5}\sqrt{5x}

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