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timama [110]
3 years ago
7

Find the volume of a right prism with height h=10 cm, The base is equilateral triangle with side 4 cm, base altitude of ≈ 3.5 cm

.
Mathematics
1 answer:
cestrela7 [59]3 years ago
3 0
<h2>Answer:</h2>

\boxed{V=40\sqrt{3}cm^3}

<h2>Step-by-step explanation:</h2>

A prism is a solid object having two identical bases, hence the same cross section along the length. Prism are called after the name of their base. In a right prism every edge that connects the base and the opposite face makes right angles with both faces. Moreover, a triangular prism is a solid whose base is a triangle. In general, a prism's volume is always equal to the area of its base, which has the same area of the top face, times its height. In mathematical language:

V=A_{b}\times H \\ \\ Where: \\ \\ A_{b}:Base \ Area \\ \\ H:Height

Since the base is an equilateral triangle with side 4 cm, then we'll use Heron's formula to find the area. This formula uses triangle's side lengths and the semiperimeter. A polygon's semiperimeter s is half its perimeter. So the area of a triangle can be found by A=\sqrt{s(s-a)(s-b)(s-c)} being a,\:b\:and\:c the corresponding sides of the triangle. So:

s=\frac{4+4+4}{2}=6cm \\ \\ a=b=c=4cm \\ \\ A_{b}=\sqrt{6(6-4)^3}=4\sqrt{3}cm^2

Finally:

V=4\sqrt{3}\times 10 \\ \\ \boxed{V=40\sqrt{3}cm^3}

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A 12 foot board is split into 5 equal pieces. Which expression shows the length of each piece
Molodets [167]

Answer:

Find out the which expression shows the length of each piece .

To prove

As given

A 12 foot board is split into 5 equal pieces.

Than

Length\ of\ each\ piece = \frac{Total\ length\ of\ board}{Total\ number\ of\ pieces}

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3 years ago
How do you get -4 to 4
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3 0
3 years ago
S=a1/1-r
valentinak56 [21]

Answer:

4

Step-by-step explanation:

This is an <em>infinite geometric series</em>. This has a sum of  \frac{a}{1-r}

Where

a is the first term, and

r is the common ratio (one term divided by the previous term)

Let's figure out the first 2 terms by plugging in n = 1 first and then n = 2 for the series.

<u />

<u>First term:</u>

3(\frac{1}{4})^{n-1}\\=3(\frac{1}{4})^{1-1}\\=3(\frac{1}{4})^0\\=3(1)\\=3

<u>Second term:</u>

3(\frac{1}{4})^{n-1}\\=3(\frac{1}{4})^{2-1}\\=3(\frac{1}{4})^1\\=3(\frac{1}{4})\\=\frac{3}{4}

<em>Let's see the common ratio:  \frac{\frac{3}{4}}{3}\\=\frac{3}{4}*\frac{1}{3}\\=\frac{1}{4}</em>

<em />

<em>Thus we have a = 3 and r = 1/4</em><em>. Plugging into the formula of the infinite sum, we get:</em>

<em>s=\frac{a}{1-4}=\frac{3}{1-\frac{1}{4}}=\frac{3}{\frac{3}{4}}=3*\frac{4}{3}=4</em>

<em />

<em>So, </em><em>the answer is 4</em>

4 0
3 years ago
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