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3 years ago

Gcf using prime factorization of 52 and 65

Mathematics

1 answer:

Leto [7]3 years ago

3 0

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What is the volume of a pyramid whose base is a square of area 36 and whose four faces are equilateral triangles?

irina1246 [14]

Answer:

$V = 36\sqrt{2}$

Step-by-step explanation:

The volume of a pyramid is

$V = \dfrac{1}{3}Bh$

where B = area of the base, and h = height of the pyramid

The base is a square.

$A = s^2$

$s = \sqrt{A}$

$s = \sqrt{36}$

$s = 6$

The side of the base has length 6. Each face of the pyramid is an equilateral triangle with side of length 6.

An altitude of this triangle measures

$a = \sqrt{6^2 - 3^2}$

$a = \sqrt{27}$

The pyramid is formed by 4 equilateral triangles whose bases form a square. The tips of the faces meet at a single point on top. The vertical distance from that point to the center of the base is the height of the pyramid.

$h = \sqrt{(\sqrt{27})^2 - 3^2 }$

$h = \sqrt{27 - 9}$

$h = \sqrt{18}$

$h = 3 \sqrt{2}$

Volume of the pyramid:

$V = \dfrac{1}{3}Bh$

$V = \dfrac{1}{3}(36)(3\sqrt{2})$

$V = 36\sqrt{2}$

5 0

3 years ago

A direct variation includes the points (3, 12) and (n, 8). Find n.

vampirchik [111]

For a direct variation between each point (x, y),

$\begin{gathered} x\propto y \\ x=ky \\ k=\frac{x}{y} \end{gathered}$

For (x₁, y₁) = (3, 12),

$\begin{gathered} k=\frac{3}{12} \\ k=0.25 \end{gathered}$

To find n, consider (n, 8) = (x, y)

$\begin{gathered} x=ky \\ \end{gathered}$

Substituting,

$\begin{gathered} n=0.25\times8 \\ n=2 \end{gathered}$

Therefore, the value of n is 2

5 0

1 year ago

Round 30,944 to the nearest ten thousand

Arte-miy333 [17]

Actually none of the answers is correct - it's neither 30,900 nor 40,000.

30,944 rounded to the nearest ten thousand will give us 30,000. It's because 30,944 is closer to 30,000 than to 40,000.

6 0

2 years ago

4x^1/2 to radical form

Lyrx [107]

$x^ \frac{m}{n}= \sqrt[n]{x^m}$
pemdas, so exponent first before multiply
4(x^1/2)=4x^2
this is different from
(4x)^1/2

so

$x^ \frac{1}{2}= \sqrt[2]{x^1}$
times that by 4
4√x

7 0

2 years ago

Read 2 more answers

Choose the answer. 1. (1 pt) use any model you choose to solve the story problem. a fisherman separated of his catch into 2 equa

-BARSIC- [3]

50% of it will be in each bin

8 0

3 years ago