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]
Related Questions
Answer each question and round your answer to the nearest whole number
Answers
Explanation:
Let the width and height of the original triangle be w1 and h1
w1 = 5 in
h1 = 4 in
Let the width and height of the enlarged triangle be w2 and h2
w2 = 25 in
h2 = ?
(Since the triangles are similar, we can use the ratio of the given sides)
h2 / h1 = w2 / w1
h2 / 4 = 25 / 5
h2 / 4 = 5
h2 = 5 x 4
h2 = 20 in
pupils are required to spend 3/8 of the day at school and 2/3 of that time in class. How much time do they spend doing Mathematics? Give your answer in minutes.
Answers
Answer:
[tex]Time \ in\ school = \frac{3}{8} \ of \ the \ day[/tex]
= [tex]\frac{3}{8} \times 24 = 9 \ hours \ in \ school[/tex]
[tex]Time \ in \ class = \frac{2}{3} \ of \ the \ time \ in \ school = \frac{2}{3} \times 9 = 6 \ hours \ in \ class[/tex]
1 hour = 60 minutes
Therefore, 6 hours = 360 minutes
So , 360 minutes they spent doing mathematics.
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:
A fair die is rolled once. Let A be the event of rolling an even number, and let B be the event of rolling a number greater than 3. Find A ∩ B
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;
A = {2, 4, 6}
If B be the event of rolling a number greater than 3, then;
B = {4, 5, 6}
A ∩ B are the values that are common to both sets
A ∩ B = {4, 6}
6 less than half of r : translate into expression
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
What is the value of x in the equation
-x =2 - 3x +6?
1) 8
2) 4
3) -4
4) -8
Answers
Answer:
x=4 Postive
Step-by-step explanation:
See the steps below:)
19,X, 4, 12,4
mean=11
X=
Answers
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
Combine Like Terms.
39+x/5=11
Use random x values to determine x.
39+16=55
55/5=11
x=16
Insert x into the equation to make sure you're correct.
19+16+4+4+12=55
55/5=11
In a class of students, the following data table summarizes how many students passed
a test and complete the homework due the day of the test. What is the probability that
a student chosen randomly from the class did not complete the homework?
Answers
Answer:
3/16
Step-by-step explanation:
The total number of students = no. of students passed + number of students who failed.
i.e, 13+3=16
probability = 3/16 = 0.1875
Hope u understand
Please mark as the brainliest
Thank You
Pls i need help on these I HAVE BEEN STUCK
Answers
Answer:
5. D
6. B
7. B
Step-by-step explanation:
At his new job, Jeremiah can choose an hourly rate of $9 plus a $50 weekly bonus for opening the store, or an hourly rate of $10 per hour with no opening bonus. The equations model his salary options.
Answers
y=9x +50
y=10x
The coordinates of points A and B are?
Answers
B.) (-1, 3) , (3, 2)
Step-by-step explanation:
Not sure how to explan...
Answer: B: 3,2 A: -1,3
Step-by-step explanation:
PLS HELL
please tell me the answer and explain how you got it ty
Answers
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,
Now, we need to know how many values were above 30.
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.
In 30-45 we have a frequency of 3.
In 45-60 we have a frequency of 2.
In 60-75 we have a frequency of 2.
To find the amount of values above 30, we must add these all together:
3+2+2
=
7
So 7 values have a price above 30!
Hope this helps!
What is the value of x?
K
83°
L
M
(9x + 40)
Answers
Answer:
This inscribed angle is half of the intercepted arc JL, so 2(83)= 9x +40.
166 -40 = 9x, x=14.
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.
The inscribed angle is half of the intercepted arc.
83 = 1/2(9x+40)
Now let us find the value for x
83= 9/2x + 20
Subtract 20 from both sides to isolate the x variable
83-20=9/2x
63=9/2x
126=9x
Divide both sides by 9
14 is value of x
x=14
To learn more on Angles click:
https://brainly.com/question/28451077
#SPJ2
The ratio of two radii of two spheres is 15:8. If the surface area of larger sphere is 706.9 mm2, fine the surface area of the smaller sphere.
Answers
Answer:
201.1 mm²
Step-by-step explanation:
Smaller sphere = 8
Larger sphere = 15
Larger sphere surface area = 706.9 mm²
Smaller sphere surface area = x
Hence:
Since we are dealing with surface area
8²/15² = x/ 706.9
Cross Multiply
15² × x = 706.9 × 8²
x = 706.9 × 8²/15²
x = 201.07377778 mm²
x ≈ 201.1 mm²
Therefore, the surface area of the smaller sphere is 201.1 mm²
Solve the following system.
y = -2x 2 + 3x - 1 and x + y = -1.
The solutions are
and
Answers
x = 0, y = -1
x = 2, y = -3
Step-by-step explanation:
Pls help no links pls this is due and i need help
Answers
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:
Please answer!!
I’ll give brainlist!
Answers
Answer:
1st Question: 15 2nd Question: 52
Step-by-step explanation:
Each shape is a right triangle, that means it's 90 degrees. If you subtract the number shown by 90, you will have your missing value.
What is the volume of a hollow ball whose other radius is 200m and inner radius of 100m? What is the mass if it is iron?
Answers
Solution :
Volume of ball = Volume of outer ball - Volume of inner ball
[tex]V = \dfrac{4\pi R^3}{3} - \dfrac{4 \pi r^3}{3}\\\\V = \dfrac{4\pi}{3}( R^3 - r^3 )\\\\V = \dfrac{4\pi}{3}( 200^3 - 100^3 )\\\\V = \dfrac{4\pi}{3}(2^3 - 1^3) \times 10^6\\\\V = 2.93 \times 10^7 \ m^3[/tex]
Now, density of iron is, d = 7300 kg/m³.
So, mass of iron ball is :
[tex]m = d\times V\\\\m = 7300\times 2.93 \times 10^7 \ kg\\\\m = 2.14 \times 10^{11}\ kg[/tex]
Hence, this is the required solution.
Which of the following are maximum and minimum points of the function y= 2 cos x - 1?
A) Maximums: (0, 3), (2π, 3); Minimum: (π, -3)
B) Maximums: (0, 1), (2π, 1); Minimum: (π, -3)
C) Maximums: (0,3), (2π, 3); Minimum: (π, -1)
D) Maximums: (0, 1) (π/2, 1); Minimum: (3^π/2, -3)
Answers
Answer:
B) Maximums: (0, 1), (2π, 1);
Minimum: (π, -3)
In which function is the range equal to the domain?
1) y = 2
2) y=x?
3) y = log x
4) y = x
Answers
Please help me almost due!!!:):$:
Answers
Answer:
Our two selected points:
-3, 3
2, -4
-4 -(3) 7
_____ = - _____ = -7/5, D is your answer
2 - (-3) 5
How does this make you feel?
Answers
Answer:
sad to be honest
Step-by-step explanation:
Answer:
yo lemme stand in that dark door way
there
Step-by-step explanation:
The slope of the line below is -4. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y-side.
(-2, 2)
Answers
Answer:
y - 2 = - 4(x + 2)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Here m = - 4 and (a, b) = (- 2, 2 ) , then
y - 2 = - 4(x - (- 2) ) , that is
y - 2 = - 4(x + 2)
I just need someone to help me with this, I will give brainilist I just need someone to put these numbers in the correct order!!!!!!!
Answers
Answer: I think it’s C
Answer:
A is the correct answer to this problem.
Pls help me! Look at this ss
Answers
Answer:
4
Step-by-step explanation:
Given that Δ C A T ≅ Δ D O G, select all statements that must be true
Answers
reduce 287/861 to the simplest term in fractions
Answers
Answer:
1/3
hope this helps
have a good day :)
Step-by-step explanation:
I need help with the answer immediately!!!!!
Answers
Answer:
y= - 1/6x + 2
Step-by-step explanation:
I know you need it quick
This is the correct answer
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
The height of a refrigerator would be about?
A. 7 inches
B. 7 feet
C. 7 yards
D. 7 miles
Answers
Answer:
i think its b) 7 feet
Step-by-step explanation: