Answers
Answer: see proof below
Step-by-step explanation:
Use the following Power Reducing Identities:
[tex]\cos^2 A = \dfrac{1}{2}(1 + \cos 2A)\\\\\sin^2 A = \dfrac{1}{2}(1 - \cos 2A)[/tex]
Use the following Product to Sum Identity:
[tex]\cos A\cdot \cos B=\dfrac{1}{2}\bigg[\cos(A+B)+\cos(A-B)\bigg][/tex]
Proof LHS → RHS
[tex]\text{LHS:}\qquad \qquad \qquad \cos^2\beta\cdot \sin^4\beta\\.\qquad \qquad \qquad =\cos^2\beta\cdot \sin^2\beta\cdot \sin^2 \beta[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{1}{2}\bigg(1+\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\dfrac{1}{2}\bigg(1-\cos 2\beta\bigg)\\\\\\.\qquad \qquad \qquad \quad =\dfrac{1}{8}(1+\cos 2\beta)(1-\cos 2\beta)(1-\cos 2\beta)[/tex]
[tex]\text{Expand:}\qquad \qquad \dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^3 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{8}\bigg(1-\cos 2\beta-\cos^2 2\beta+\cos^2 2\beta \cdot \cos \2\beta\bigg)[/tex]
[tex]\text{Power Reducing:}\qquad \dfrac{1}{8}\bigg(1-\cos 2\beta -\dfrac{1}{2}(1+\cos 4\beta)+\dfrac{1}{2}(1+\cos 4\beta)\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(2-2\cos 2\beta -1-\cos 4\beta +\cos 2\beta +\cos 4\beta \cdot \cos 2\beta \bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta+\cos 4\beta \cdot \cos 2\beta \bigg)[/tex]
[tex]\text{Product to Sum:}\quad \dfrac{1}{16}\bigg(1-\cos 2\beta -\cos 4\beta +\dfrac{1}{2}[\cos(4\beta+2\beta)+\cos (4\beta-2\beta)]\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(2-2\cos 2\beta -2\cos 4\beta +\cos 6\beta +\cos 2\beta\bigg)\\\\.\qquad \qquad \qquad =\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]
[tex]\text{LHS=RHS:}\\ \dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)=\dfrac{1}{32}\bigg(\cos 6\beta-2\cos 4\beta -\cos 2\beta +2 \bigg)[/tex]
Related Questions
solve the equation for x. x/3 = (2x + 3)/7A. B. 2 C. 3 D. 3/7 E. -3
Answers
Answer:
x = 9Step-by-step explanation:
[tex] \frac{x}{3} = \frac{2x + 3}{7} [/tex]
Cross multiply
That's
7x = 3( 2x + 3)
Multiply the terms
That's
7x = 6x + 9
Subtract 6x from both sides
We have
7x - 6x = 6x - 6x + 9
Simplify
We have the final answer as
x = 9Hope this helps you
2x + 3 = -7
What is the answer?
Answers
-3=-7-3=-10
2x=-10
X=-5
Answer:
x = -5
Step-by-step explanation:
Original Equation: 2x + 3 = -7
Subtract 3 from both sides:
2x + 3 - 3 = -7 - 3
Simplify:
2x = -10
Divide both sides by 2:
[tex] \frac{2x}{2} = \frac{ - 10}{2} [/tex]
Simplify:
x = -5
You are a contractor and charge $45 for a site visit plus an additional $24 per hour for each hour you spend working at the site. Write and solve an equation to determine how many total hours you have to work to earn $810 working at two separate work sites. Let the number of hours you work be y.
Answers
Answer:
Equation: 810= (90 + 24y)
y = 30 hours
Step-by-step explanation:
Given:
Site visit = $45 per site
cost per hour worked = $24
for each work site, the total amount of money earned
= site visit fee + cost for working
But the question mentions TWO sites, hence there will be two site visits. Therefore for TWO sites, we have to account for TWO site visit fee.
Therefore for TWO sites, the total amount of money earned
= site 1 visit fee + site 2 visit fee + cost for working
= (2 x site visit fee) + cost for working ------ Equation 1
We are further given that we worked y hours at the hourly work rate of $24 per hour.
Hence the cost for working
= y hours x hourly rate
= y x $24
= $24y (substituting this into equation 1 above)
for TWO sites, the total amount of money earned
= (2 x site visit fee) + cost for working
= (2 x $45) + $24y
= $90 + $24y
= $(90 + 24y)
We are also given that we have to earn $810 for two sites, hence
810 = 90 + 24y
810 - 90 = 24y
24y = 720
y = 720/24
y = 30 hours
For Thanksgiving, a family of 9 is trying to share 4 store-bought pies fairly. If each pie is pre-cut into 8 slices, and everyone gets the same number of slices, how many slices will be left over?
Answers
Answer:
5
Step-by-step explanation:
The largest prime factor of thirty-five is _____. 7 5 9 11
Answers
Answer:
7
Step-by-step explanation:
Since 9 and 11 do not factor 35, they are not the answer.
5 is a factor of 35, but not the largest. So, the answer is 7.
Answer:
the largest prime factor of 35 is 5
Find the slope of each line defined below and compare their values.
Equation of Line A:
-1=
(x – 6)
Graph of Line B:
10
7
6
5
3
2
-Q-
8-7-6
-5
-3
-2 -1
2
3
4
5
6
8
to
g
-3
The slope of Line A is
and the slope of Line B is
Therefore the slope
of Line A is
the slope of Line B.
Answers
Step-by-step explanation:
The equation of line A:
y - 1 = 0.5x - 3
y = 0.5x - 2. Hence its gradient is 0.5.
For line B, its y intercept is -8, so y = mx - 8.
When x = -4, y = -4m - 8 = 0 as shown in the graph. This means that m = -2.
So the equation of line B:
y = -2x - 8. Its gradient is -2.
Since |-2| > |0.5|, line B is steeper than line A.
The slope of the line A(1/2) > slope of line B(2).
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Take Points from the graph as (-4, 0) and (0, 8)
so, the slope is
m = (8-0)(0-(-4))
m = 8/ 4
m = 2
So, the slope- intercept form
y- 0 = 2(x- (-4))
y= 2x + 8
Hence, the slope of the line A(1/2) > slope of line B(2).
Learn more about slope here:
https://brainly.com/question/3605446
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The distance to the sun in inches is 1.116 x 10^9 How many fireflies would it take to reach the sun if they were put end to end?
show work please
Answers
Answer:
THE DISTANCE OF SUB IS 5892480000000IN
1MI=63630 IN
930000000MI=93000000×63360 IN=589248000000IN
X=NUMBER OF FIREFLIES
X=0.4IN=5892480000000IN
X=58924800000000IN×0.4IN
X=147312000000000
Answer:
This is wrong, I used this answer too and it was wrong.
Step-by-step explanation:
What is the ratio of 1:2 of 1250
Answers
12500 skiers and 2500 snowboarders!
In which graph is y a direct variation of x?
A.
B.
C.
D.
Answers
Answer:
D
Step-by-step explanation:
The line is going through the origin.
In the visit to the Old Folks' Home last weekend, Alice spent time chatting with Mr Han and helping him with simple chores. She found that Mr Han is 36 years older than her. 7 years later, Mr Han will be 3 times as old as her. How old is Mr Han now?
Answers
I think Mr. Han is around the 60 or 70 age.
I am really sorry that I couldn't answer this problem. Try starting with 21 and multiply that by 3. To check if you can do it, add 43 to the number you multiply 3 with. Again, i am really sorry that i only wrote a hint. Good luck finding the answer!
Now the age of Mr. Han will be 54 years old.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Let x be the age of Mr. Han and y be the age of Alice.
She found that Han is 36 years older than her. Then the equation will be
x = y + 36 ...1
7 years later, Han will be 3 times as old as her. Then the equation will be
(x + 7) = 3(y + 7)
x = 3y + 14 ...2
From equations 1 and 2, we have
3y + 14 = y + 36
2y = 22
y = 11
Then the value of x will be
x = 11 + 36
x = 47
The age of Mr. Han will be
⇒ 47 + 7
⇒ 54
Now the age of Mr. Han will be 54 years old.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
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PLEASE HELP ME! How do I find x?????????
Answers
Answer:
Here you have to use the vertically opposite angle
your answer is 35
because vertically opposite angles are equal
x=35
Step-by-step explanation:
Answer:
x = 35
Step-by-step explanation:
X and 35 are vertical angles and vertical angles are equal
WILL GIVE BRAINLET !!
2/6 + - 5/12 ( show how u get the answer )
Answers
Answer:
[tex]-\frac{1}{12}[/tex]
Step-by-step explanation:
So we have the expression:
[tex]\frac{2}{6}-\frac{5}{12}[/tex]
To subtract, we want to have a common denominator. So, let's find a common denominator by using the LCM.
The LCM of 6 and 12 is 12.
Since the second term is already 12, let's multiply the first term by 2 to get its denominator to be 12:
[tex]=(\frac{2}{2})\frac{2}{6}-\frac{5}{12}[/tex]
Multiply:
[tex]=\frac{4}{12}-\frac{5}{12}[/tex]
Now, we can combine the fractions:
[tex]=\frac{4-5}{12}[/tex]
Subtract:
[tex]=\frac{-1}{12}[/tex]
And we are done!
Ryan has a collection of 220 baseball cards he letshis brother have 1/4 of his collection until 20% of his collection to the baseball card shop she takes 15 cards to school to give his friend how many baseball cards remaining Ryan's collection
Answers
Stu had quite a collection of baseball cards. One day he decided to give half of them to his brother Seth. Then he gave one-third of what he had left to a friend. Then he gave half of what was left to another friend. Stu now has 50 baseball cards. How many did he start with? It seems that I should work
let Stu have x cards
he gave half to seth
so he had x/2 cards
He had x/2 he gave 1/3 of x/2 to a friend
=x/6.
Now he had x/2 - x/6 = x/3 with him balance
1/2 of x/3 he gave to another friend =x/6
Balance he had was x/3 - x/6 = x/6
x/6 = 50
multiply by 6
x= 300
Answer:
Now he had x/2 - x/6 = x/3 with him balance
1/2 of x/3 he gave to another friend =x/6
Balance he had was x/3 - x/6 = x/6
x/6 = 50
multiply by 6
x= 300
Step-by-step explanation:
I can collect 1.6 pecks of chile peppers a day. How many liters or peppers could I collect in a week?
Answers
Answer:
11.2
Step-by-step explanation:
multiply 1.6 by 7 since that's how many days there are in a week
Answer:
11.2
Step-by-step explanation:
you collect 1.6 packs of chile peppers a day there is 7 days in a week 1.6x7=11.2
hope it helps.
I’m stuck on this question
Answers
Answer:
x= 0.4
Step-by-step explanation:
x^2 = 4/25 (0.16)
x = 0.4 Square root both sides
A football team lost 5 yards on each of 3 plays.Explain how you could use a number line to find the teams change in field position after 3 plays.Then find and interpret the change in position
Answers
Answer:
Kindly check explanation and attached picture
Step-by-step explanation:
Given that:
A football team lost 5 yards on each of 3 plays
Using a number line we could show the loss in yard after each play. With a loss of 5 yards after each play, there will be a total of:
(Number of plays * yards lost) = (3 * 5) = 15 yards
The attached picture shows a number line moving a distance of 5 yards to the left ( negative direction) after each play after which it arrives at a total loss of 15 yards after the third play.
I need the answer and the work (it’s geometry)
Answers
Answer:
D
Step-by-step explanation:
The starting point is B and the ray extends towards A.
So the asnwer is D.
Pls help me on this question ASAP I wil make the anyone who can answer this for me the brainliest
Answers
Answer:
Forget it, i'm confused
Step-by-step explanation:
(3x+2)+(5x-5)=8x-3
(17x-7)-(8x-3)=9x-10
Double Check
9x-10+5x-5+3x+2
17x-15+2
17x-13
when twelve is subtracted from three times a certain number and the number and the is divided by four, the answer is eighteen. find the number?
Answers
Answer:
[tex]<font color=pink>[/tex]
According to the question, we get the equation :
[tex]<font color=blue>[/tex]
3x-12=18
[tex]<font color=black>[/tex]
⛈Let's find x :
[tex]3x - 12 = 18 \\ ⟹ 3x = 18 + 12 \\ ⟹ x = \frac{30}{3} \\ ⟹x = 10[/tex]
Hope you understand
Randy walks his dog each morning. He walks StartFraction 7 Over 12 EndFraction of a mile in 7 minutes. How many miles does he walk in 1 minute?
i found the answer its 1/12 you just dived 7 and 7 and then leave the bottom number alone, and then what do you get 1/12.
Answers
Answer:
1/12
Step-by-step explanation:
Answer:
1/12
Step-by-step explanation:
I got the question purposely wrong so I could see the right answer
an apple orchard sells apples in a bags of 10. the orchard sold a total of 20,430 apples in one day. how many bags of apples was it
Answers
Answer:
2043
Step-by-step explanation:
you divide 20430 by 10 and you get your answer
What time is 3 ¾ hours after 10:37 pm? ( Your answer must contain am or pm )
Answers
Answer:
2:23
Step-by-step explanation:
Answer:
10:37 pm + 3 3/4 hours = 2:22 am
Step-by-step explanation:
10:37
3: 45
2:22
+ :23 minutes from 3:45 to 10:37, which gets you to 11 pm, leaves you with 3 hours and 22 minutes
11pm + 3:22= 2:22 am
Cindy brought chocolate and vanilla cupcakes to school for her birthday. 15 students decided to take a cupcake, and 9 of them picked vanilla. What percentage of the students picked a vanilla cupcake?
Answers
Answer:
37.5%
Step-by-step explanation:
There are 24 students that decided to pick a cupcake at all. 9 out of 24 students chose vanilla. Therefore, 37.5% of students chose vanilla.
It's a staple of American school lunches: peanut butter sandwiches (usually with jelly, too). The average American child will eat 1500 peanut butter sandwiches by the time she graduates from high school! (On average, that's one sandwich every four days.) It takes 850 peanuts to make an 18-oz jar of peanut butter, and an average sandwich has two ounces of peanut butter on it. How many peanuts will be needed to make all of the sandwiches a child will eat by graduation?
Answers
Answer:
The number of peanuts that will be needed to make all the sandwiches a child will eat by graduation is approximately 141,667 peanuts
Step-by-step explanation:
The number of peanut butter sandwiches that an average American child will eat by the time she graduates from high school = 1500 peanut butter sandwiches
The number of sandwich taken every four days = 1 sandwich
The number of peanuts required to make 18-oz jar of peanut butter = 850 peanuts
The amount of peanut butter in an average sandwich = Two ounces
Therefore, we have by the time of graduation;
Each American child will have taken 1500 sandwiches
The 1500 sandwiches will have = 1500 × 2 ounce = 3,000 ounces of peanut butter
The number of 18-oz jars of peanut butter that will contain up to 3000-oz of peanut butter = 3000-oz/(18-oz) = 166.67 Jars
The number of peanuts required to make the 166.67 Jars of peanut butter = 850 peanuts/jar × 166.67 Jars = 141666.67 ≈ 141,667 peanuts
The number of peanuts that will be needed to make all the sandwiches a child will eat by graduation ≈ 141,667 peanuts.
Please help with d. Thank you!!
Answers
Step by step is below
Solve for n: 4n = 2n + 6
A. 1
B. 2
C. 3
D. 4
E. 12
Answers
2n=6
n=6/2
n=3
Your answer is C. 3
D
B
8 cm
8 cm
16 cm
С
Find the area of triangle ABC.
Answers
What is the x-value in the solution to this system of linear equations? 2x − y = 11 x + 3y = −5
Answers
Answer:
x = 4
Step-by-step explanation:
Given the 2 equations
2x - y = 11 → (1)
x + 3y = - 5 → (2)
Multiply (1) by 3 and add to (2) to eliminate the y- term
6x - 3y = 33 → (3)
Add (2) and (3) term by term to eliminate y, that is
7x = 28 ( divide both sides by 7 )
x = 4
Answer:
x-4
Step-by-step explanation:
79,000 people live in a circular region with a population density of 513 people per square mile. What is the radius of the region
Answers
Answer:
step by step
Step-by-step explanation:
the answer is 7
I’m literally begging someone please help (just number 10. show work)
Answers
Answer:
[tex]h = \frac{2A}{b +B } [/tex]
Height= 16 feet
Step-by-step explanation:
Please see attached picture for full solution.