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iris [78.8K]
3 years ago
9

Solution of. sin 18​

Mathematics
1 answer:
guapka [62]3 years ago
5 0

Answer:

sin 18° = sin A = −1±5√4

Step-by-step explanation:

Let A = 18°                          

- Therefore, 5A = 90°

2A + 3A = 90˚

2θ = 90˚ - 3A

- Taking sine on both sides, we get

sin 2A = sin (90˚ - 3A) = cos 3A

2 sin A cos A = 4 cos^3 A - 3 cos A

2 sin A cos A - 4 cos^3A + 3 cos A = 0

cos A (2 sin A - 4 cos^2 A + 3) = 0

- Dividing both sides by cos A = cos 18˚ ≠ 0, we get

2 sin θ - 4 (1 - sin^2 A) + 3 = 0

4 sin^2 A + 2 sin A - 1 = 0, which is a quadratic in sin A

- Therefore, sin θ = −2±−4(4)(−1)√2(4)

sin θ = −2±4+16√8

sin θ = −2±25√8

sin θ = −1±5√4

- Now sin 18° is positive, as 18° lies in first quadrant.

- Therefore, <em>sin 18° = sin A = −1±5√4</em>

<em />

<em>(Good luck! I hope this helped. ^_^)</em>

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The shark are fed three times a day during the morning feeding 2/15 of a ton. During the afternoon feeding the weight of fish fe
UNO [17]

Answer:

The shark are fed \frac16 \ ton of fish during the night.

Step-by-step explanation:

Given:

Weight of fish fed in the morning = \frac{2}{15}\ ton

Also Given:

During the afternoon feeding the weight of fish fed will be 1/15 of a ton more than the fish fed during the morning.

Weight of fish fed in the afternoon = \frac{2}{15}+\frac{1}{15}=\frac{2+1}{15}=\frac{3}{15}\ ton

Total fish fed in whole day = \frac12 \ ton

We need to find the Weight of fish fed in the night.

Solution:

Now we can say that;

Weight of fish fed in the night can be calculated by by subtracting Weight of fish fed in the morning and Weight of fish fed in the afternoon from Total fish fed in whole day .

framing in equation form we get;

Weight of fish fed in the night = \frac{1}{2}-\frac{2}{15}-\frac{3}{15}= \frac{1}{2}-(\frac{2}{15}+\frac{3}{15})=\frac{1}{2}-\frac{2+3}{15}= \frac{1}{2}-\frac{5}{15} = \frac{1}{2}-\frac{1}{3}

Now we will use LCM for making the denominator common we get;

Weight of fish fed in the night = \frac{1\times3}{2\times3}-\frac{1\times2}{3\times2} = \frac{3}{6}-\frac{2}{6}

Now denominator are common so we will solve the numerators.

Weight of fish fed in the night = \frac{3-2}{6}=\frac16 \ ton

Hence The shark are fed \frac16 \ ton of fish during the night.

3 0
3 years ago
Write the equation of the circle below to complete the square. Also determine the area of the circle.
diamong [38]

Answer: (x-7)^2+(y+2)^2=11^2 ; A=121\pi

Step-by-step explanation:

I have never done a problem like this, so this is my first time attempting it.

The standard form for the equation of a circle is:

(x-a)^2+(y-b)^2=r^2

Begin by grouping the 'x' terms and 'y' terms:

(x^2-14x)+(y^2+4y-68)=0

Complete the square for the second polynomial:

(\frac{b}{2} )^2=(\frac{4}{2} )^2=4

(x^2-14x)+(y^2+4y+4-4-68)=0

(x^2-14x)+(y^2+4y+4)-4-68=0

(x^2-14x)+(y^2+4y+4)-72=0

(x^2-14x)+(y+2)^2-72=0

Do the exact same process with the other polynomial:

(x^2-14x-72)+(y+2)^2=0

Complete the square:

(\frac{14}{2} )^2=49

(x^2-14x+49-49-72)+(y+2)^2=0

(x^2-14x+49)-49-72+(y+2)^2=0

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(x-7)^2-121+(y+2)^2=0

Bring the 121 to the other side to get:

(x-7)^2+(y+2)^2=121

(x-7)^2+(y+2)^2=11^2

The above expression is the equation of our circle in standard form. It is centered at the coordinates (7, -2) and has a radius of 11 units. The area of a circle if given by:

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8 0
2 years ago
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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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