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3 years ago

Sin(-120) in exact value

Mathematics

1 answer:

cupoosta [38]3 years ago

3 0

Step-by-step explanation:

$\because \: sin \: ( - \theta) = - sin \: \theta \\ \\ \therefore \: sin \: ( - 120 \degree) = - sin \: 120 \degree \\ \\ = - sin \: ( 180\degree- 60 \degree) \\ \\ = - sin \: 60 \degree \\ \\ = - \frac{ \sqrt{3} }{2} \\ \\ \purple{ \boxed{\therefore \: sin \: ( - 120 \degree) =- \frac{ \sqrt{3} }{2} }}$

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What is a description

ValentinkaMS [17]

Answer:

Description is the pattern of narrative development that aims to make vivid a place, object, character, or group. Description is one of four rhetorical modes, along with exposition, argumentation, and narration. In practice it would be difficult to write literature that drew on just one of the four basic modes.

Step-by-step explanation:

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2 years ago

I WILL AWARD BRAINLIEST!! PLEASE HELP!!!<br> Find the areas of the trapezoids.

Galina-37 [17]

Answer:

A = 12 units ^2

Step-by-step explanation:

The area of the trapezoid is found by

A = 1/2 (b1+b2)h

b1 = 2

b2 = 4

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I found these by looking at the graph

A = 1/2(2+4) 4

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2 years ago

A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far

ValentinkaMS [17]

Answer:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

$\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}$ (1)

And this formula is expanded by definition of vectors in rectangular and polar form:

$(x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})$ (1b)

Where:

$x, y$ - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

$r_{1}, r_{2}$ - Length of each vector, in kilometers.

$\theta_{1}, \theta_{2}$ - Bearing of each vector in standard position, in sexagesimal degrees.

If we know that $r_{1} = 42\,km$ , $r_{2} = 28\,km$ , $\theta_{1} = 32^{\circ}$ and $\theta_{2} = 154^{\circ}$ , then the resulting coordinates of the final position of the surveyor is:

$(x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})$

$(x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km]$

$(x,y) = (10.452, 34.531)\,[km]$

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

$\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}$

$\theta \approx 16.840^{\circ}$

And the distance from the camp is calculated by the Pythagorean Theorem:

$r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}$

$r = 36.078\,km$

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

5 0

2 years ago

What are the zeros of the polynomial function?

Genrish500 [490]

Hello from MrBillDoesMath!

Answer:

x = 2 and 10

Discussion:

Approach 1:

20 = (-10)*(-2) and (-10) + (-2) = -12 the coefficients of the polynomial. Hence

x^2 -12x + 20 = ( x- 2) * ( x-10)

Approach 2:

From the quadratic formula ( a = 1, b = -12, c = 20)

x = ( -(-12) +\- sqrt( ((-12)^2 - 4*1*20) ) / (2 * 1)

= ( 12 +\- sqrt( 144-80) ) /2

= (12 +\- sqrt(64) ) /2

= (12 +\- 8 ) /2

x = ( 12 + 8) /2 = 20/2 = 10

x = ( 12 - 8)/ 2 = 4/2 = 2

Thank you,

MrB

5 0

3 years ago

Read 2 more answers

I Need help! If you help me you'll get 10 points!!

natka813 [3]

To solve this problem you must apply the proccedure shown below:

1. You have that the number of innings are expressed as a mixed number in the exercise:

$102^{\frac{2}{3} }$

2. If you want to write it as a decimal, you can convert the fraction as a decimal by dividing the numerator by the denominator and then, you must add this to the whole number part:

$102+\frac{2}{3}=102+0.67=102.67$

The answer is: 102.67

7 0

2 years ago