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Sedaia [141]
2 years ago
13

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

Mathematics
1 answer:
abruzzese [7]2 years ago
8 0

Note that

108° = 90° + 18°

so

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.

You might be interested in
The point-slope form of the equation of the line that passes through (–5, –1) and (10, –7) is y + 7 = (x – 10). What is the stan
Crank

Answer:

<h3>2x + 5y = –15.</h3>

Step-by-step explanation:

We are given coordinates of the line passed through (–5, –1) and (10, –7) .

Applying slope formula,

Slope=\frac{y_2-y_1}{x_2-x_1}

\left(x_1,\:y_1\right)=\left(-5,\:-1\right),\:\left(x_2,\:y_2\right)=\left(10,\:-7\right)

Therefore,

m=\frac{-7-\left(-1\right)}{10-\left(-5\right)}

m=-\frac{2}{5}

Therefore, slope is m=-\frac{2}{5}.

Applying point-slope form y-y_1=m(x-x_1), we get

y+7 = -\frac{2}{5}(x-10)

y+7=-\frac{2}{5}(x-10)

On multiplying both sides by 5, we get

5(y+7)=5\times-\frac{2}{5}(x+1)

5y+35=-2(x-10)

5y+35=-2x+20

Adding 2x on both sides, we get

5y+25+2x=-2x+20+2x

2x+5y+35=20

Subtracting 35 from both sides, we get

2x+5y+35-35=20-35

2x+5y=-15.

Therefore, required equation is :

<h3>2x + 5y = –15.</h3>
6 0
3 years ago
In a popular tale of wizards and witches, a group of them finds themselves in a room with unmarked doors which change position,
SSSSS [86.1K]

Answer:

Expected number of hours before the the group exits the building = E[Number of hours] = 3.2 hours

Step-by-step explanation:

Expected value, E(X) is given as

E(X) = Σ xᵢpᵢ

xᵢ = each variable

pᵢ = probability of each variable

Let X represent the number of hours before exiting the building taking each door. Note that D = Door

D | X | P(X)

1 | 3.0 | 0.2

2 | 3.5 | 0.1

3 | 5.0 | 0.2

4 | 2.5 | 0.5

E(X) = (3×0.2) + (3.5×0.1) + (5×0.2) + (2.5×0.5) = 3.2 hours

Hope this Helps!!!

7 0
3 years ago
18.0*18.9 please help, please!
kicyunya [14]

Answer:

340.2

Step-by-step explanation:

18.0 x 18.9 = 340.2

5 0
3 years ago
Read 2 more answers
What does the point (2,24) represent?
almond37 [142]

Answer:

not sure what you mean here but..... 2 represents your x value which will go on the x intercept. And 24 represents your y value. When you have both of these values, you can plot it on a coordinate graph.


4 0
3 years ago
Evaluate: 5-3[2+(-5)]2-8
trasher [3.6K]

Answer:

15

Step-by-step explanation:

5 - 3[ 2 + (-5)] 2 - 8

Subtract 5 from 2 to get −3.

5 - 3 (-3) × 2 - 8

Multiply 3 and −3 to get −9.

5 - (-9 × 2) - 8

Multiply −9 and 2 to get −18.

5 - (-18) - 8

The opposite of −18 is 18.

5 + 18 - 8

Add 5 and 18 to get 23.

23 - 8

Subtract 8 from 23 to get 15.

15

Hope it helps and have a great day! =D

~sunshine~

7 0
2 years ago
Read 2 more answers
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