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motikmotik
3 years ago
8

An artist creates a​ cone-shaped sculpture for an art exhibit. If the sculpture is 6 feet tall and has a base with a circumferen

ce of 21.352 ​feet, what is the volume of the​ sculpture? Use 3.14 for pi.
Mathematics
1 answer:
Scorpion4ik [409]3 years ago
6 0

Answer:

Step-by-step explanation:

Cone Volume = (π • r² • h) ÷ 3

109.9 = PI * 5 * radius^2 / 3

3* 109.9 / (3.14 * 5) = radius^2

329.7 / 15.7

radius^2 = 21

radius = 4.582575695

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Gnoma [55]

Answer:

  • <u>10 pairs</u>
  • <u>It is a combination</u>

<u></u>

Explanation:

This is a combination because the order does not matter: the Beagle - Collie couple is the same as the Collie - Beagle couple, so it is only counted once.

The formula for combinations is:

           C(m,n)=\dfrac{m!}{n!\cdot (m-n)!}

For five diffferent dogs to be put in pairs, the number of different pairs is:

         C(5,2)=\dfrac{5!}{2!\cdot (5-2)!}=\dfrac{5\times 4}{2}=10

4 0
3 years ago
A laptop computer is purchased for $2700. Each year, it’s value is 70% of its value the year before after how many years will la
n200080 [17]

<u>Answer:</u> 5 years!

<u>Reasoning:</u>

Year 1: 2700 x .70=1890

Year 2: 1890 x .70= 1323

Year 3: 1323 x .70= 926.1

Year 4: 926.1 x .70= 648.27

Year 5: 648.27 x .70=453.79

3 0
4 years ago
Ex 3.6<br> 6. find the area enclosed between the curve y= -2x²-5x+3 and the x-axis
Xelga [282]
When y=0,

-2{ x }^{ 2 }-5x+3=0\\ \\ 2{ x }^{ 2 }+5x-3=0\\ \\ \left( 2x-1 \right) \left( x+3 \right) =0

\\ \\ \therefore \quad x=\frac { 1 }{ 2 } \\ \\ \therefore \quad x=-3

--------------------

\int _{ -3 }^{ \frac { 1 }{ 2 }  }{ -2{ x }^{ 2 } } -5x+3dx

\\ \\ ={ \left[ -\frac { { 2x }^{ 2+1 } }{ 2+1 } -\frac { 5{ x }^{ 1+1 } }{ 1+1 } +3x \right]  }_{ -3 }^{ \frac { 1 }{ 2 }  }

\\ \\ ={ \left[ -\frac { 2{ x }^{ 3 } }{ 3 } -\frac { 5{ x }^{ 2 } }{ 2 } +3x \right]  }_{ -3 }^{ \frac { 1 }{ 2 }  }

\\ \\ \\ =\left\{ -\frac { 2 }{ 3 } { \left( \frac { 1 }{ 2 }  \right)  }^{ 3 }-\frac { 5 }{ 2 } { \left( \frac { 1 }{ 2 }  \right)  }^{ 2 }+3\left( \frac { 1 }{ 2 }  \right)  \right\} -\left\{ -\frac { 2 }{ 3 } { \left( -3 \right)  }^{ 3 }-\frac { 5 }{ 2 } { \left( -3 \right)  }^{ 2 }+3\left( -3 \right)  \right\}

\\ \\ \\ =-\frac { 2 }{ 3 } \cdot \frac { 1 }{ 8 } -\frac { 5 }{ 2 } \cdot \frac { 1 }{ 4 } +\frac { 3 }{ 2 } -\left\{ -\frac { 2 }{ 3 } \left( -27 \right) -\frac { 5 }{ 2 } \cdot 9-9 \right\}

\\ \\ =-\frac { 2 }{ 24 } -\frac { 5 }{ 8 } +\frac { 3 }{ 2 } -\left\{ \frac { 54 }{ 3 } -\frac { 45 }{ 2 } -9 \right\}

\\ \\ =-\frac { 2 }{ 24 } -\frac { 15 }{ 24 } +\frac { 36 }{ 24 } -\frac { 54 }{ 3 } +\frac { 45 }{ 2 } +9

\\ \\ =\frac { 19 }{ 24 } -\frac { 54 }{ 3 } +\frac { 45 }{ 2 } +\frac { 18 }{ 2 } \\ \\ =\frac { 19 }{ 24 } -\frac { 54 }{ 3 } +\frac { 63 }{ 2 }

\\ \\ =\frac { 343 }{ 24 }

Answer: 343/24 units squared.
6 0
4 years ago
Read 2 more answers
X/72 = 135/90 what is x?
enot [183]
Hey! I'll provide the steps required.

First, solved the proportion by cross multiplication.

X(90) = (135)(72)

Then use the commutative property to reorder the terms as well as multiply the numbers.

90x = 9720

Finally, divide it by 90.

x = 108
5 0
3 years ago
Question 2 (1 point)<br> Which graph shows the solutions to 2x&lt;6?
Studentka2010 [4]
Answer: C
^ because the plot starts on 2, unlike all other choices & it passes 6.
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3 years ago
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