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2 years ago

1) Simplify the following expressions: a) sin²108° + sin² 18°

Mathematics

1 answer:

abruzzese [7]2 years ago

8 0

Note that

108° = 90° + 18°

sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)

Then

sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1

by the Pythagorean identity.

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3 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:

$5$ ÷ $\frac{1}{3} =5*\frac{3}{1}$

$5$ ÷ $\frac{1}{3}=15$

Third:

third means $\frac{1}{3}$

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

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

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)

$3$ ÷ $\frac{1}{5}=3*5=15$

Fifth: means $\frac{1}{5}$

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

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

$3\ of\ \frac{1}{5}=3*\frac{1}{5}=\frac{3}{5}=0.6$

rounding 0.6 equals to 1

thus whole is 1.

3 0

3 years ago

What is the missing length?

TEA [102]

Answer: 13.722 km ; or, write as: 13 13/18 km .
___________________________________________________
Explanation:
___________________________________________________
Area = Length * width ;
___________________________________________________
or, write as: A = L * w ;
________________________

Given: A = 247 km² ;

L = 18 km ;

w = "y" ;
________________________
Find: "y"
______________________________
A = L * w ;
______________________________
Plug in our values:
______________________________
247 km² = 18 km * "y" ; solve for "y" (in units of "km") ;

_____________________________
18 y = 247 ;
___________________________________________________________
Divide each side of the equation by "18"; to isolate "y" on one side of the equation; and to solve for "y" :
___________________________________________________________
18 y / 18 = 247 / 18 ;
_____________________________________________
to get:
_____________________________________________
y = 13.7222222222222222...... km ; round to: 13.722 km

or; y = 13 13/18 km .
_______________________________________________

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3 years ago

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vladimir2022 [97]

I believe the answer to this question is A

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4 years ago

1) Simplify the following expressions: a) sin²108° + sin² 18° ​

1) Simplify the following expressions: a) sin²108° + sin² 18°