use a power reduction identity to simplify 8cos^4x

Answers

Answer 1
The answer to a power reduction to simply 8cos^4x is 2(cos2a + 1)^2
Answer 2

The simplified value is 8*cos^4(x) = 3+ 4 cos2x + cos 4x.

What is power reduction identity?

The trigonometric power reduction identities allow us to rewrite expressions involving trigonometric terms with trigonometric terms of smaller powers. This becomes important in several applications such as integrating powers of trigonometric expressions in calculus.

Given:

Using the power reduction identity, we have that:

cos² x= 1/2( 1+ cos 2x)

cos^4(x) = (cos² x)²= (1/2( 1+ cos 2x))²

cos^4(x) =  1/4( 1+ cos² 2x+ 2 cos (2x))

Again, cos² 2x= 1/2( 1+ cos 4x)

cos^4(x) =  1/4( 1+ 1/2( 1+ cos 4x)+ 2 cos (2x))

cos^4(x) =  1/4( 1+ 1/2 +1/2 cos 4x+ 2 cos (2x))

cos^4(x) =  1/4( 3/2 + 2 cos2x + 1/2 cos 4x)

8*cos^4(x) =  8*1/4( 3/2 + 2 cos2x + 1/2 cos 4x)

8*cos^4(x) =  2( 3/2 + 2 cos2x + 1/2 cos 4x)

8*cos^4(x) = 3+ 4 cos2x + cos 4x

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Related Questions

describe fully the single transformation that maps triangle a onto triangle b

Answers

Answer:

Reflection about y=2

Step-by-step explanation:

Triangle A should be reflected about y=2 to map it onto Triangle B.

Answer:

reflection across y=2

Step-by-step explanation:

can someone do my ixl its 6th grade math!! only 3 and you have to get 85 and higher i will give 25 points!! and mark as brainlist

Answers

Answer:

Okkk I will answer

Answer:

what question do you have?

Step-by-step explanation:

21) Natalie kicked a soccer ball. The equation ℎ=−162+50 describes the height of the ball t seconds after it was kicked. Approximately how many seconds went by before the ball hit the ground?

Answers

25/8 or 3.125 seconds

To find the time until the ball hits the ground, you need to solve the quadratic as the height equals zero.

0 = -16t^2+50t

This gives us a classing quadratic that you can factor or use the quadratic formula to solve.

x = 0, x = 25/8

If you graph this, think of y = 0 as the ground, so when the parabola intersects the x-axis on the right that represents how much time would have passed.

Hope this helps you out! Good luck with your homework! Stay safe and stay healthy.

what is 9x=4.5 if u can solve this u are very smart

Answers

Answer:

x = 1/2

Step-by-step explanation:

9x=4.5

Divide each side by 9

9x/9 = 4.5/9

x = 45/90

x = 1/2

Answer:

x = 1/2 or x = 0.5

Step-by-step explanation:

9x = 4.5/9

= 45/90

= 1/2 or 0.5

Hope this helps, and please mark me brainliest if it does!

Please answer correctly !!!!! Will mark brainliest !!!!!!!!

Answers

Answer:

k(-7) = = -89

Step-by-step explanation:

k(t) = 10t -19

Let t = -7

k(-7) = 10*-7 -19

      = -70-19

      = -89

Answer:

-89

Step-by-step explanation:

K(t) = K(-7)

10 is being multiplied by t. t = -7

so:

10(-7) = -70

-70 - 19 = -89

Hope this helps!

Simplify the following expression (x-8y)-(2x-4y)

Answers

Answer:

-x - 12y

Step-by-step explanation:

(x-8y)-(2x-4y)=

x-8y-2x-4y=

x-2x-8y-4y=

-x - 12y

Answer: -x - 4y

Step-by-step explanation:

(x-8y)-(2x-4y)

x-8y-2x+4y

-x-4y

Here is a map of a town.
The map shows a centimetre ruler.
5 km is represented by 1 cm.
Find the real-life distance between the ice rink and the museum.

Answers

Answer:

10km

Step-by-step explanation:

2x5=10km

Alegbra 4 questions giving brainlist!

Answers

Answer:

1) 4

2) 1

3) -7

4) 13

Step-by-step explanation:

Instructions:

a) Subtract or add the slope from each side

( it doesn't matter which one you pick )

b) Subtract or add the # next to the slope from each side

( it doesn't matter which one you pick )

c) Divide Each number by the slope

d You have you answer

____________________________________________

1) 9x - 35 = - 7x + 29

+7x + 7x

_____________________

16x - 35 = 29

+ 35 +35

_____________________

16x = 64

_____________________

16 16

x = 4

2). - 2x - 2 = 9x - 13

+2x +2x

_____________________

- 2 = 11x - 13

+ 13 + 13

_____________________

11 = 11x

_____________________

11 11

1 = x

3). 3x + 29 = - 5x - 27

+5x + 5x

_____________________

8x + 29 = - 27

-29 -29

_____________________

8x = -56

_____________________

8 8

x = -7

4). x - 11 = 3x - 37

- x - x

______________________

-11 = 2x - 37

+37 +37

______________________

26 = 2x

_______________________

2 2

13 = x

Hope this helps! (:

damian rides his bike 38 miles each week for 15 weeks how many total miles did he ride in 15 weeks

Answers

Answer:

570 miles

Step-by-step explanation:

If Damian rides 38 each week and we want to know how much it was for 15 weeks, then we just multiply the two to get 570 miles in a 15 week period.

Answer:570

Step-by-step explanation:

38 times 15= 570

Please answer correctly !!!! Will mark brainliest !!!!!!!!!

Answers

Answer:

[tex]=\left(x-4\right)^2[/tex]

Step-by-step explanation:

[tex]x^2-8x+16\\\mathrm{Rewrite\:}x^2-8x+16\mathrm{\:as\:}x^2-2x\cdot \:4+4^2\\x^2-8x+16\\\mathrm{Rewrite\:}16\mathrm{\:as\:}4^2\\=x^2-8x+4^2\\\mathrm{Rewrite\:}8x\mathrm{\:as\:}2x\cdot \:4\\=x^2-2x\cdot \:4+4^2\\\mathrm{Apply\:Perfect\:Square\:Formula}:\quad \left(a-b\right)^2=a^2-2ab+b^2\\a=x,\:b=4\\=\left(x-4\right)^2[/tex]

Answer:

0

Step-by-step explanation:

Since it is asking you to factor out the quadratic, you need to make it equal zero first. -4 times -4 is both 16 and -8. So that means (x-4)^2

Which expression has a value of 15 when n=7 ?

Answers

19-28/n

n=7

19-28/7

19-4

=15

Answer:

d for the lazy people like me  :D PROPS TO THE PERSON ON TOP OF ME

Step-by-step explanation:

You need to solve a system of equations. You decide to use the elimination
method. Which of these is not allowed?
3x-2y = 7 Equation 1
3x+4y= 17 Equation 2
A. Subtract equation 2 from equation 1.
B. Subtract the left side of equation 2 from the left side of equation
1.
C. Multiply equation 1 by 2. Then add the new equation to equation
2.

Answers

Answer:

Step-by-step explanation:

Both B and C would be using e

Option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two linear equations or systems of equations:

3x-2y = 7 Equation 1

3x+4y= 17 Equation 2

As we know, in the elimination method:

We try to eliminate the variables at a time by making a similar coefficient of the x or y.

In option (B) Subtract the left side of equation 2 from the left side of equation 1.

It is not allowed to perform because first, we have to make the coefficient of y similar.

Thus, option (B) Subtracting the left side of equation 2 from the left side of equation 1 would be the correct choice.

Learn more about the linear equation here:

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1. Uma escada possui comprimento igual a 30m. Sabe-se que ela se encontra encostada em um muro, formando com este um ângulo de 60º. Podemos afirmar que a altura da escada, em m. é igual am:

Answers

Answer:

The height of the ladder is 15 meters.

Step-by-step explanation:

To find the height of the ladder, we just need to use the cosine relation of the 60 degrees angle.

The adjacent side to the angle is the height of the ladder, and the hypotenuse of the triangle created is the length of the ladder. So, we have that:

cos(60) = height / length

0.5 = height / 30

height = 30 * 0.5 = 15 meters

The height of the ladder is 15 meters.

To number the apartments in a building, metal plates with digits were used: one digit on each plate. How many plates were used to number 136 apartments in the building?

Answers

Answer:

301 plates

Step-by-step explanation:

For numbers between 0 and 9, 1 plate was used each.

This means that 10 plates were used.

For numbers between 10 and 99, 2 plates were used for each.

This means that the number of plates used will be:

2 * 90 = 180 plates

For numbers between 100 and 136, 3 plates were used for each.

This means that the number of plates used is:

3 * 37 = 111 plates

The total number of plates used is therefore:

10 + 180 + 111 = 301 plates

301 plates were used in total.

Pleaseee help meee struggling currently

Answers

Answer: 2908.92435 inches.

Step-by-step explanation for shape 1: A = 2(wl + hl + hw) = 2 · (30 · 13 + 13 · 13 + 13 · 30) = 1,898 inches.

Step-by-step explanation for shape 2:

Using the formulas:

A=2AB+(a+b+c)h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c

2

Solving for A:

A=ah+bh+ch+1

2﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4=9·30+13·30+9·30+1

2·﹣94+2·(9·13)2+2·(9·9)2﹣134+2·(13·9)2﹣94≈1010.92435

Step-by-step explanation for total volume: 2908.92435 inches.

Answer: 6825 in^3

Step-by-step explanation:

First divided the whole shape into two shapes.

The first shape will be a rectangular prism and the second shape will be a triangular prism.

The rectangular prism will have a length of 13, a width of 30 and the height of 13.

Now find the volume of the rectangular prism by multiplying the length by the width then by the height.

V= 13 * 30 * 13

V = 5070

This means the volume of the rectangular prism is 5070 cubic inches.

Now will will need to find the volume of the triangular prism.

The triangular prism has a triangle at the base, with a base of 9 and a height of 13. If you multiply the the area of the base by the whole height of the triangular prism which is 30 then you will get the volume.

Find the area of the base.

The area  is base time height times 1/2.

A = 9 * 13 * 1/2

A =  58.5  

Now multiply the area by 30.

58.5 * 30 = 1775

Finally, add both volumes to find the full volume of the figure.

5070 + 1775 = 6825

whats the answer to 5^-2

Answers

Hey!!

Solution,

(5)^-2

=1/5^2

=1/25

The answer is 1/25

hope it helps

Good luck on your assignment

If 48 % of students in a certain college are female and there are 1,440 female students, what is the total number of students in the college? Please show work

Answers

Answer:

The total number of students in the college is 3,000.

Step-by-step explanation:

[tex]\frac{48}{100}=\frac{1,440}{x}[/tex]               Set up a proportion.

[tex]48x=144,000[/tex]         Cross-multiply.

[tex]x=3,000[/tex]                 Divide both sides by 48.

What segment is a reflection of segment ab over the line x=1

Answers

Answer:

    The correct answer is: (Line segment E F)

Need help ASAP!! Thank youu!

Answers

Answer:

The answer is 7.

Step-by-step explanation:

If you want to find what FE is, you have subtract GF from GE (GE - GF = FE).

Since GE = 13 and GF = 6, you have to subtract 6 from 13 which equals 7.

(13 - 6 = 7)

Which ordered pair comes from the table?

Answers

Answer: A. (6,5)

Explanation: (6,5) is the only ordered pair that is in the table shown in the picture, which means it could not be any of the other ordered pairs.

Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
-3x + 3y = 9
2x – 7y = -14

Answers

Answer:

x= -7/5 y=8/5

Step-by-step explanation:

1. choose a variable to eliminate (i chose 6)

2. multiply the first equation by 2 and the second equation by 3

3. now you have

-6x+6y=18

6x-21y=-42

and the x's can now cancel out when you add the equations together

4. after adding the equations, you get

-15y=-24

5. solve for y (y= 8/5)

6. now plug in 8/5 for the y in one of the original equations to solve for x. (i chose the first one)

7. -3x+3(8/5)=9

-3x+24/5=9

-3x=21/5

x= -7/5

Can you pls help i really NEED IT

WANT BRAINIEST

Answers

Answer:

V =13/150 yd^3

Step-by-step explanation:

The volume of a rectangular prism is given by

V = l*w*h

V = 1/2*( 13/15)* 1/5

V =13/150 yd^3

Answer:

13\150 yd³

Step-by-step explanation:

V=height×weight×legth

1\2×13\15×1\5=13\150 yd³

Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym Two-thirds the distance from Ping's home to Ari's home.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

Where is the gym?

Answers

Answer: (15th street, 14th Avenue)

Step-by-step explanation:

Given the following :

Ping's residence = (3rd street, 6th Avenue)

Ari's residence = (21st street, 18th Avenue)

Gym location = 2/3 the distance of Ping's residence to Ari's residence

So, distance between Ping's home to Ari's home

Distance = (21st street, 18th Avenue) - (3rd street, 6th Avenue)

Distance = (21 - 3) street, (18 - 6) avenue

Distance between ping and Ari = (18th , 12th )

Gym distance = 2/3 of distance between ping and Ari

Gym distance = 2/3 × (18), 2/3 ×(12)

Gym distance = (12, 8)

Gym location = Ping's location + gym distance

Gym location = (3rd street, 6th Avenue) + (12th street, 8th Avenue)

Gym location = (15th street, 14th Avenue)

Answer:

d) 15th Street and 14th Avenue

This chart shows the growth of a maple tree. If the tree's height increases in this same pattern, what will be the height of the tree, in inches, after 8 months?



Months
Height of Tree
1
10 inches
2
13 inches
3
16 inches
4
19 inches

Answers

Answer:

31 inches

Step-by-step explanation:

you can get this answer by 2 ways. one is using number patterns.

find the difference between each of the heights.

13-10=3

16-13=3

19-16=3

therefore the common difference is 3

now create a number pattern.

first term + common difference× (n-1)= nth term

a+(n-1)d

let's check this with the 2nd month

10+ 3× (2-1)

10+3=13

in second month 13 inches

so this pattern works

let's find the height in 8th month

10+ 3(8-1)

10+ 21=31 inches

height in 8th month is 31 inches.

you can find this by just adding too. but forming an equation is always good and safe

find the coordinates of D' after a Glide reflection of the triangle: translation 1 unit up and 5 units left and reflection across y= 3. Write your answer in (a,b). Part 2a​

Answers

Answer:

D' = (-2, 1)

Step-by-step explanation:

Translating the point D one unit up and five units left moves it to (-2, 5)

Reflecting it across y=3 moves it from (-2, 5), to (-2, 1)

Answer:

D = (-2, 1)

This answer is 100% right hope it helps

will mark brainliest!! factor the following equation: f(x)=3x²+7x+2​

Answers

Answer:

(x + 2) (3x + 1)

Step-by-step explanation:

3x² + 7x + 2

3x² + 6x + x + 2

3x(x + 2) + 1(x + 2)

(x + 2) (3x + 1)

(X+2) (3x+1) is the answer!

2. A hemispherical water tank with a volume of 2094 m will have a radius of which
length?
?
a. 5 m
b. 25 m
c. 2.5 m
d. 10 m

Answers

2.5 m jsjwnejdogondbsjsofj find

Find the sum of the first eight terms of the geometric series 1 + 2 + 4 + ...

Answers

8 16 32 64 128 are the next four terms to the sequence

Answer:

The sum of all of the terms would be 255

Step-by-step explanation:You would continue to multiply all of the answers by 2 until you hit 128. Then you would add all of them together 128+64+32+16+8+4+2+1=255

The equation __ describes the relationship

Answers

Answer:

y= 1/3x

Step-by-step explanation:

points on the graph

(0,0), (3,1)

function as per above two points:

y= 1/3x

A box of 120 crayons contains variations of three colors: blue, red, and purple. The ratio of blue crayons to red crayons is 11:2, and the ratio of the number of red crayons to purple crayons is 2:7. If all of the purple crayons were removed, how many crayons would be left in the box?

Answers

Answer: there would be 106,am not sure

Step-by-step explanation:

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Doris Lessings childhood homes Julie needs to cut 4 pieces of yam, each with the same length, and a piece of yarn 7.75 inches long. Let x represent thelength of each of the equal pieces of yarn that Julie decides to cut. What is the equation that can be used to determine thetotal length of all of the yarn that she ends up cutting, y is the graph of the equation continuous or discrete? How would you like a cheese sandwich for lunch? Bread and cheese. A certain group of microorganisms is responsible, in part, for the production of both the bread and cheese we eat. These microorganisms are members of the kingdom PLEASE HELP ASAP URGENT!!!!! Which statement is true of AC current?A. It uses a battery as a power source.B.It can easily be transformed from high voltages to low voltages.C.It is typically low voltage.D.the electrons are moving in one directionE.It was the first type of electric current invented. five less than 2 times a number is equal to the sum of the number and 3. What is the number? Help, What is the answer? What are some current issues you feel are still a concern regarding your right to vote in the United States? Should non citizens be allowed to vote in the United States? Why or why not? Level 1R.18 Identify equivalent linear expressions II KARSelect the expressions that are equivalent to -7(75 + 1).75-77(-75 + 1)-7(-5 + 8 + 1)-7s - 49 what did thomsons model of the atom called A group of college students eager to get to Florida on a spring break drove the710-mitrip with only minimum stops. They computed their average speed for the trip to be55.7mi/h.How many hours did the trip take? Dorinda worked 2 part- time jobs and earned $234.50 for working a total of 30 hours at both jobs. She is paid $7.50 per hour at Job A and $8.00 per hour at Job B. How many hours did Dorinda work at Job A? State two characterstics of matter demostredbyDiffusion.) Brownian mation Sarah purchased a swing set for $1,450 using a six-month deferred payment plan. The interest rate after the introductory period is 19.99%. No down payment is required, but there is a minimum monthly payment of $20. What is the balance at the beginning of the seventh month if only the minimum payment is made each month during the introductory period Whats the correct answer for this question? Our current understanding of evolution is called a theory because itches been What was the ORIGINAL price of an item that cost $55.50 AFTER a 75%discount? * Lenders charge a loan origination fee to A. cover the expenses involved in generating the loan B. guard against charges of usury C. guard against losses in the event of a short sale D. cover the losses involved if the borrower repays the loan before the end of the loan term. A key problem for germany after the war, especially in rebuilding its economy, came fromA. Allied trade embargos B. Development of workers unionsC. Loss of the upper class D. High unemployment How many moles of iron(lll) sulfide, Fe2S3, would be produced from the complete reaction of 449 g iron(lll) bromide, FeBr3? what order do the changes in the succession of an ecosystem occur? Rearrange the boxes so that the first change to occur is on the left and the last change to occur is on the right.