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ASHA 777 [7]
3 years ago
9

An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal rin

g. The distance around each dot is 24pi inches. The artist plans to fill the inside of each dot with blue colored glass.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.
Mathematics
2 answers:
IgorLugansk [536]3 years ago
6 0
\bf \textit{"The distance around each dot is 24}\pi \textit{ inches."}\\\\
\textit{circumference of a circle}\\\\
C=2\pi r\quad 
\begin{cases}
r=radius\\
-----\\
C=24\pi 
\end{cases}\implies 24\pi =2\pi r\implies \cfrac{24\pi }{2\pi }=r
\\\\\\
\boxed{12=r}\\\\
-------------------------------\\\\
\textit{area of a circle}\\\\
A=\pi r^2\quad 
\begin{cases}
r=radius\\
-----\\
r=12
\end{cases}\implies A=\pi 12^2\implies A=144\pi
kari74 [83]3 years ago
5 0

Answer:

The answer gives above me gives you the answer, but not in pi, so the answer in pi is 144 pi

Step-by-step explanation:

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the combined age of april and laura is 23 years. laura's age is two years more than half of april's age. what is laura's age
Kipish [7]

Laura's age is 9 years.

Solution:

Let x be the age of April.

Laura's age = 2 years more than half of April's age

<u>Convert statement into algebraic expression:</u>

Half of April's age = \frac{x}{2}

2 years more than half of April's age = \frac{x}{2}+2

Combined age of April and Laura = 23

⇒ April's age + Laura's age = 23

$\Rightarrow \ \ x+(\frac{x}{2}+2) =23

$\Rightarrow \ \ x+\frac{x}{2}+2 =23

$\Rightarrow \ \ \frac{x}{1}+\frac{x}{2}+\frac{2}{1} =23

To add the fractions make the denominators same.

Multiplying 2 on both numerator and denominator of unlike terms, we get

$\Rightarrow \ \ \frac{x\times2}{1\times2}+\frac{x}{2}+\frac{2\times2}{1\times2} =23

$\Rightarrow \ \ \frac{2x}{2}+\frac{x}{2}+\frac{4}{2} =23

Denominators are same, now add the fractions.

$\Rightarrow \ \ \frac{2x+x+4}{2} =23

Do cross multiplication.

$\Rightarrow \ \ 2x+x+4=23\times2

$\Rightarrow \ \ 3x=46-4

$\Rightarrow \ \ 3x=42

$\Rightarrow \ \ x=14

Aprils's age = 14 years

Laura's age = \frac{14}{2}+2

                    = 7 + 2

Laura's age = 9

Hence Laura's age is 9 years.

8 0
3 years ago
Ummm sooo I’m really confused and it’s due tomorrow please help me
MaRussiya [10]

Answer:

75

Step-by-step explanation:

If the triangles are similar, it means the ratio between the two give sides is the same. As seen from the smaller triangle the ratio of the two top sides would be 16:50 or 8:25.

Since the first side of the bigger triangle (24) is three times 8 (it's ratio side), then the other side must be 3x25 = 75, which maintains the ratio 8:25 between the two sides (24:75).

Hope this helped!

4 0
3 years ago
How many 100 dollar bills are in 1 thousand
bonufazy [111]
100 goes into 1,000 ten times. The answer is 10. 
5 0
3 years ago
What is the difference of the rational expressions below? 6x - 1/ 2x^2 - 3/x
Burka [1]

-x/2x^3

-1/2x^2

6 0
3 years ago
1. The exponential function modeled below represents the number of square
Umnica [9.8K]

Answer:

600,000 km²

Step-by-step explanation:

Using the exponential regression calculator : the regression fit obtained for the data is :

36510 * (1.08^x)

After 40 years ;

x = 40

Hence,

y = 36510 * 1.08^40

y = 36510 * 21.72452

y = 793,162.27 km

Hence, y is closest to 800,000 km

7 0
2 years ago
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