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bija089 [108]
3 years ago
9

Diego is making a circular table. He is cutting the largest circle possible from a piece of square wood with sides 6 feet long.

What is the approximate area of the word left over after Diego cuts out the circle? Show your work. Use pi=3.14

Mathematics
1 answer:
Flauer [41]3 years ago
3 0
Area of wood = 6x6 = 36
area of circle = 3.14x9 = 28.26
left over = 36 - 28.26 = 7.74
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<img src="https://tex.z-dn.net/?f=%5Cint%7B%5Bsin%289x%29cos%289x%29%5D%7D%20%5C%2C%20dx" id="TexFormula1" title="\int{[sin(9x)c
Sladkaya [172]

Recall the double angle identity,

sin(2x) = 2 sin(x) cos(x)

Then we can write

sin(9x) cos(9x) = 1/2 sin(2 • 9x) = 1/2 sin(18x)

Then

∫ sin(9x) cos(9x) dx

= 1/2 ∫ sin(18x) dx

= -1/2 • 1/18 cos(18x) + C

= -1/36 cos(18x) + C

though you could continue with another double angle identity,

cos(2x) = cos²(x) - sin²(x)

to rewrite the antiderivative as

= -1/36 (cos²(9x) - sin²(9x)) + C

= 1/36 (sin²(9x) - cos²(9x)) + C

5 0
2 years ago
Eureka Math : 5 ÷ 1/3= ____. There are ___ thirds in 1 whole. There are ___ thirds in 5 wholes. If 5 is 1/3, what is the whole?
oksian1 [2.3K]

Let me edit your question to simplify it.

Eureka Math :

A)5 ÷ 1/3= ____.

B) There are ___ thirds in 1 whole.

C) There are ___ thirds in 5 wholes.

D) If 5 of 1/3, what is the whole? ___

E) 3 ÷1/5= ____ .

F) There are ___ fifths in 1 whole.

G) There are ___ fifths in 3 wholes.

H) If 3 of 1/5, what is the whole?___

Answer:

A) 15

B) three thirds

C) 15 wholes

D) whole is 2

E) 15

F) five fifths

G) 15 fifths

H) whole is 1

Step-by-step explanation:

A)

  • 5÷\frac{1}{3} =5*\frac{3}{1}
  • 5÷\frac{1}{3}=15

<u>Third:</u>

  • third means \frac{1}{3}<u> </u>

B)

  • To make 1 whole from thirds, we need three thirds i.e. \frac{1}{3}+\frac{1}{3}+\frac{1}{3}=\frac{3}{3}=1\ Whole

C)

  • In 1 whole there are three thirds, so in 5 wholes there are 5*3=15 wholes.

D)

  • In 5\ of\ \frac{1}{3}=5*\frac{1}{3} =\frac{5}{3}
  • \frac{5}{3}=1.6
  • The whole of 1.6 or \frac{5}{3} is 2 (rounding 1.6 to 2)

E)

  • 3÷\frac{1}{5}=3*5=15

<u>Fifth:</u> means \frac{1}{5}

F)

  • To make 1 whole of fifths we need five fifths i.e. \frac{1}{5} +\frac{1}{5} +\frac{1}{5} +\frac{1}{5} +\frac{1}{5}=\frac{1+1+1+1+1}{5}=\frac{5}{5}=1

G)

  • In 1 whole we have 5 fifths, so in 3 wholes we have 3*5=15 fifths

H)

  • 3\ of\ \frac{1}{5}=3*\frac{1}{5}=\frac{3}{5}=0.6
  • rounding 0.6 equals to 1
  • thus whole is 1.

 

3 0
3 years ago
What is 25.5% as a decimal​
KonstantinChe [14]

Answer:

0.255

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Please sol<br>ve this real quick
Kobotan [32]

Answer:

for question two: 12

for question four: 1/3

for question six: 25.75 (rounded to two decimal places)

8 0
3 years ago
Please help me please
Tamiku [17]

Answer:

(4,-3)

Step-by-step explanation:

is 4<3? no

is -2<3? yes but is 1>_ 8? no

etc etc

6 0
3 years ago
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