Given:
[tex]\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)[/tex]
To prove:
The given statement.
Proof:
We have,
[tex]\cos^4 \alpha+\sin^4\alpha=\dfrac{1}{4}(3+\cos 4 \alpha)[/tex]
[tex]LHS=\cos^4 \alpha+\sin^4\alpha[/tex]
[tex]LHS=(\cos^2 \alpha)^2+(\sin^2 \alpha)^2[/tex]
[tex]LHS=(\cos^2 \alpha+\sin^2\alpha)^2-2\sin ^2\alpha\cos^2 \alpha[/tex] [tex][\because a^2+b^2=(a+b)^2-2ab][/tex]
[tex]LHS=(1)^2-2(1-\cos^2 \alpha)\cos^2 \alpha [/tex] [tex][\because \cos^2 \alpha+\sin^2\alpha=1][/tex]
[tex]LHS=1-2\cos^2 \alpha+2\cos^4 \alpha [/tex]
Now,
[tex]RHS=\dfrac{1}{4}(3+\cos 4 \alpha)[/tex]
[tex]RHS=\dfrac{1}{4}[3+(2\cos^2 2\alpha-1)][/tex] [tex][\because \cos 2\theta=2\cos^2\theta -1][/tex]
[tex]RHS=\dfrac{1}{4}[2+2\cos^2 2\alpha][/tex]
[tex]RHS=\dfrac{1}{4}[2+2(2\cos^2 \alpha-1)^2][/tex] [tex][\because \cos 2\theta=2\cos^2\theta -1][/tex]
[tex]RHS=\dfrac{1}{4}[2+2(4\cos^4 \alpha-4\cos \alpha+1)][/tex] [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]
[tex]RHS=\dfrac{1}{4}[2+8\cos^4 \alpha-8\cos \alpha+2][/tex]
[tex]RHS=\dfrac{1}{4}[4+8\cos^4 \alpha-8\cos \alpha][/tex]
[tex]RHS=1+2\cos^4 \alpha-2\cos \alpha[/tex]
[tex]RHS=1-2\cos^2 \alpha+2\cos^4 \alpha [/tex]
[tex]LHS=RHS[/tex]
Hence proved.
I’ll give brainley , pleaseee helppp
Answer:
Vertical Stretch & horizontal translation
Step-by-step explanation:
the vertical stretch makes the line bigger
Horizontal translation will move the shape 2 left of the x axis
Answer:
Srry bro its way to blurry for me to read... Also dont show your password to randoms.
Step-by-step explanation:
what is the image point of ( -8,-1 ) after a transition left 3 units and up 4 units
Answer:
(-11,3)
Step-by-step explanation:
7(4p + 2q + 3r) =????????????
Answer:
28p+14q+21r
Step-by-step explanation:
7(4p + 2q + 3r)
Use distributive property
(7)(4p)+(7)(2q)+(7)(3r)
=28p+14q+21r
Which statement about numbers is true?
All integers are natural numbers.
O All rational numbers are integers.
All na ural numbers are whole numbers.
All rational numbers are natural numbers.
Answer:
All natural numbers are whole numbers
Step-by-step explanation:
If 4% of packages get lost in the mail, then how many packages will get lost if 3.000 packages are shipped?
Answer:
250 packages if 3,000 packages are shipped
there are 84 calories in 100g of banana there are 87 calories in 100g of yoghurt priti has 60 g of banana and 150g of yoghurt for breakfast work out the total number of calories in this breakfast
Total calories intake of Priti is 180.9 calories
Given that;
Number of calories in 100g banana = 84 calories
Number of calories in 100g yoghurt = 87 calories
Amount of banana and yoghurt Priti have = 60g and 150g respective
Find:
Total calories intake of Priti
Computation:
Total calories intake of Priti = 60[84/100] + 150[87/100]
Total calories intake of Priti = 50.4 + 130.5
Total calories intake of Priti = 180.9 calories
Learn more:
https://brainly.com/question/18087985?referrer=searchResults
Elijah works at Chick-fil-A and gets paid weekly. He does not have any money in his bank account yet, but will
start saving for a PlayStation 5. After 4 weeks, he has $150. In 8 weeks, he has $300.
SOMEBODY PLS HELP ILL MARK U BRAINLIEST
Answer:
- 16x + 3y
Step-by-step explanation:
this can be done in two ways- vertical method or horizontal :
I did one:
( i hope this is right)
jojos bizzare adventure
Answer:
nice anime lol
Step-by-step explanation:
I like aot better
Plis help me plis! I need help with this
Answer:
The light blue/greenish one that says T=PV/K or Greeland
Step-by-step explanation:
We can make the equation more simplier by multiplying both sides by P to remove fractions.
It would become VP=KT
The only answer with VP or PV is B, or the T=PV/K
also, to isolate T, divide the VP=KT by K on both sides to isolate T.
VP/K=T
what is the greatest common factor of 7 and 21
Answer:
7
Step-by-step explanation: calculate the prime factors of 7 and 21, than find the greatest common factor
The greatest common factor of 7 and 21 is 7.
What is Number system?A number system is defined as a system of writing to express numbers.
To find the greatest common factor (GCF) of 7 and 21, we can list the factors of each number and identify the largest factor they have in common.
The factors of 7 are 1 and 7
The factors of 21 are 1, 3, 7, and 21.
The largest factor that they have in common is 7.
Therefore, the greatest common factor of 7 and 21 is 7.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ5
Which angle(s) are supplementary to angle BAD?
Answer:
hi
Step-by-step explanation:
Who knows how to get the answer for X?
Answer:
x=60
Step-by-step explanation:
The total interior angles of all triangles add up to 180 degrees.
Since this is an equilateral triangle, all angles are equivalent.
In conclusion the answer is x=60
dude why are still up my friend and are you ready for Christmas
U is between G and B. R is between G and U. if GR is 3x-2, RU is 5x+7 , UB is 12 and GB is 15x-11.
x is ____
GR is ____
GB is ____
please help!
Answer:
x is 4
GR is 10
GB is 49
Step-by-step explanation:
If U is between G and B, then GU + UB = GB .... 1
If R is between G and U, GR + RU = GU ....2
Given
GR is 3x-2
RU is 5x+7
UB is 12
GB is 15x-11
Substitute2 into 1;
Frim 1;
GU + UB = GB
(GR+RU) + UB = GB
3x-2+5x+7+12 = 15x-11
8x+17 = 15x-11
8x-15x = -11-17
-7x = -28
x = 28/7
x = 4
Get GR:
GR = 3x-2
GR = 3(4)-2
GR = 12-2
GR = 10
Get GB:
GB = 15x-11
GB = 15(4)-11
GB = 60-11
GB = 49
If the probability of writing the correct answer to the question on an exam is 2/5, what are the odds against writing the correct answer?
Explanation
The probability of getting the correct answer is 2/5. This means there are 2 events of getting it right out of 5 events total. Since there are 2 events of getting it right, there are 5-2 = 3 events of getting it wrong.
The odds against getting the right answer is 3:2. We list the number of ways to get it wrong first, a colon, then the number of ways of getting it right.
will select brainliest if ur answer is correct
Answer:
B (I think)
Step-by-step explanation:
A function can't have two X values that are the same (If I remember correctly) and the second table is the only one that doesn't have duplicated X values
Answer:
the correct answer is b
Step-by-step explanation:
2x-2y=-10 Standard to Slope Intercept form
Answer:
y=x-5
Step-by-step explanation:
2x-2y=10
1.) subtract 2x from both sides
-2y=-2x+10
2.) Divide by -2 to get y by itself
y=x-5
Answer:
y= x+5
Step-by-step explanation:
y =mx+b is slope intercept form
The temperature was 9 degrees below zero at 11 A.M. By 2 P.M. the temperature had risen 3 degrees. What was the temperature at 2 P.M.?
Answer:
-6 degrees
Step-by-step explanation:
9 degrees below zero is the same as -9, so -9 + 3 = -6
Can someone help me I need help quickly!!!
Answer:
c 0.269
Step-by-step explanation:
2x3=6 2x6=18 3x6=24 so its non repeating here i bless the eyes
Answer:
a
Step-by-step explanation:
When a number has a line over like in B and C it means it repeats forever. D has periods so it continues, similar in writing. The only answer left would be A.
1 2⁄3 ÷ 3 1⁄3 =
answer ASAP please
Answer:
0.5 or 1/2 ☺
Step-by-step explanation:
Answer:
1/2
Step-by-step explanation:
Please solve I’ll gift brainliest to the First correct answer
Answer:
X =-3
Step-by-step explanation:
....................
Help me on this question pls
Answer:
d. x = 14; angle measurement is 28 degrees
Step-by-step explanation:
2x is equivalent 28 so divide 28 by 2 to get 14
Given f(x) = 3/2x - 8, solve for x when f(x)= 7
Answer:
x is 10 when f(x) = 7
Step-by-step explanation:
f(x) is another way of saying y=. The question is basically asking, what is the value of x when the 3/2x - 8 = 7
So, to do this, you are going replace y with it's numerical value. The numerical value given to you is 7. Now, you are going to solve for x (by isolating x).
[tex]7= \frac{3}{2} x-8\\7+8= \frac{3}{2} x-8+8\\15 = \frac{3}{2} x\\15 / \frac{3}{2} = (\frac{3}{2}x) / 3/2\\10=x[/tex]
f(10) = 7
Check your work?
Plug in 10 where you see x.
y = 3/2x - 8
y = (3/2)(10)-8
y = 7 ✅
Help please!! Due in 30 minutes
Answer:
Yes you got it right 4x-3y>-12
Step-by-step explanation:
WILL NAME BRANLIST OR WHATEVER Find the value of x. Write your answer in simplest radical form, if necessary.
Answer:
x= sqrt141
Step-by-step explanation:
x^2 + 22^2 = 25^2 by the pythagorean theorem
x^2 + 484 = 625
x^2 = 141
x= sqrt141
What is the probability of 63?
Which number is equivalent to this expression?
3 + 0.1 + 0.004
Here are the instruction plz help asap
Part 1
You will need to measure five different people. Record your measurements on a piece of paper. Using a tape measure or ruler, measure the length (in inches) of a person’s left foot and then measure the length (in inches) of that same person’s forearm (between their wrist and elbow). Refer to the diagrams below. You will have two measurements for each person.
(An easy way to measure the length of a foot is to have your subject stand on a piece of paper. Then, trace their foot and measure the outline once they move off the paper.)
To measure the forearm, measure inside the arm, between the wrist and the elbow.
Part 2
Organize your data and find the rate of change.
Create a table of the measurements for your data. Label the forearm measurements as your input and the foot measurements as your output.
Select two sets of points and find the rate of change for your data.
Describe your results. If you had to express this relation as a verbal statement, how would you describe it?
Part 3
Compare rates of change.
The equation below can be used to find the length of a foot or forearm when you know one or the other.
(length of the foot) = 0.860 • (length of the forearm) + 3.302
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to
y = 0.860x + 3.302.
Using this equation, how long would the foot of a person be if his forearm was 17 inches long?
What is the rate of change of the equation from Part A?
Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different?
Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer.
For this option you will submit the details from all three parts. Submit your measurements, the table, and description that you created in Parts 1 and 2. Submit your answers to the questions from Part 3.
Answer:
again please don't just straight up copy it just use it as a base please also i tried my best and don't know if i got it right
Step-by-step explanation:
Part 2
Organize your data and find the rate of change.
I’m sorry i didn’t know how to make a table so i just did this
Person number 1- Left foot is 9 inches Forearm is 8.5 inches
Person number 2- Left foot is 7.5 inches Forearm is 7 inches
Person number 3- Left foot is 11 inches Forearm is 10.5 inches
Person number 4- Left foot: is 10 inches Forearm is 9.5 inches
Person number 5- Left foot is 6 inches Forearm is 5.5 inches
The rate of change equals y=x-0.5
I believe that it's a function because there is a relationship between 2 variables.
Part 3
Compare rates of change.
The equation below can be used to find the length of a foot or forearm when you know one or the other.
(length of the foot) = 0.860 • (length of the forearm) + 3.302
If you let y = length of the foot and x = length of the forearm, this equation can be simplified to
y = 0.860x + 3.302.
Using this equation, how long would the foot of a person be if his forearm was 17 inches long?
i don’t know how to type all my formulas and work so i'm just going to say the answer i got the rate of change = 0.86x or y=0.86x+3.302
What is the rate of change of the equation from Part A?
For Part A i got y=x-0.5 and that part A has the greater rate of change.
Compare the equation from Part A to your data. Are they the same? Which has a greater rate of change? Why do you think the values are different?
Well, the values have to be different because there are different rates of change and different linear coefficients; and also each input value will result in a different output value because they all have different parameters as well.
Is the relation in your data a function? Why or why not? Could the equation in Part A represent a function? Why or why not? Explain your answer.
Yes, it is a function because each input from part A fits well together with the output on the other set, which matches the definition of a function.
Answer:
11.9
Step-by-step explanation:
which of the following is true
Answer:
b
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Can anyone help me please??
