please prove this...​

Please Prove This...

Answers

Answer 1

Answer:  see proof below

Step-by-step explanation:

Use the following Sum to Product Identities:

sin (A) - sin (B) = 2 cos (A+B)/2 · sin (A-B)/2

sin (A) + sin (B) = 2 sin (A+B)/2 · cos (A-B)/2

Given:  sin Ф = k sin β      -->   (sin Ф)/(sin β) = k

Proof RHS → LHS

[tex]\text{RHS:}\qquad \qquad \qquad \dfrac{k-1}{k+1}\tan\dfrac{\theta+\beta}{2}[/tex]

[tex]\text{Given:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-1}{\frac{\sin \theta}{\sin \beta}+1}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Simplify:}\qquad \qquad \dfrac{\frac{\sin \theta}{\sin \beta}-\frac{\sin \beta}{\sin \beta}}{\frac{\sin \theta}{\sin \beta}+\frac{\sin \beta}{\sin \beta}}}\cdot \tan\dfrac{\theta +\beta}{2}\\\\\\.\qquad \qquad \qquad = \dfrac{\sin \theta -\sin \beta}{\sin \theta +\sin \beta}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Product to Sum:}\qquad \quad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \tan\dfrac{\theta +\beta}{2}[/tex]

[tex]\text{Expand:}\qquad \qquad \dfrac{2\cos \frac{\theta+\beta}{2}\cdot \sin \frac{\theta-\beta}{2}}{2\sin \frac{\theta+\beta}{2}\cdot \cos \frac{\theta-\beta}{2}}\cdot \dfrac{\sin\frac{\theta +\beta}{2}}{\cos \frac{\theta +\beta}{2}}[/tex]

[tex]\text{Simplify:}\qquad \qquad \quad \quad \dfrac{\sin \frac{\theta +\beta}{2}}{\cos \frac{\theta+ \beta}{2}}\\\\\\.\qquad \qquad \qquad \quad =\tan\dfrac{\theta +\beta}{2}[/tex]

 [tex]\text{LHS = RHS:}\quad \tan\dfrac{\theta +\beta}{2}=\tan\dfrac{\theta +\beta}{2}\quad \checkmark[/tex]

Please Prove This...
Please Prove This...

Related Questions

What is the ratio for 2 red paper clips to 6 blue paper clips? Write it as a fraction.

Answers

Answer:

2 over 6 as a fraction simplifies as 1 over three.

Step-by-step explanation:

If you are writing as a fraction, you put 2 over 6 and simplify. Your answer is 1 over 3

Answer:

2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  2/6  

Step-by-step explanation:

its just 2/6

What does x equal?
2(3x - 2) = 20

Answers

Answer:

4

Step-by-step explanation:

2(3x-2)=20

3x-2=10

3x=12

x=4

Answer:

x=4

Step-by-step explanation:

889×27+50 is blank than 889×27

Answers

Answer:

50

Step-by-step explanation:

889*27=24003

889*27+50=24053

24053

-24003

00050

Convert the given amount to the given unit.
27 yd; ft
27 yd = ft

Answers

Answer:

81 ft

Step-by-step explanation:

1 yard=3ft

27 x 3=81

So the answer is 81 ft

That would be 81 feet

What is 350 divided by 55 as a decimal? A) 6.6 B) 6.36 C) 6.363 D) 6.363

Answers

The number 350 is called the numerator or dividend, and the number 55 is called the denominator or divisor. The quotient of 350 and 55, the ratio of 350 and 55, as well as the fraction of 350 and 55 all mean the same: 350 divided by 55, often written as 350/55. Read on to find the result of 350 divided by 55 in decimal notation, along with its properties.

350 divided by 55 = 6.36

The result of 350/55 is a non-terminating, repeating decimal. The repeating pattern above, 36, is called repetend, and denoted overlined with a vinculum. The answer is C

6.363 is the correct answer as it represents the repeating decimal correctly.

So, the correct answer is D) 6.363

To find the decimal equivalent of the division 350 divided by 55, you simply divide 350 by 55 using long division. Here's the step-by-step calculation:

   6.363636...

 _______________

55 | 350.000000

    - 330

    _______

      200

      - 165

      ______

        350

        - 330

        ______

          200

          - 165

          ______

            350

            - 330

            ______

              200

              - 165

              ______

                ...

The division continues indefinitely with the decimal repeating the sequence 36.

Therefore, the decimal equivalent of 350 divided by 55 is 6.363636...

Based on the options provided:

A) 6.6 is not correct as it rounds up the decimal prematurely.

B) 6.36 is not correct as it does not account for the repeating decimal.

C) 6.363 is not correct as it rounds down the decimal prematurely.

D) 6.363 is the correct answer as it represents the repeating decimal correctly.

So, the correct answer is D) 6.363.

Learn more about repeating decimal click;

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What is the greatest four-digit integer that meets the following three restrictions? 1- All of the digits are different. 2- The greatest digit is the sum of the other three digits. 3- The product of the four digits is divisible by 10 and not equal to zero.

Answers

I think that the greatest number that is all of these things is:9432

solve for x: 4/x=5/10

Answers

simplify 5/10 to 1/2
1. 4/x = 1/2

multiply both sides by x
2. 4= 1/2 x

simply 1/2x to x/2
3. 4= x/2

multiply both sides by 2
4. 4x2= x


simplify 4 x 2 to 8
5. 8= x

switch sides
x= 8

ANSWER; x= 8

Answer:

x = 8

Step-by-step explanation:

4/x = 5/10

=> 4/x = 1/2

=> 4 x 2 = x

=> 8 = x

=> x = 8

Which statement is true? 2.289 < 2.297 2.297 < 2.289 3.01 < 2.297 2.289 > 3.01​

Answers

Answer:

The first one, 2.2289<2.297

Step-by-step explanation:

Answer:

The answer is 2.2289<2.297 because if you look in the hundredths place there is a 9 in 2.297 but in 2.2289 there is an 2 and 9>2 so that is your answer.

Solve the following:


2x-7\4 = x+3/3


Hope u get this!

Answers

Answer:

hello it is so

Step-by-step explanation:

simple simply do the division if don't I can

The correct answer is X=33/2

PLEASE HELP ASAP Write the following equation in general form.
-x - 5y = -19

–x - 5y + 19 = 0
x + 5y - 19 = 0
x + 5y + 19 = 0

Answers

Answer:  -x - 5y + 19 = 0, choice A

All we're doing is adding 19 to both sides to get everything on the same side.

General form is Ax+By+C = 0. Some books use Ax+By = C which is just a variation of the same idea.

Daniel growing corn in a square field. The length of one side is 100 yards he needs to purchase fertilizer for the corn field. Each bag covers 50 square yards .How many bags do he need?

Answers

Answer:

200 bags are needed

Step-by-step explanation:

First let us determine the area of the corn field:

Shape of cornfield = square

Area of a square = Length × Length

where: Length = 100 yards

∴ Area = 100 × 100 = 10,000 square yards

1 bag of fertilizer is needed to cover 50 square yards:

50 square yards = 1 bag of fertilizer

[tex]\therefore 1 \ square\ yard\ = \frac{1}{50}\ bag\\10,000\ square\ yards\ =\ \frac{1}{50} \times 10,000 = \frac{10l000}{50} \\ = 200 bags[/tex]

Hence, 200 bags are needed.

Answer:

200 bags are needed

Step-by-step explanation:

I did the test and got it correct good luck everyone !!

How do I solve this problem?​

Answers

Answer:

Step-by-step explanation:

The first 2 pieces of this function agree at pi/4, so we will set them equal to each other and sub in pi/4 for x to solve for k:

[tex]ksin(\frac{\pi}{4})+(\frac{\pi}{4})^2=\frac{\pi}{4}+2[/tex] and

[tex]k(\frac{\sqrt{2} }{2})+\frac{\pi^2}{16}=\frac{\pi}{4}+2[/tex] and we'll multiply everything by 16 to get rid of the fractions. Doing that gives us:

[tex]8k\sqrt{2}=4\pi+32-\pi^2[/tex] and

[tex]k=\frac{4\pi+32-\pi^2}{8\sqrt{2} }[/tex] so

k = 3.067

The next one is a bit tricky if you're not up on your natural log equations.

Again, we set these equal to each other because they meet at the value of e. We sub in e for x and solve for m:

[tex]x +2=mlne^x[/tex]

We'll sub in e for x. ln of e to the x power is equal to x, so

e + 2 = me and

[tex]m=\frac{e+2}{e}[/tex] so

m = 1.736

Hope that helps!

What is the value of x in the equation -x = 6 - 3x + 8?

Answers

Answer:

x=7

Step-by-step explanation:

Collect like terms:

-x=6-3x+8

-x+3x=6+8

Simplify

2x=14

Simplify

x=7

I NEED HELP ASAP!

7x-3y= 6; х= 3

Answers

Answer:

If you are looking for y it's 5

Step-by-step explanation:

Plug in 3 for x

7(3) -3y = 6

21 - 3y = 6

subtract 21 from both sides

-3y = - 15

divide by three from both sides

y = 5

This question is confusing. Please help me!

Answers

Answer:

C. 490.

Step-by-step explanation:

25% = 0.25.

If the number of emails that Ryan and Taylor each received  is x emails then Sara received  2x + 0.25 * 2x = 2.5 emails.

So 2x + 2.5x = 882

x = 882/4.5

x = 196.

So Sara received 2.5 * 196

= 490 emails.

- 3(4r - 8) = 36 - 2r

Answers

Answer:

r= -1.2

Step-by-step explanation:

first use distributive property

- 3(4r - 8) = 36 - 2r

-12r +24 = 36-2r

+2r.           +2r

-10r +24= 36

-24.           -24

-10r = 12

/-10.     /-10

r= -1.2

Answer:

Step-by-step explanation:

Equation: -3(4r - 8) = 36 - 2r

Step 1:

-12r + 24 = 36 - 2r       Multiply (4r - 8) by -3 using the Distributive Property.

Step 2:

-10r + 24 = 36        Add -12r and -2r by 2r.

Step 3:

-10r = 12        Subtract 24 and 36 by 24.

Step 4:

r = -12/10          Divide both sides by -10

Step 5:

r = -6/5           Simplify the fraction.

write an expression that represents the total amount of fencing needed to enclose the two fields. -how would you do this?-

Answers

Answer:

8x + 60

Step-by-step explanation:

4(x + 5) + 2(x - 10) + 2(x + 30)

= 4x + 20 + 2x - 20 + 2x + 60 (combine like terms)

= 8x + 60

Solve the inequation (2x+3x)4 using distributive method.

Answers

Answer:

First, distribute the 4.

2x times 4  = 8x

3x times 4 = 12x

then add/ combine like terms.

8x + 12x = 20x

Step-by-step explanation:

Answer:

20x

Step-by-step explanation:

distribute the 4 to the 2x and 3x: 4 * 2x= 8x and 4 * 3x= 12x

then add the x's together: 8x+12x=20x

so the answer is 20x

Point Q'Q ′ Q, prime is the image of Q(0,6)Q(0,6)Q, left parenthesis, 0, comma, 6, right parenthesis under the translation (x,y)\to(x+7,y-5)(x,y)→(x+7,y−5)left parenthesis, x, comma, y, right parenthesis, \to, left parenthesis, x, plus, 7, comma, y, minus, 5, right parenthesis. What are the coordinates of Q'Q

Answers

Q is located at (0,6)

The translation rule is [tex](x,y) \to (x+7,y-5)[/tex] which says to add 7 to the x coordinate and subtract 5 from the y coordinate. Doing that to (0,6) moves it to (7,1) which is where point Q' is located.

In other words, if you shift point Q(0,6) seven units to the right and five units down, then it arrives at Q ' (7,1)

Answer: (7, 1)

The coordinates of Q' are [tex]Q'(x,y) = (7, 1)[/tex].

Note - There are typing mistakes in the question. Correct statement is presented below:

Point Q' is the image of [tex]Q(0,6)[/tex] under the translation [tex](x,y) \to (x+7, y-5)[/tex]. What are the coordinates of Q'.

In this question we should use the point and the operation described in statement. Vectorially speaking, a translation is defined by the following operation:

[tex]P'(x,y) = P(x,y) + T(x,y)[/tex] (1)

Where:

[tex]P(x,y)[/tex] - Original point.[tex]P'(x,y)[/tex] - Translated point. [tex]T(x,y)[/tex] - Translation vector.

If we know that [tex]Q(x,y) = (0,6)[/tex], then the coordinates of [tex]Q'(x,y)[/tex] are:

[tex]Q'(x,y) = Q(x,y) + (7,-5)[/tex]

[tex]Q'(x,y) = (0,6) + (7,-5)[/tex]

[tex]Q'(x,y) = (7, 1)[/tex]

The coordinates of Q' are [tex]Q'(x,y) = (7, 1)[/tex].

We kindly invite to see this problem on rigid transformations: https://brainly.com/question/18613109

8(4√7 - √18) I breed the answer fast please

Answers

Answer:

32[tex]\sqrt{7}[/tex] - 24[tex]\sqrt{2}[/tex]

Alternative form:

≈50.72292

Step-by-step explanation:

Step one,

Simplify the radical expression:

8(4√7 - √18)  

Still Stuck?  *( √18 Simplified is 3√2)*

Your answer should look like this:  8(4√7 - 3√2)

Step two,

Distribute 8 through the parentheses:

8(4√7 - 3√2)

Still Stuck?   *( Use distribuitave property to distribute 8 to (4) and (-3). You should get (32) and (-24)*

Your answer should look like this: 32√7 - 24√2

Solution,

32[tex]\sqrt{7}[/tex] - 24[tex]\sqrt{2}[/tex]

Alternative form:

≈50.72292

*For alternative form, plug the final answer into your calculator. Round it if necessary*

alternative form:50.72292

Point E is on line segment DF. Given DE = 2x, EF = 2x – 6, and
DF = 3x + 5, determine the numerical length of EF.

Answer: EF =

Answers

Answer:

EF is 16.  

Step-by-step explanation:

So we know that Point E is somewhere on Line DF. In other words, DE plus EF must equal DF. In an equation, this is:

[tex]DF=DE+EF[/tex]

We are given that DE is 2x, EF is 2x-6, and DF is 3x+5. So, substitute:

[tex](3x+5)=(2x)+(2x-6)[/tex]

Now, solve for x.

On the right, combine like terms:

[tex]3x+5=4x-6[/tex]

Subtract 4x from both sides:

[tex]-x+5=-6[/tex]

Subtract 5 from both sides:

[tex]-x=-11[/tex]

Divide both sides by -1:

[tex]x=11[/tex]

Now that we know x is 11, substitute this back into the equation for EF to find EF.

[tex]EF=2x-6[/tex]

Substitute 11 for x:

[tex]EF=2(11)-6[/tex]

Multiply:

[tex]EF=22-6[/tex]

Subtract:

[tex]EF=16[/tex]

And we're done!

Is 22 + 32 = 42 a true statement?

Answers

False because 22 + 32 =54

Answer:

No. 22+32=54

Step-by-step explanation:

what is the horonzontial distance between the two points(3,4) and (8,4)

Answers

Answer:

Distance  =  5.099

Step-by-step explanation:

Given h(x)= 4x^2, find h(3)

Answers

Answer: 36

Explanation:

h(x) = 4x^2

Find h(3):

Simply plug x = 3 in the function:
h(3) = 4(3)^2
h(3) = 4(9)
h(3) = 36
You can make x 3 in this to help get the answer. h(3)= 4(3)^2. Using the order of operations, we do 3^2 first. The answer for that is 9. Then we do 9 times 4, which is 36. 36 is our final answer. Hope this helps!

9. This piecewise function represents the Social Security taxes for 2009. How much did Rachel pay in Social
Security tax if she earned $102,000 in 2009?
(0.062x
when 0< x < 106,800
($6,621.60
when x > 106,800
Nax)
a. $6,824.60
b. $6,355.10
c. $6,324.00
d. $6,220.00

Answers

Answer:

Option c.

Step-by-step explanation:

It is given that the piecewise function represents the Social Security taxes for 2009.

[tex]Tax=\begin{cases}0.062x & \text{ when } 0< x < 106,800 \\ \$6,621.60 & \text{ when } x > 106,800 \end{cases}[/tex]

We need to find Rachel's security tax if she earned $102,000 in 2009.

Since 102,000 lies in [tex]0<x<106,800[/tex], therefore

[tex]Tax=0.062x[/tex]

Put x=102000.

[tex]Tax=0.062(102000)[/tex]

[tex]Tax=6324[/tex]

So, the Social  Security tax is $6324.

Therefore, the correct option is c.

1.5y-9.82=-9.37-10.1y-14.37 solve for y

Answers

Step-by-step explanation:

1.5y - 9.82 = -9.37 - 10.1y - 14.37

1.5y + 10.1y = 9.82 -9.37 - 14.37

11.6y = −13.92

y = (-13.92)/11.6

y = -1.2

O points
Mr. Freeman has a square cornfield. Which of the following could be the
area of the cornfield if the sides are measured in whole numbers?
150 square acres
189 square acres
200 square acres
225 square acres

Answers

Step-by-step explanation:

Notice that 15 squared = (3 * 5)^2 = 9 * 25 = 225.

So the area of the cornfield can be 225 square acres.

Consider this expression.
(x + 9)(x - 2) - 9x - 6
What is equivalent?

Answers

Answer:

We can find an expression equivalent to the one given by expanding the expression given,

[tex](x + 9)(x - 2) - 9x - 6\\x^2-2x+9x-18-9x-6\\x^2-2x-24[/tex]

So [tex]x^2-2x-24[/tex] is a possible expression.

The required expression equivalent to (x + 9)(x - 2) - 9x - 6 is  (x + 4)(x - 6).

Given that,
(x + 9)(x - 2) - 9x - 6, an equivalent expression is to be determined.

What are functions?

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

= (x + 9)(x - 2) - 9x - 6
= x² + 9x -2x -18 - 9x - 6
= x² - 2x - 24
= x² -6x + 4x - 24
= x (x - 6) + 4 (x - 6)
= (x + 4)(x - 6)

Thus, the required expression equivalent to (x + 9)(x - 2) - 9x - 6 is  (x + 4)(x - 6).

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x2 + y2 = 13
x² - y2 = -16
Solve

Answers

x + y = 3 , 2x - 8y = 19
x + 2y = 4 , x - y = -3
x - y = 9 , x - y = 6

There

10
Write the numbers in order from least to greatest (**HINT: You need to
make them all decimals or all fractions***): 5/1000, 0.003, 9/1000

Answers

Answer:

0.003, 5/1000, 9/1000

Step-by-step explanation:

0.003 is thousandths.

5/1000 is thousandths.

9/1000 is thousandths.

I converted them to fractions.

5/1000 is already a fraction

Same for 9/1000

0.003=3/1000

So 3/1000, 5/1000, 9/1000

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