(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.
Answers
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: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
The graph of f(x) = xx is reflected across the x-axis and then across the y-axis to create the graph of function g(x).
Which statements about the functions f(x) and g(x) are true? Check all that apply.
The functions have the same range.
The functions have the same domains.
The only value that is in the domains of both functions is 0.
There are no values that are in the ranges of both functions.
The domain of g(x) is all values greater than or equal to 0.
The range of g(x) is all values less than or equal to 0.
Answers
Answer:C and F are correct
Step-by-step explanation:
got it right on edge
Plsssssss answer this fast guys plssssss
Answers
Answer:You cant get someone to do all of this try doing a few or getting help from someone older that's what I did
I asked help for one problem and the explanation and now I understand how they did it so the other problems I can do now
It's better to make an effort and try doing some of them instead of asking someone to do all of it
Because when the test comes it won't be that easy so next time just try putting a few so that way you can try understanding it and you can apply it to similar problems
Answer:
Don't ask someone to do this if your question is a test
Step-by-step explanation:
I really need help with this
Answers
Answer:
8/5
Step-by-step explanation:
There are 8 jokers combined, and 5 decks, so the mean is 8/5.
Match each number with its place in order from smallest (1st) to largest (6th). 1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48
Answers
Answer:
Numbers provided:
-56, 90, -84, 59, -80, 48
The smallest number is -84.
The highest number is 90.
1st: -84
2nd: -80
3rd: -56
4th: 48
5th: 59
6th: 90
Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial. $\[x^2 + 22x + \underline{~~~~}.\]$
Answers
Answer:
[tex]$\[x^2 + 22x + 121\]$[/tex]
Step-by-step explanation:
Given
[tex]$\[x^2 + 22x + \underline{~~~~}.\]$[/tex]
Required
Fill in the gap
Represent the blank with k
[tex]$\[x^2 + 22x + k\]$[/tex]
Solving for k...
To do this, we start by getting the coefficient of x
Coefficient of x = 22
Divide the coefficient by 2
[tex]Result = 22/2[/tex]
[tex]Result = 11[/tex]
Take the square of this result, to give k
[tex]k= 11^2[/tex]
[tex]k= 121[/tex]
Substitute 121 for k
[tex]$\[x^2 + 22x + 121\]$[/tex]
The expression can be factorized as follows;
[tex]x^2 + 11x + 11x + 121[/tex]
[tex]x(x + 11)+11(x+11)[/tex]
[tex](x+11)(x+11)[/tex]
[tex](x+11)^2[/tex]
Hence, the quadratic expression is [tex]$\[x^2 + 22x + 121\]$[/tex]
please help giving brainlest and points !! send picture or explain
Answers
Answer:
1. [1,-8,-7]
2.[4,-3,-2]
3.[9,-7,-2]
srry if wrong
2.[11, -7, 4]
3.[-2,-1,-3]
this is the right answer!!
Estimate the difference to the nearest tenth.
0.612 – 0.185
Answers
Answer:
I can’t understand that
Step-by-step explanation:
Solve x*2+5x+6=5x+10
Answers
Answer:
x = -2, 2.
Step-by-step explanation:
x*2 + 5x + 6 = 5x + 10
x^2 + 5x - 5x + 6 - 10 = 0
x^2 - 4 = 0
x^2 = 4
x = -2, 2 ( 2 solutions).
An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. The executive then boarded the helicopter and flew to the corporate offices at an average speed of 78 mph. The entire distance from his home to the office was 169.5 if the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work
Answers
Answer:
3 hours
Step-by-step explanation:
Speed is the ratio of distance traveled to time taken, it is given as:
Speed = distance / time
An executive drove from his home at an average speed of 35 mph to an airport where a helicopter was waiting. He then took the helicopter and flew to the corporate offices at an average speed of 78 mph. Given that the executive spent the same amount of time in the car as he did the helicopter how long did it take the executive to get to work.
Let the amount of time the executive spent in the car be t hours, therefore the amount of time spent in the helicopter = t hours.
For car:
Speed = distance / time
35 = distance ([tex]d_1[/tex]) / t
[tex]d_1=35t[/tex]
For helicopter:
Speed = distance / time
78 = distance ([tex]d_2[/tex]) / t
[tex]d_2=78t[/tex]
The total distance traveled = 169.5 miles
[tex]d_1+d_2=169.5\\35t+78t=169.5\\113t=169.5\\t=169.5/113\\t=1.5\ hours[/tex]
The time taken for the executive to get to work = time spent on car + time spent on helicopter = 1.5 + 1.5 = 3 hours
HELPP! QUICKKKK! Lol
Problem:
Last year I attended the Jurassic World Dinosaur Exhibit with my family and my friend and her family. My
family includes 2 adults (including myself) and my child we paid a total of $94. Her family includes 2
adults and 2 children she paid a total of $110. What was the admission price for an adult ticket and how
much was it for the admission price for a child ticket?
Let a represent adult ticket price
Let c represent child ticket price
Answers
Answer:
Child ticket = $16.
Step-by-step explanation:
Let adult tickets = a;
child ticket = c.
2a + c = 94 — eq no. 1,
2a + 2c = 110 — eq no. 2,
then,from eq 1,
c = 94 - 2a. —eq no. 3.
Substitute eq 3 into eq 2,
2a + 2(94 - 2a) = 110
2a - 4a = 110 - 188
-2a /-2 = -78 / -2
a = 39.
Substitute value of a into eq 3,
c = 94 - 2(39)
= 94 - 78
c = 16.
Thus, child ticket = $16.
Because, for the first family 39a+16c= $94 total for that family and just do the math for the other one :)
Eighty eighths in cups
Answers
if you have 88 tablespoons and you convert them into cups you would have 5.5 then you would convert that into a fraction which would be 5 1/2
Mathematics, probability and chance Can somebody help me, I always thank and vote
Answers
PLEASE HELP!!! Will give brainliest to quickest CORRECT answer. No explanation needed :) Rebekah manages a yoga studio that charges each customer a one-time initial fee of $35 and an additional fee of $12 per class taken. Rebekah's goal is for each customer to spend at least $100 at the studio, and she wants to know the minimum number of classes a customer needs to take to meet that goal. Let C represent the number of classes a customer takes. 1) Which inequality describes this scenario? A. 35+C≤100 B. 35+3≥100 C. 35+12C≤100 D. 35+12C≥100 2) What is the minimum number of classes a customer can take for Rebekah to meet her goal?
Answers
35 dollar fee + 12 per class taken, to reach the amount of 100 :)
100-35= 65
65/12 = 5 if you aren’t using remainders, if you are it would be 5.416 repeated
The inequality that describes the scenario will be; 35 + 12C ≥ 100.
The minimum number of classes a customer can take for Rebekah to meet her goal is 6
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
One-time initial fee = $35
Additional fee per class = $12
Minimum target = $100
Number of classes = C
One-time initial fee + (Additional fee per class) x (Number of classes) ≥ Minimum target
The inequality that describes the scenario will be;
35 + 12C ≥ 100
Then Solve for C to know the minimum number of classes a customer can take for Rebekah to meet her goal,
12C ≥ 100 - 35
12C ≥ 65
C ≥ 65 / 12
C ≥ 5.42
Thus, The minimum number of classes a customer can take for Rebekah to meet her goal is 6
Learn more about inequality ;
brainly.com/question/14164153
#SPJ2
Question 9 of 10
Which of the following are exterior angles? Check all that apply.
O A. 24
O B. _3
O c. 7
O D. 25
O E. 2.
O F. 26
Answers
Explanation:
Angle 3, 4, and 2 are the exterior angles because it locates outside
Answer:
[tex]\boxed{\sf A, \ B \ and \ E}[/tex]
Step-by-step explanation:
[tex]\sf Exterior \ angles \ are \ the \ angles \ located \ outside \ of \ the \ triangle.[/tex]
Circles
1. RS and ST are tangent lines. Find the value of x.
R
9x - 30
c.
S
3x
T
Answers
Answer:
x = 15
Step-by-step explanation:
9x-30 = 3x (tangent lines are congruent)
- move the variables to one side
9x-3x=30
6x=30
x=5
--------------
9(5)-30=3(15)
45-30=15
15=15
Done!
x = 15
The volume of this prism is cubic inches.
Answers
Answer:
140
Step-by-step explanation:
The prism shown is a rectangular prism
Volume of a rectangular prism = length * width * height
Given length: 3 1/2
Given width: 5
Given height: 8
Volume = 3.5 * 5 * 8 = 140
Answer:
[tex]A=140[/tex]
Step-by-step explanation:
The volume of a three-dimensional object is the amount of space the object takes up. In this case, the prism is a rectangular prism, its volume can be found using the following formula,
[tex]A=l*w*h[/tex]
Substitute the given values into this formula,
[tex]A=l*w*h[/tex]
[tex]A=8*5*3\frac{1}{2}[/tex]
Simplify,
[tex]A=8*5*3\frac{1}{2}[/tex]
[tex]A=40*3\frac{1}{2}[/tex]
Convert the mixed number into an improper fraction, this can be done by multiplying the "number" part of the mixed number by the denominator (number under the fraction bar). Then one adds the result to the numerator (number over the fraction bar).
[tex]A=40*3\frac{1}{2}[/tex]
[tex]A=40*\frac{(3*2)+1}{2}[/tex]
[tex]A=40*\frac{6+1}{2}[/tex]
[tex]A=40*\frac{7}{2}[/tex]
To simplify further, one must divide the number the fraction is being multiplied by the denominator of the fraction,
[tex]A=40*\frac{7}{2}[/tex]
[tex]A=20*7[/tex]
Multiply to finish simplifying and get the answer,
[tex]A=20*7[/tex]
[tex]A=140[/tex]
Which system of equations has no solution?
Answers
Answer:
B.
[tex]{ \binom{7x - 2y = 9}{7x - 2y = 13} }[/tex]
A store pays $10 for each shirt it buys. The store sells each shirt for 60%
more. What is the price of a shirt at the store?
Answers
Answer:
16$ per shirt
Step-by-step explanation:
60% of 10 is 6
10 + 6 = 16
16% of 10 is 6
10+6=16
Ms. Canton went to the store to buy grapes. She bought four bunches of purple grapes. Each bunch had the same amount of grapes (x) She also bought two bunches of green grapes.Each bunch of green grapes had the same amount of grapes in them (y). Write an expression that will show how many bunches of grapes Ms. Canton purchased. *
Answers
4x+2y
Explanation:
x represents the purple grapes in one bunch, while y represents the green grapes in one bunch.
Given: 4 bunches of purple grapes (x), 2 bunches of green grapes (y)
Combine to get the expression 4x +2y
Hope this helps
Halfway through the second quarter, what fructional part of the game is left?
Answers
Answer:
5/8 of the game
Step-by-step explanation:
Half of a quarter is 1/2, and 1 quarter is already done, therefore 1/2, or to simplify it 1/8, plus 2/8, would be 3/8. Now, a quarter is 1/4th of something therefore there must be 4 quarters in a total.so that means that there are 8 halfves in total , so 8-3=5, so the fractional parts of the game left is 5/8.
The part of the game i.e. left should be [tex]5\div 8[/tex]
Calculation of the part of the game:Since the half of the quarter is one-half. And, the one quarter is done so one-half is remaining. That means
[tex]= 1\div 8 + 1\\\= 2\div 8[/tex]
Since one-fourth should be of something also there are total 4 quarters that means there are 8 halves.
So, remaining it should be
= 8 -3
= 5
Hence, The part of the game i.e. left should be [tex]5\div 8[/tex]
Learn more about game here: https://brainly.com/question/1415899
What is D+26/-17 = - 25
Answers
Answer:
-399/17
Step-by-step explanation:
D+26/-17=-25
D=-25-(-26/17)
D=-25+26/17
D=-425/17+26/17
D=-399/17
The answer is D= -399/17
If h(x) = x2-5x + 7
find: h(-5)
Answers
Answer:
h(-5)=22
Step-by-step explanation:
Replace x with -5.
[tex]h(-5) = (-5)2-5(-5) + 7[/tex]
Simplify.
[tex]h(-5)=-10+25+7[/tex]
Simplify.
[tex]h(-5)=22[/tex]
use the tables below to find (p-q)(2)
Answers
Answer:
[tex]\boxed{5}[/tex]
Step-by-step explanation:
[tex](p-q)(2)[/tex]
[tex]p(2)-q(2)[/tex]
[tex]\sf When \ x \ is \ 2, \ p(x) \ is \ 3 \ and \ q(x) \ is \ -2.[/tex]
[tex](3)-(-2)[/tex]
[tex]3+2=5[/tex]
—————-////——
A 20% discount on pants, and its price became 48 after the sale, what was its price before
Answers
Answer:
$60
Step-by-step explanation:
Represent the original price by p. Then:
1.00 p = original price
0.20 p = discount
0.80p = price after discount = $48
Solving for p, we divide both sides by 0.80:
$48
p = ---------- = $60
0.80
Two boxes are shown below
What is the difference in the surface areas, in square feet, of the two boxes?
Answers
Answer:
Option (B):3
Step-by-step explanation:
S.A of Box J =57ft^2 ; using formula 2(lb+lh+hb)
S.A of BoxF=54Ft^2;using formula (6a^2)
Differenceof S.A of boxes:57-54=3
{(-2,8),(4,6),(10,4)} Which point, when added to the set, would form a relation that is not a function?
Answers
Answer:
Point : ( -2, 15 )
Step-by-step explanation:
A point that would make this relation not a function would be one that shares a common x - value with the other points. One common domain values for two range values would, when graphed, not follow the vertical test, hence making the relation not a function.
Let's say that the point is ( -2, 15 ). It has a common x - value with respect to the first point, ( -2, 8 ), and therefore would make this set not a function.
Answer:
Point : ( -2, 15 )
Step-by-step explanation:
if all the possible values of x are indicated by the shaded part of the number line above, which number line best shows all possible values of 1/x? (the shaded part in the number line is 0.5 to 1.5, the whole number line segment is from 0 to 3)
Answers
Answer:
can i see a picture of the number line?
Step-by-step explanation:
5 Sandeep bought 30 punnets of strawberries for £20. 1/6 of the punnets were rotten so he threw them away. He sold the remaining punnets for £1.50 each. Work out Sandeep's profit.
Answers
Answer:
£17.50
Step-by-step explanation:
30 punnets / £20
= 30 / 20
= 1.5
1 punnet costs £1.5
30 strawberries * (1/6 punnets)
= 30 * (1/6)
= 30/6
= 5
5 punnets were rotten.
5 rotten punnets * £1.5
= 5 * 1.5
= 7.5
Sandeep lost £7.5 in profits.
6/6 punnets - 1/6 rotten punnets
= 6/6 - 1/6
= 5/6
5/6 punnets are good
30 punnets * 5/6 good punnets
= 30 * 5/6
= 150/6
= 25
Sandeep has 25 punnets left to sell
25 punnets to sell * £1.50
= 25 * 1.5
= 37.50
Sandeep will get £37.50 from selling the punnets. However, you must take into account that he lost £20 when he bought the strawberies. THat money while be added back with some extra money left over:
£37.50 - £20
= 37.50 - 20
= 17.50
Put all into 1 equation:
{[30 * (5/6)] * 1.50} - 20
= {(150/6) * 1.50} - 20
= {25 * 1.50} - 20
= 37.50 -20
= 17.50
Overall, Sandeep's actual profits are equal to 17.50
I hope this is correct! Please tell me if the answer or info I gave was wrong!
find the value of a answers: a:15 b:14 c:19 d:16
Answers
Answer:
6a+10= 3a+55
6a-3a= 55-10
3a= 45
a= 45/3
a= 15
The answer is (A) 15
Hope this helps^°^
Answer:
A. 15
Step-by-step explanation:
The angles are vertical angles, therefore they are congruent. We can set the two measures equal to each other.
[tex]6a+10=3a+55[/tex]
Now, solve for a. We must get a by itself on one side of the equation.
First, subtract 3a from both sides of the equation.
[tex]6a-3a+10=3a-3a+55[/tex]
[tex](6a-3a)+10=55[/tex]
[tex]3a+10=55[/tex]
Next, subtraction 10 to both sides of the equation. We subtract because 10 is being added to 3a. The inverse of addition is subtraction.
[tex]3a+10-10=55-10[/tex]
[tex]3a=55-10[/tex]
[tex]3a=45[/tex]
3 and a are being multiplied. The inverse of multiplication is division. Divide both sides of the equation by 3
[tex]3a/3=45/3[/tex]
[tex]a=45/3[/tex]
[tex]a=15[/tex]
The value of a is 15 and choice A is correct.
In △ABC, AB = BC = 20 and DE ≈ 9.28. Approximate BD. (made a second one since trollers ruined my last one :/ )
Answers
Answer:
approximately 5.36
Step-by-step explanation
20 - 9.28 = 10.72
BD = EC
10.72/2 = 5.36