(k) 2 cos 16A + 1 = (2 cos 2A - 1).(2 cos 2A + 1).(2 cos 4A-1).(2cos 8A-1).
I need help to prove this......
Qno. k.​

(k) 2 Cos 16A + 1 = (2 Cos 2A - 1).(2 Cos 2A + 1).(2 Cos 4A-1).(2cos 8A-1).I Need Help To Prove This......Qno.

Answers

Answer 1

Answer:  see proof below

Step-by-step explanation:

Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

                              ↓                 ↓                  ↓                 ↓

                                factor last              factor 2nd    factor 1st

Proof LHS → RHS:

Given:        2 cos16A + 1

                  let α = 8A, then 2·cos2α + 1

Identity:     2(2cos²α - 1) + 1

Distribute:  4cos²α - 2 + 1

Simplify:    4cos²α - 1

Factor:     (2cosα - 1)(2cosα + 1)

Substitute: (2cos8A - 1)(2cos8A + 1)

                                       let β = 4A, then 2·cos2β + 1

Identity:                           2(2cos²β - 1) + 1

Distribute:                      4cos²β - 2 + 1

Simplify:                         4cos²β - 1

Factor:                           (2cosβ - 1)(2cosβ + 1)

Substitute:                     (2cos4A - 1)(2cos4A + 1)

                                                           let Ф = 4A, then 2·cos2Ф + 1  

Identity:                                               2(2cos²Ф - 1) + 1

Distribute:                                          4cos²Ф - 2 + 1

Simplify:                                             4cos²Ф - 1

Factor:                                               (2cosФ - 1)(2cosФ + 1)

Substitute:                                        (2cos2A - 1)(2cos2A + 1)      

(2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1) = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)   [tex]\checkmark[/tex]

                 

Answer 2

Answer:Use the following Double Angle identity: cos 2A = 2cos²A - 1

We are going to find one factor at a time:

2 cos16A + 1 = (2cos2A - 1)(2cos2A + 1)(2cos4A - 1)(2cos8A - 1)

Step-by-step explanation:


Related Questions

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Classwork for Alge.
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Pretest: Circles with and Without Coordinates
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Reade
18
The curved parts of the figure are arcs centered at points A and C. What is the approximate length of boundary ABCD? Use the value = 3
and round the answer to one decimal place.
5
С
30°
А
120°
5

Answers

Answer:

The correct answer is

C. 23.1

Step-by-step explanation:

i think this is correct

The answer is 23.1 formal

The quotient of 32 and 4 divided by the sum of 1 and 3

Answers

Answer:

2

Step-by-step explanation:

32 divided by 4 = 8 (quotient)

1 + 3 = 4 (sum)

8 divided by 4 = 2

Answer:

88

Step-by-step explanation:

Name four fractions between 5/11 and 5/6

Answers

5/10, 5/9, 5/8, 5/7.

These are all between 5/11 and 5/6.

Answer:

6/11,  20/33,  2/3,  25/33  (answers vary)

Step-by-step explanation:

First, we need to convert both of these fractions to the same denominator. To do that, we need to find the least common denominator for both fractions.

6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72

11: 11, 22, 33, 44, 55, 66, 77

The LCM of 6 and 11 is 66. (6 * 11 = 66)

Now, we multiply 5/6 by 11/11 and 5/11 by 6/6.

[tex]\frac{5}{6} *\frac{11}{11}=\frac{55}{66}\\\\\\\frac{5}{11} *\frac{6}{6} =\frac{30}{66}[/tex]

Now, we can just choose four numbers between 30 and 55 and get our answer (remember to simplify!).

[tex]\frac{36}{66} =\frac{6}{11}[/tex]

[tex]\frac{40}{66}=\frac{20}{33}[/tex]

[tex]\frac{44}{66} =\frac{2}{3}[/tex]

[tex]\frac{50}{66} =\frac{25}{33}[/tex]

What are the restrictions of the domain of f(g(x))?

a) x is not equal to -5
b) x is not equal to -3
c) x is not equal to 2
d) There are no restrictions.

Answers

I think that it’s D and there are no restrictions
The answer would be D) hope I helped and good luck

4/3 to the third power as a simplified fraction

Answers

Answer:

64/27

Step-by-step explanation:

(4/3)^3=(4/3)*(4/3)*(4/3)=64/27

Answer:

[tex]2 \frac{10}{27}[/tex]

Step-by-step explanation:

4/3 × 4/3 × 4/3 = 64/27

You can turn it into a mixed number ([tex]2 \frac{10}{27}[/tex]).

Hope that helps and maybe earns a brainliest!

Have a great day! :)

What is the equation that is perpendicular to the line y=2x-3 and passes through the point (-6,5)? Show all of your work.

Answers

Answer: y=(-1/2)x+5.5

Step-by-step explanation:

y=2x+3

This equation is in the slope-intercept form y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

m=2

The slope of the perpendicular line is -1/2.

(y-y1)=m(x-x1)

(y-4)=(-1/2)(x-3)

y-4=(-1/2)x+1.5

add 4 to both sides

4+y-4=(-1/2)x+1.5+4

y=(-1/2)x+5.5

Answer:

y = -1/2x + 2

Step-by-step explanation:

The slope of a perpendicular line will be the opposite reciprocal (opposite sign, and reciprocal)

The line's slope is 2, so the perpendicular line's slope will be -1/2.

Now, we know part of the equation: y = -1/2x + b

Plug in the point given:

5 = -1/2(-6) + b

5 = 3 + b

2 = b

Now, we can plug in b into the equation:

y = -1/2x + 2

An exponential function f(x)= ab^x passes through the points (0,10) and (3,1250). What are the values of a and b?

a = I know it’s 10
b = ?

Answers

Answer:

a = 10 and b = 5

Step-by-step explanation:

We write out f(x)= ab^x for x = 0 and x = 3 to create two equations in a and b that must be solved simultaneously:

(0, 10):  10 = a*b^0

This tells us that 10 = a*1, or a = 10.

(3, 1250):  1250 = a*b^3 => 10*b^3, or

1250 = 10*b^3, or

125 = b^3.  Taking the cube root of both sides, we obtain b = 5.

a = 10 and b = 5

a = 10 and the next would probably be b=5

A building casts a 33-m shadow when the sun is at an angle of 27° the vertical. How tall is the building to the
nearest meter? How far is it from the top of the building to the tip of the shadow?

Answers

Answer:

1. EF = 65m

2. DF = 73m

Step-by-step explanation:

1. EF = height of the building = h = 33 / tan 27 = 65m

2. DF = sqrt (65² + 33²) = 73m

The building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.

From the triangle DEF, we find the value of EF by using tan function.

tan function is a ratio of opposite side and adjacent side.

tan(27)= 33/FE

0.5095 = 33/FE

Apply cross multiplication:

FE=33/0.5095

FE=64.76

Now DF is the hypotenuse, we find it by using pythagoras theorem.

DF²=DE²+EF²

DF²=33²+64.76²

DF²=1089+4193.85

DF²=5282.85

Take square root on both sides:

DF=72.68

In a triangle the the sum of three angles is 180 degrees.

∠D + 27 +90 =180

∠D + 117 =180

Subtract 117 from both sides:

∠D =63 degrees.

Hence, the building is 64.76 meters long and 73 meters far from the top of the building to the tip of the shadow.

To learn more on trigonometry click:

https://brainly.com/question/25122835

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Graph the line 2x + 3y = 12

Answers

Answer:

your answer y=4 x=6

Step-by-step explanation:

Y=4 X=6 I’m pretty sure that’s right

You weigh six packages and find the weights to be 34, 24, 74, 29, 69, and 64 ounces. If you include a package that weighs 154 ounces, which will increase more, the median or the mean? A. The median and the mean will stay the same. B. The median and mean are affected the same amount. C. The mean increases more. D. The median increases more.

Answers

Answer:

C. the mean increases more

Step-by-step explanation:

the mean is more affected by outliers because it is an average of all the numbers.

Answer:

C. the mean increases more

Step-by-step explanation:

Sam's Lawn Service uses the equation, y = 15x + 25 to calculate the cost, y, to work on a
customer's lawn for x number of hours.
Ron's Lawn Service uses the table below to calculate the cost to work on a customer's
lawn.

Answers

Answer:

Rons costs less by 4 dollars

Step-by-step explanation:

Sams

y = 15x+25

x=3

y = 15*3+25

  = 45+25

  =70

Rons

Using averaging

for 3 hours  Add 2 and 4 hours and divide by 2

(49+ 83) / 2 = 132/2= 66

Rons costs less by

70-66 =4

Y=15x+25
Find the x intercept zero
X=-5/3
X=-1 2/3
X=1.6

Enrique has to pay 80% of a $200 phone bill. Explain how to use equivalent ratios to find 80% of $200. please help

Answers

Answer:

Heres a simple way:

Step-by-step explanation:

80% in to dec. 0.8

0.8 x 200 = 160

So,

80% of $200 is

$160

So 10% of 200 is 20
And so 80% is 20• 8
That’ll give you the answer of 160$!

A percent is the numerator of a ratio whose denominator is A. 25 B. 50 C. 75 D. 100

Answers

I am sure the answer is D

Answer:

D 100

Step-by-step explanation:

60% = 60/100

70% =70/100

Sally is swimming in a race that has 5 laps. Swimming 2 lengths of the pool
counts as one lap. If Sally is halfway through the fourth lap, what fractional
part of the total laps in the race is left for Sally to finish?

Answers

Answer:

3/10

Step-by-step explanation:

Sally has to run 5 laps(2000m)

One lap = 400m  

So we multiply 3.5( 3 1/2) [this the the distance Sally ran] by 400

The answer we get is 1400( this the total distance in meters she ran)

Next we subtract 1400( total distance she ran in meters) from 2000(total distance in meters she needs to complete.

The answer we get is 600 meters( this is the distance she is left with)

As a fraction is 600/2000

THE ANSWER REDUCED TO ITS LOWEST TERM IS 3/10.

Answer:

3/10

Step-by-step explanation:

15 POINT!!!!!!!!!!!!!!!!!!!! Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k. Graph of two lines. f of x passes through 2, 0 and 3, 2, and g of x passes through two thirds, 0 and 1, 2. 3 one third negative one third −3

Answers

Answer:

k=(-1,5)=-5

Step-by-step explanation:

Answer:

ok i got the same question and i think it is and dont qoute me boy i aint said it but i think its B sorry if im wrong

Step-by-step explanation:

Find the term that must be added to the equation x2+4x=1 to make it into a perfect square

Answers

Answer:

add 4 to each side

Step-by-step explanation:

x^2+4x=1

Take the coefficient of the x term

4

Divide by 2

4/2 =2

Square it

2^2 =4

Add this to each side

x^2+4x +4=1+4

(x+2) ^2 = 5

xbdhehhddhddh dheheh

helpyffhvjvjnvhdfuguig​

Answers

Answer:

x = 0, x = 4

Step-by-step explanation:

12x - 21 = 5x + 7(x - 3)

First, foil out the right side --> 5x² - 15x + 7x - 21, which simplifies down to 5x² - 8x - 21.

Move the 12x - 21 to the right side by subtracting --> 0 = 5x² - 20x.

Factor out a 5x --> 0 = 5x(x - 4)

If you want to solve for x, set 5x = 0 and x - 4 = 0.

For 5x = 0, divide both sides by 5 to isolate the x --> x = 0/5, which simplifies down to x = 0.

For x - 4 = 0, add 4 to both sides to isolate the x --> x = 0 + 4, which simplifies down to x = 4.

Plug the values back into the original equation to check if it works

12(0) -21 = 5(0) + 7((0) - 3) --> -21 = -21

12(4) - 21 = 5(4) + 7((4) -3) --> 27 = 27

Hope this helps!

I can’t read it so I can’t help u

*PLEASE ANSWER TY* What is the density of a 50-gram pyramid with rectangular base 4 cm x 8 cm and height 10 cm?

Answers

Answer:

[tex]\frac{0.47 g}{cm^{3} }[/tex]

Step-by-step explanation:

→ First work out volume of pyramid using the formula  [tex]\frac{lwh}{3}[/tex]  where 'l' is the length, 'w' is the width and 'h' is the height

[tex]\frac{lwh}{3}[/tex]  ⇔ [tex]\frac{4*8*10}{3}[/tex] ⇔  [tex]\frac{320}{3}[/tex] ⇔ 320 ÷ 3 = 106.666666667

→ Volume of pyramid = 106.666666667. Substitute this value into the density formula

Density = Mass ÷ Volume

Density = 50 ÷ 106.666666667

Density = 0.46875 to 1 decimal place is 0.47

Graph the function. h ( x ) = 8 ⋅ ( 3 4 ) x h(x)=8⋅( 4 3 ​ )

Answers

answer....

Step-by-step explanation:

h

(

x

)

=

3

x

+

8

Bro wtfdtm oof nvm I’m being a dum ad

help me plz i dont get this

Answers

Answer:

56 [tex]in^2[/tex]

Step-by-step explanation:

We can first break this down into 2 smaller rectangles.

1x2x4 rectangle

4x3x4 rectangle.

Then we can find out the area of each, and we get 8+48 = 56.

You also could find this out by subtracting the area that is missing.

Answer:

The volume of the container is 56 in^3

Step-by-step explanation:

To solve, I split this figure vertically at the corner between the two steps. We know that the formula for volume of a container is V= l*w*h. The first, smaller portion of the container has a length of 4, a width of 1, and a height of 2. 4*1*2= 8 in^3

The second, larger portion of this container has a length of 4, (look at the side of the first portion), a width of 3, (4-1=3), and a height of 4. 4*3*4= 48 in^3.

Finally, add together the volumes of the two portions and that is the volume of the whole figure. V= 56 in^3

12
121 °
9
can it make a triangle if so what the area ?

Answers

Answer:

no it can not

Step-by-step explanation:

Triangle is always 180° in total.

Nope it definitely can’t

What is the determinant of A = -3 6 1 -6

Answers

Step-by-step explanation:

ydudhdhdjjdbdjdmdjdkdjd

What are the coordinates of the vertices of the polygon in the graph that are in Quadrant II? A) (4,–2) B) (4,3), (0,5), (0,1) C) (–5,2), (–3,2), (–3,4) D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)

Answers

Answer:

C) (–5,2), (–3,2), (–3,4)

Step-by-step explanation:

A) (4,–2)

B) (4,3), (0,5), (0,1)

C) (–5,2), (–3,2), (–3,4)

D) (–1,0), (–5,2), (–3,2), (–3,4), (0,5), (0,1)

For quadrant two the points are always (-x,y) and x is always negative.

Image shows quadrant places.

C. ) (-5,3), (-3, 2), (-3, 4)

Of a group of boys and girls at Central Middle School’s after-school party, 15 girls left early to play in a volleyball game. The ratio of boys to girls then remaining was 2 to 1. Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1. How many students attended the party?

Answers

Answer:

  90

Step-by-step explanation:

Let g and b represent the number of girls and boys attending, respectively.

After 15 girls left, the ratio of boys to girls was ...

  b/(g -15) = 2/1

  b = 2g -30 . . . . . multiply by (g-15)

__

After 45 boys left, the ratio of girls to boys was ...

  (g -15)/(b -45) = 5/1

  g -15 = 5b -225 . . . . . . multiply by (b-45)

  g = 5b -210

Using the latter to substitute into the former, we have ...

  b = 2(5b -210) -30

  450 = 9b . . . . . add 450-b

  50 = b . . . . . . 50 boys attended

  g = 5(50) -210 = 40 . . . . . 40 girls attended

The number of students who attended the party was 50 +40 = 90.

_____

Check

After 15 girls left, the ratio of boys to girls was 50/25 = 2/1.

After 45 boys left, the ratio of girls to boys was 25/5 = 5/1.

Answer:

let b = original number of boys

let g = original number of girls

:

Of a group of boys and girls at Central Middle School's after-school party, 15 girls left early to play in a volleyball game.

The ratio of boys to girls then remaining was 2 to 1.

b%2F%28%28g-15%29%29 = 2%2F1

Cross multiply

b = 2(g-15)

b = 2g - 30

:

Later, 45 boys left for a football game. The ratio of girls to boys was then 5 to 1.

%28%28g-15%29%29%2F%28%28b-45%29%29 = 5%2F1

cross multiply

g - 15 = 5(b-45)

 

g - 15 = 5b - 225

g = 5b - 225 + 15

g = 5b - 210

Replace b with (2g-30)

g = 5(2g-30) - 210

g = 10g - 150 - 210

g = 10g - 360

360 = 10g - g

360 = 9g

g = 360/9

g = 40 girls originally

find b

b = 2(40) - 30

b = 50 boys originally

" How many students attended the party?"

40 + 50 = 90 students

18 silly bands are equally shared by 6 children. 2 children put their silly bands in the same drawer. How many silly bands are in the drawer?

Answers

Answer:

6

Step-by-step explanation:

18 silly bands / 6 children = 3 silly bands per child.

2 children * 3 bands each = 6 bands total

Answer:

6 silly bands

Step-by-step explanation:

18 divided by 6 = 3  , so each child gets 3 so 3 + 3 is 6 which means 6 silly bands are in the drawer

What is the volume of the square pyramid shown to the nearest tenth? The figure is not drawn to scale. width of 16 and a length of 17 A. 1,280.0 ft^3 B. 85.3 ft^3 C. 1,920.0 ft^3 D. 3,840.0 ft^3

Answers

Hggo add my boi huch back scooter

The volume of the pyramid is 1,280 cubic feet. Thus, the correct option is A.

What is the volume of the pyramid?

Let h be the height of the pyramid, l be the slant height, and A be the base area of the pyramid. Then the volume of the pyramid will be given as,

Volume = (1/3) × A × h

The slant height is given as,

l² = (half of the side)² + h²

Given that:

Slant height, l = 17 ft

Side length, a = 16 ft

The height of the pyramid is calculated as,

17² = (16/2)² + h²

h = 15

The volume of the pyramid is calculated as,

V = 1/3 x 16 x 16 x 15

V = 256 x 5

V = 1,280 cubic feet

Thus, the correct option is A.

More about the volume of the pyramid link is given below.

https://brainly.com/question/17615619

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can somewon help me i am bad at math

Answers

Answer:

480 in3

Step-by-step explanation:

10 * 8 * 5 + ( 4 * 4 * 5 ) = 480in3

Answer:

480 in^3

Step-by-step explanation:

The first, smaller container where I split it has an equation of V= 4*4*6=80 in^3 and the second, larger container has an equation of V= 5*10*8= 400 in^3

80+400= 480 in^3

Find the median of the data in the dot plot below.

Answers

Answer:

40

Step-by-step explanation:

The median is the middle value of the data arranged in ascending order. If there is no exact value in the middle then it is the average of the values either side of the middle.

The data is arranged in ascending order within the dot plot

There are 10 values in the data set

Thus the median is between the fifth and sixth values.

Counting from the left (35)

The fifth value = 39 and the sixth value = 41, thus

median = [tex]\frac{39+41}{2}[/tex] = [tex]\frac{80}{2}[/tex] = 40

Answer:

Step-by-step explanation:

Data:

35 ,  38, 38 , 39 , 39, 41, 42 , 43, 43, 44

Total number of data = 10

Number of data is even. so, median is the average of (n/2)th term & ([tex]\frac{n}{2}+1[/tex] ) middle term,

Median = average of  5th and 6th term

            = (39 + 41)/2 = 80/2 = 40

Factor 3x^2 – 12x – 36.

Answers

Answer:

The answer is 3( x - 2)(x + 6)

Step-by-step explanation:

3x² - 12x - 36

To factorize the expression first factor 3 out of the expression

That's

3( x² - 4x - 12)

Factorize the terms in the bracket

To do so write - 4x as a difference

That's

3( x² + 6x - 2x - 12)

Factor out x from the expression

3[ x( x + 6) - 2 ( x + 6) ]

Next factor x + 2 out

We have the final answer as

3( x - 2)(x + 6)

Hope this helps you

3(x^2 - 4x - 12)

Just divide it all by 3

What is the area of the polygon shown below? (in the image). A. 322 mm^2 B. 364 mm^2 C. 520 mm^2 D. 584 mm^2 Show all work please!

Answers

Answer:

A. 322 mm^2

Step-by-step explanation:

First split the shape into two (a rectangle and a triangle).

Then calculate the area of those shapes.

Rectangle: 20 x 14 =  280 mm^2

Triangle: 6 x 14 / 2 = 42 mm^2

Add them together.

280 + 42 = 322 mm^2

Just multiply or use PEMDAS
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Sales projections for the first five months of the upcoming year show the estimated unit sales of the planters each month to be as follows: Inventory at the start of the year was 975 planters. The desired inventory of planters at the end of each month should be equal to 25% of the following month's budgeted sales. Each planter requires four pounds of polypropylene (a type of plastic). The company wants to have 30% of the polypropylene required for next month's production on hand at the end of each month. The polypropylene costs $0.20 per pound. Number of planters to be soldJanuary 3900February 3200March 3700April 4400 May 4900Required:Prepare a production budget for each month in the first quarter of the year, including production in units for each month and for the quarter. The combination of one or more communication tools used to inform prospective buyers about the benefits of the product, persuade them to try it, and remind them later about the benefits they enjoyed by using the product is referred to as the Can I name my Angle VTS as STV? And use it interchangeably in proving? Tom and Lynda also inform you that the monthly individual membership fee is $100and that the monthly family membership fee is $160. Hercules offers a 10% discount if amember pays the entire years fee in a lump sum. About 180 individuals and 60 families takeadvantage of this offer these numbers are spread evenly throughout the year. Herculespays for 60% of its purchases during the month of the purchase, and the remainder thenext month. Other variable costs (paid in cash) amount to $25 per month for each individualmembership and $45 per month for each family membership. Hercules also incurs$41,000 (which includes $12,500 in depreciation) toward fixed costs each month. Finally,Tom and Lynda inform you that they have to pay $20,000 toward the purchase of newequipment in September, and that they take out $15,000 each month as their profit. Finally,Hercules began September with a cash balance of $6,000.Required:What is Hercules cash budget for September? Calculate the monthly implicit costs for a business owner who devotes 200 hours per month to his business that could be spent working at $50/hour for someone else. A scientist is carrying out an experiment to determine the index of refraction for a partially reflective material. To do this, he aims a narrow beam of light at a sample of this material, which has a smooth surface. He then varies the angle of incidence. (The incident beam is traveling through air.)The light that gets reflected by the sample is completely polarized when the angle of incidence is 46.5.(a) What index of refraction describes the material?n =(b) If some of the incident light (at i = 46.5) enters the material and travels below the surface, what is the angle of refraction (in degrees)? who invented biology A school aged child is brought to the clinic by her parents. The parents state that the child will be engaged in some activity at home and then just stop suddenly for a few seconds and then pick up the activity again as if there had been no break in what she was doing. This child should be assessed for what neurological disorder?a.) Tonic-clonic seizuresb.) Absence seizuresc.) Myoclonic seizuresd.) Status epilepticus Calculate the pH of a 0.20 M NH3/0.20 M NH4Cl buffer after the addition of 25.0 mL of 0.10 M HCl to 65.0 mL of the buffer. Which examination technique is the visualization of body parts in motion by projecting x-ray images on a luminous fluorescent screen? Question #2: Where should the RUN-ON SENTENCE be divided? You wash 1 while I iron 2 later on, we will 3 go out. A.1 B.2 C.3 ABC Corporation, after many profitable years, declares a one-time special cash dividend of $10.00 per share. After the announcement, the stock is trading at $100 per share. Your customer holds 1 ABC Jan 110 Call. As of the ex date, the customer will have: