Find the exact value, without a
calculator.
710
6
sin
2
tan
12
6
2
7Tt/6
COS
Answers
Answer:
[tex]-2 -\sqrt{3}[/tex]
Step-by-step explanation:
First consider numerator
[tex]sin \frac{\frac{7\pi}{6}}{2} = sin \frac{7\pi}{12}= sin (\frac{\pi}{4} + \frac{\pi}{3})[/tex]
Using the formula : sin (A + B) = sin A cos B + cos A sin B
[tex]sin \frac{\pi}{4} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{4} = \frac{\sqrt{2} }{2}\\\\sin \frac{\pi}{3} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{3} = \frac{1}{2}[/tex]
[tex]sin(\frac{\pi}{4} + \frac{\pi}{3}) = sin \frac{\pi}{4} \cdot cos \frac{\pi}{3} + cos \frac{\pi}{4} \cdot sin \frac{\pi}{3}[/tex]
[tex]=\frac{\sqrt{2} }{2} \cdot \frac{1}{2} + \frac{\sqrt{2} }{2} \cdot \frac{\sqrt{3} }{2} \\\\= \frac{\sqrt{2} }{4} + \frac{\sqrt{6} }{4}\\\\=\frac{\sqrt{2} +\sqrt{6} }{4}[/tex]
Second consider denominator
[tex]cos \frac{\frac{7\pi}{6}}{2} = cos \frac{7\pi}{12}= cos (\frac{\pi}{4} + \frac{\pi}{3})[/tex]
Using the formula : cos (A + B) = cos A cos B - sin A sin B
[tex]sin \frac{\pi}{4} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{4} = \frac{\sqrt{2} }{2}\\\\sin \frac{\pi}{3} = \frac{\sqrt{2} }{2}, \ cos \frac{\pi}{3} = \frac{1}{2}[/tex]
[tex]cos(\frac{\pi}{4} + \frac{\pi}{3}) = cos \frac{\pi}{4} \cdot cos \frac{\pi}{3} -sin \frac{\pi}{4} \cdot sin \frac{\pi}{3}[/tex]
[tex]=\frac{\sqrt{2} }{2} \cdot \frac{1}{2} - \frac{\sqrt{2} }{2} \cdot \frac{\sqrt{3} }{2}\\\\=\frac{\sqrt{2}}{4} - \frac{\sqrt{6}}{4}\\\\= \frac{\sqrt{2} -\sqrt{6} }{4}[/tex]
Therefore,
[tex]tan \frac{7\pi}{12} = \frac{sin \frac{7\pi}{12}}{cos\frac{7\pi}{12}}[/tex]
[tex]= \frac{\frac{\sqrt{2} +\sqrt{6} }{4}} {\frac{\sqrt{2} -\sqrt{6} }{4} }\\\\=\frac{\sqrt{2} +\sqrt{6} }{4} \times \frac{4 }{\sqrt{2} -\sqrt{6}}\\\\=\frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} -\sqrt{6}}[/tex]
Either we can stop here or Rationalize the denominator:
[tex]\frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} -\sqrt{6}} \times \frac{\sqrt{2} +\sqrt{6} }{\sqrt{2} +\sqrt{6}} = \frac{(\sqrt{2} +\sqrt{6})^{2} }{(\sqrt{2})^2 -(\sqrt{6})^2} = \frac{2 + 6 +2\sqrt{12} }{2-6} = \frac{8+2\sqrt{12} }{-4} = \frac{8+ 4\sqrt{3} }{-4} = -2-\sqrt{3}[/tex]
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Step-by-step explanation:
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Answers
Answer:
201.1 mm²
Step-by-step explanation:
Smaller sphere = 8
Larger sphere = 15
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The height of a refrigerator would be about?
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B. 7 feet
C. 7 yards
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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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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Answer:
7
Step-by-step explanation:
So basically, there are 4 segments: 15-30, 30-45, 45-60, 60-75.
There is also a list of values.
If these values fall between 15-30, for example, it is considered a freqeuncy of 1.
If a second value also falls between 15-30, it is considered to then have a frequency of 2.
Every value that falls under a range of values, such as 15-30, is counted as a freqeuncy of 1.
So, lets look at 15-30.
There is a freqeuncy of 3.
This means that 3 values were in between 15 and 30,
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This means we do not count values that are in the 15-30 segment.
However, we do want to look at the freqeuncy in 30-45, 45-60, and 60-75.
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In 45-60 we have a frequency of 2.
In 60-75 we have a frequency of 2.
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83°
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Answers
Answer:
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Step-by-step explanation:
The value of x in the given figure is 14 which we obtain by inscribed angle is half of the intercepted arc.
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Step-by-step explanation:
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h2 = ?
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Step-by-step explanation:
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Step-by-step explanation:
See the steps below:)
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Answer:
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Answers
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Step-by-step explanation:
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Answers
Answer:
A ∩ B = {4, 6}
Step-by-step explanation:
A die had 6 faces
S = {1, 2, 3, 4, 5, 6}
If A be the event of rolling an even number, then;
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mean=11
X=
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Statistics
Vocabulary
-------------------------
Mean is the average of a data set.
Find the Mean by adding all numbers and dividing by how many numbers there are in the data set.
19+4+12+4+x/5
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Step-by-step explanation:
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Answers
Solution :
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Answer:
angle 1=127 degree
angle 3=127 degree
angle 2=53 degree
angle 4=53 degree
angle 5=37 degree
angle 6=90 degree
angle 7=53 degree
angle 8=37 degree
angle 9=37 degree
angle 10=143 degree
angle 11=37 degree
angle 12=143 degree
Step-by-step explanation:
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Answer: I think it’s C
Answer:
A is the correct answer to this problem.
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Answers
Answer:
r/2 -6
Step-by-step explanation:
less than means it comes after
half of r
r/2
6 less than means subtract
r/2 -6
Part II: Constructed Response (2 pt)
4) (LT #5) One of the games at a carnival involves trying to ring a bell with a ball by hitting a
lever that propels the ball into the air. The height of the ball is modeled by the equation
h(t) = -10t2 + 30t. If the bell is 25 ft above the ground, will it be hit by the ball. Explain or justify
your response
Students, draw anywhere on this side!
Answers
Answer:
here hereh ehreh ehe
Step-by-step explanation:
I made some brownies and cookies to sell for a local fundraiser. The cookies sold for $0.75 each and the brownies sold for $1.25 each. If I sold 51 baked goods and made $53.25 from the bake sale, which item’s sales made the most money? Cookies Brownies
Answers
Answer:
Brownies made the most money
Step-by-step explanation:
Let c = cookies
b = brownies
We sold 51 items so c+b = 51
Cookies are .75 and brownies are 1.25
.75c + 1.25 b = 53.25
We have 2 equations and 2 unknowns
c = 51-b
Substituting into the second equation
.75(51-b) + 1.25b = 53.25
Distribute
38.25-.75b +1.25b = 53.25
Combine like terms
38.25+.5b = 53.25
Subtract 38.25 from each side
38.25 +.5b -38.25 = 53.25 -38.25
.5b =15
Divide each side by .5
.5b/.5 = 15/.5
b = 30
Now find c
c =51-b
c = 51-30
c = 21
They sold 30 brownies and 21 cookies
30 brownies * 1.25 =37.50
21 cookies *.75 = 15.75
Brownies made the most money