[tex]( \sin^{2} ( \frac{\pi}{ 4 } - \alpha ) ) = \frac{1}{2} (1 - \sin(2 \alpha ) )[/tex]
Prove​

Answers

Answer 1

Step-by-step explanation:

[tex] \sin^2 (\frac{\pi}{4} - \alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

Use the identity

[tex] \sin^2 \theta = \dfrac{1 - \cos 2\theta}{2} [/tex]

on the left side.

[tex] \dfrac{1 - \cos [2(\frac{\pi}{4} - \alpha)]}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

[tex] \dfrac{1 - \cos (\frac{\pi}{2} - 2\alpha)}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

Now use the identity

[tex] \sin \theta = \cos(\frac{\pi}{2} - \theta) [/tex]

on the left side.

[tex] \dfrac{1 - \sin 2\alpha}{2} = \frac{1}{2}(1 - \sin 2\alpha) [/tex]

[tex] \frac{1}{2}(1 - \sin 2\alpha) = \frac{1}{2}(1 - \sin 2\alpha) [/tex]


Related Questions

please help i’ll give brainliest! thank you!

Answers

Answer:

no correlation

Step-by-step explanation:

the dots are scattered randomly and not in a positive or negative correlation

is 3x+11/x-4 = 4/x(x-4)​

Answers

Answer:

x= -5

Step-by-step explanation:

BRANLIEST AND 50 POINTS



What is the prime factorization of 135?

3 × 5 × 9
3 × 5 3
3 2 × 5 2
3 3 × 5

Answers

The prime factorization for 135 is 3,3,3, and 5.

Answer:

3×5×9

Step-by-step explanation:

It's the only answer that can be applied

But you have to expand it farther

2×5×9

2×3×3×5

Note:if you want the answer from your options the answer is 2×5×9

Otherwise 2×3×3×5

JK has endpoints located at J(15, - 13) and K(-9, 27). What are the coordinates of the midpoint of JK?

Answers

Answer:

[tex](3,7)[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Midpoint Formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]

Step-by-step explanation:

Step 1: Define

Point J (15, -13)

Point K (-9, 27)

Step 2: Find Midpoint

Simply plug in your coordinates into the midpoint formula to find midpoint.

Substitute [MP]:                    [tex](\frac{15-9}{2},\frac{-13+27}{2})[/tex]Subtract/Add:                       [tex](\frac{6}{2},\frac{14}{2})[/tex]Divide:                                   [tex](3,7)[/tex]

Find the value of x. Use the photo I uploaded to help plz.
A. X=2
B. X=3
C. X=33
D. X=52

Answers

The answer should be option B

HURRY PLZZZ I WIL MARK LOTS OF POINTS Which pattern does not follow the rule subtract 8, multiply by 2, subtract 8,
multiply by 2, .?
A)15,7, 14,6, 12,..
B)20, 12, 24, 16, 30, ...
C)17,9, 18, 10, 20, .
D)24, 16, 32, 24, 48

Answers

Answer:

B)20,12,24,16,30

Step-by-step explanation:

A) 15,7,14,6,12

15 to 7: subtract 8

7 to 14: multiply by 2

14 to 6: subtract 8

6 to 12: multiply 2

B) 20,12,24,16,30

20 to 12: subtract 8

12 to 24: multiple 2

24 to 16: subtract 8

16 to 30: add 14

C)17,9,18,10,20

17 to 9: subtract 8

9 to 18: Multiply 2

18 to 10: subtract 8

10 to 20: multiply 2

D)24,16,32,24,48

24 to 16: subtract 8

16 to 32: multiply 2

32 to 24: subtract 8

24 to 48: multiply 2

You can clearly see that all of them follow the pattern except B, making B the answer.

Don't be afraid to reach out if you need any more help. I hope that helps you!

Answer:

B

Step-by-step explanation:

B becasue 30 isn't 16 times 2. It would have to be 32.

please help me get the question right away ​

Answers

Answer:

true

Step-by-step explanation:

hopefully this helps :)

True I hope you get it right

B
1
N
4
5
5
(4x+6)
(5x -5)
7
00
0
A
С
(3x + 8)
The value of x is
and the length of the base is

Answers

Answer: (2x + 3) • (x-1)

Step-by-step explanation:

1 Pull out like factors :

4x + 6 = 2 • (2x + 3)

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

(5x - 5) = 5 • (x - 1)

can anyone help and explain why this is either proportional or not? urgent!! (it needs an explanation too)

Answers

Answer:

Yes it is proportional

Step-by-step explanation:

Notice how when x goes up 1 y goes up by 1.6. There is a pattern, if there is no pattern then you would see that numbers either go up or down with no pattern.

A flagpole that is 28 feet tall casts a 15-foot shadow. At the same time, a nearby tree casts a 21 foot shadow. Find the height of the tree.

Round to the nearest tenth.

Answers

Answer:

7.5 ft tall

Step-by-step explanation:

We can find the height of the tree if you provide the actual length of the trees shadow.

Not really sure what a "toilet for a shadow" means.

Example: If the tree cast a shadow that was 4 feet long we would use a ratio:

Height/shadow = Height/Shadow

28/15 = x/4 cross multiply

15x = 4(28)

x = 4(28)/15 ≅ 7.47 ft

Rounding I would call the tree 7.5 ft tall

Hope this helps.

Answer:

39.2 feet

Step-by-step explanation:

In case of flagpole:

[tex] tan \theta = \frac {28}{15}..... (1)[/tex]

Since, a nearby tree casts a 21 foot shadow at the same time. So the angle formed will be equal.

Let the height of the tree be x feet.

Therefore,

[tex] tan \theta = \frac {x}{21}.....(2)[/tex]

From equations (1) & (2)

[tex] \frac {28}{15} = \frac {x}{21}.....(2)\\\\

x = \frac{28\times {21} }{{15} }\\\\

x = \frac{588}{{15} }\\\\

x = 39.2 \\\\

[/tex]

Below is the graph of linear equation F(x)-2x-4
AL
1. Which point represents the grach's yntercept?
A. Part A C. Point
B. Parte D. Point

2 Which point represents the grach's recept?
A. Porta C. Point
B. Part 3
D. Ponto
1 Which ont represents the grach's 2007
A. Part C. Ponto
B Parts D. Point

Answers

Answer:

1. B. point B.

2. C. point C.

3. C. point C.

Step-by-step explanation:

1. In order to find the graph's y-intercept, we need to locate the point where the line crosses the y-axis. This will always happen at x=0, therefore, the y-intercept is located at point B (0,-4)

2. In order to find the x-intercept, we need to find the point where the line crosses the x-axis. This will generally happen when y=0, so that will be point C (2,0)

3. In order to find the graph's zero, we need to find the point where y=0. In other words, the graph's zero is the point where the function is equal to zero (the x-intercept) so this will br point C again (2,0)

33+36 is the same as Blank +29

Answers

40 is the answer to the problem.

11. The chance of a woman getting breast cancer in her lifetime is 1 out of 8. At this rate, how many
women in classroom of 32 women would be expected to come down with breast cancer in her lifetime?

Answers

Answer:4

Step-by-step explanation:8x4=32

Since it is 1 out of 8, 32/8=4

Find the area of the rhombus! Please help!

Answers

Answer:

100m

Step-by-step explanation:

First, find the area of one triangle. Use l*w/2 to do that.

10*5=50

50/2=25

Multiply this by 4 to get the total area

25*4=100

Have a good day!

Jonathan wants to the new baseball game for his game console. The game costs $45.99. If sales tax is 6%, write an equation to find the total cost of the game, represented as P.

Answers

Answer:

45.99x.94=P

Step-by-step explanation:

If RSTU is translated by the rule (x,y) > (x+2, y-10) , in which quadrant will the image R'S'T'U be located ?

Answers

Answer:

D) Quadrant 3

Step-by-step explanation:

ok so lets get a random point and try it out i see -10 is a big number so i will use R and see where it is and then t

R(-8,3) so add 2 to x and minus 10 y

R'(-6,-7)

Now t

T(-4,9)

(+2,-10)

T'(2,-1)

It is Quadrant 3

If RSTU is translated by the rule (x, y) ⇒ (x + 2, y - 10) the image R'S'T'U be located at the D. Third quadrant.

What are transformations?

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

From the given diagram, the coordinate of the vertex(T) is (- 4, 10).

Let, T' be the vertex when the quadrilateral is translated by the rule

(x, y) ⇒ (x + 2, y - 10).

Therefore, The translated coordinate of the vertex(T') is,

(- 4 + 2, 10 - 10).

= (- 2, 0).

So, The quadrilateral will lie in the third quadrant.

learn more about quadrilaterals here :

https://brainly.com/question/29934440

#SPJ2

A camper leaves camp and travels 4 miles west and 3 miles north. How far is the camper from his original starting point?

Answers

Answer:

5 miles

Step-by-step explanation:

To answer this question, use the following:

According to pythagorean theorem, the hypotenuse of the triangle, c, with legs a and b, can be found with the following equation:

[tex]a^2+b^2=c^2[/tex]

Thus plugging in 3 for a and 4 for b:

[tex]c^2 = 25[/tex]

[tex]c=5[/tex]

Fay opens a credit card with an APR of 15.25% compounded monthly. How much is charged in interest this month if her balance is $1,300? (4 points)

Answers

Answer:

total charge = $ 16.52

refer to the Attachment please :)

hope this helps you ^^"

Suppose that a bond has a face value of ₱ 100,000 and its maturity date is 10 years from now. The coupon rate is 5% payable semi-annually. Find the price of the bond, assuming that the required yield is 4%.

Answers

Answer:

Bond Price​= $108,175.71

Step-by-step explanation:

Giving the following information:

Face value= $100,000

Coupon rate= 0.05/2= 0.025

YTM= 0.04/2= 0.02

Time period= 10*2= 20 semesters

To calculate the price of the bond, we need to use the following formula:

Bond Price​= cupon*{[1 - (1+i)^-n] / i} + [face value/(1+i)^n]

Bond Price​= 2,500*{[1 - (1.02^-20)] / 0.02} + [100,000/(1.02^20)]

Bond Price​=  40,878.58 + 67,297.13

Bond Price​= $108,175.71

In this exercise we have to use the knowledge of finance to calculate the stipulated value through the percentages, thus we find that:

Bond Price will be  [tex]\$108,175.71[/tex]

From the information given in the text we found that:

Face value: [tex]\$100,000[/tex] Coupon rate: [tex]0.05/2= 0.025[/tex] YTM: [tex]0.04/2= 0.02[/tex] Time period: [tex]20 \ semesters[/tex]

To calculate the price of the bond, we need to use the following formula:

[tex]Bond\ Price = cupon*{[1 - (1+i)^{-n}] / i} + [face \ value/(1+i)^n][/tex]

So with the formula already informed we will replace the values ​​given in the text find what we want.

[tex]Bond \ Price = 2,500*{[1 - (1.02^{-20})] / 0.02} + [100,000/(1.02^{20})]\\Bond Price= 40,878.58 + 67,297.13\\Bond Price= \$108,175.71[/tex]

See more about finances at: brainly.com/question/10024737

8. You deposit $2000 in an account that
earns 5% annual interest. Find the balance
after 1 year if the interest is compounded
quarterly.
A. $2,100
B. $2,101.89
C. $2,102.32
D. $2,102.49

Answers

Answer: A, $2,100

Step-by-step explanation:

2000x1.05=2,100

please help with 1-3

Answers

Number 1. is 1/5 but in decimal form it’s 0.2
1/5. ishevwheiebbdsnbssbbs

y = -2x + 13 when x = 6

Answers

Answer: 1

Work: After plugging in the 6 in the X, the new equation is -2(6) + 13. After doing the multiplication of -2 and 6, you get -12. Add -12 + 13, and the answer (Or y) equals 1.

I hope this helps, and Happy Holidays! :)

In the context of this graph, what do the slope and y-intercept mean?


Help me for a brainliest

Answers

We’re are the answer choices

The measure of an angle is 26°. What is the measure of its complementary angle?

Answers

Answer:

64

Step-by-step explanation:

Complementary angles have to add up to 90.

90-26=64.

Answer:

  64°

Step-by-step explanation:

  Complementary angle means it add up to 90°

  26° + x = 90°

           x = 64°

One litre of paint covers 1.5 square meters. How many litres must I buy so that I have enough to paint a wall 6 m long and 3 m high ?

Answers

Answer:

12 litres

Step-by-step explanation:

The area to be covered is

A = 6 × 3 = 18 m²

Divide the area by 1.5 for required amount of paint, that is

18 ÷ 1.5 = 12 litres

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.

108 is 36% of what number? Write and solve a proportion to solve the problem.

Answers

Answer: 300

Step-by-step explanation:

Let the number be represented by x.

Therefore, based on the information given in the question, this can be expressed as:

36% of x = 108

36/100 × x = 108

0.36 × x = 108

0.36x = 108

x = 108/0.36

x = 300

Therefore, the number is 300

Find the value of X and Y

Answers

Answer:

Answer: x=4, y=10

Step-by-step explanation:

Lines and Angles

When lines cross, the angles formed in the intersections meet certain properties that help us to solve some geometry problems.

We must recall the so-called linear angles, defined as the adjacent angles formed in the point where two lines cross.

Linear angles always add up to 180°

We can see line m intersects with the horizontal (unnamed) line forming two pair of linear angles, thus:

29x - 3 + 15x + 7 = 180

Simplifying:

44x +4 = 180

Subtracting 4:

44x = 176

Dividing by 44:

x = 176/44

x = 4

Now below the horizontal line, we find other pair of linear angles, thus:

13y - 17 + 15x + 7 = 180

Substituting x=4:

13y - 17 + 60 + 7 = 180

Simplifying:

13y + 50 = 180

Subtracting 50:

13y = 180 - 50 = 130

Dividing by 13:

y = 130/13 = 10

y = 10

Answer: x=4, y=10

Can someone help with this I’ll mark u as brainlist

Answers

Answer:i don’t really k ow but i need points to ask questions

Step-by-step explanation:

The graph shows a proportional relationship between y (price) and x (number of pounds of rice).



What is the unit rate, expressed in price per pound?

Answers

Answer:

0.80

Step-by-step explanation:

I just took the test I wrote the $1.67 it was wrong.

which is not solution to the folloeing linear equality

A. (-2, 1)
B. (0, 0)
C. (2, -1)
D. (-9, -9)​

Answers

Answer:

B

Step-by-step explanation:

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