sin10+sin20+sin40+sin50=sin70+sin80.prove it

Answers

Answer 1
We are going to prove it like this:
Lets use the formula sinA+sinB=2sin(A+B/2)cos(A-B/2)
 Now we are going to take the left side of equation
sin10+sin40+sin50+sin20
 Arranging =(sin50+sin10)+(sin40+sin20)
Applying the above formula. =2sin(50+10/2)cos(50-10/2)+2sin(40+20/… =2sin(30)cos(20)+2sin(30)cos(10)
=2sin30{cos20+cos10}
Again using the formula
cosA+cosB= 2cos(A+B/2)cos(A-B/2)
=2sin30{2cos(20+10/2).cos(20-10/2)}
=2sin30{2cos(15).cos(5)}
=2(1/2){2cos15.cos5} as sin30=1/2
=2cos15.cos5
Taking right side of equation sin70+ sin80
Using the formula sinA+sinB
= 2sin(A+B/2)cos(A-B/2)
=2sin(70+80/2)cos(70-80/2)
=2sin75cos5
=2sin(90-15)cos5
=2cos15.cos5 Hope this helps

Related Questions

How would i find the rule for this pattern:1280,640,320,160?

Answers

Final answer:

The rule for this pattern is to divide each number by 2 to get the next number.

Explanation:

To find the rule for this pattern, we need to identify the relationship between the numbers. In this case, each number is half of the previous number. So, to find the next number, we divide the previous number by 2.

For example, 640 is half of 1280, 320 is half of 640, and so on. This means that to find the next number, we divide 320 by 2 to get 160.

Therefore, the rule for this pattern is to divide each number by 2 to get the next number.

Molly runs each morning once around a circular path in her neighborhood. if the diameter of the path is 1.4 miles, how far does molly run each day?

Answers

To work out the distance of the path, you need to find out the circumference.
Formula for circumference = pi multiplied by the diameter

So you simply do:
pi multiplied by 1.4 miles

And you should get:
4.39822971503... miles

Simply round the result to an appropriate value (e.g. 3 decimal places).

Answer: 4.398 miles (to 3dp)
Hope the answer helps :)

The price of a pair of shoes increases from $51 to$69. what is the percent increase to the nearest percent?

Answers

Answer:

35%

Step-by-step explanation:

What are the common factors of 15 18 a d 12?

Answers

you just need to list the factors of all 3 numbers, and see what numbers they have in common!

15: 1,3,5,15

18: 1,2,3,6,9,18

12: 1,2,3,4,6,12

so in all you can say that the common factors of 15,18,12 is: 1 and 3

How can you write 23/3 as a mixed number?

Answers

23/3 = 7 2/3 <======

Reduce this algebraic fraction 27c^4d^5/9c^7d^4 ...?

Answers

The answer is [tex] \frac{3d}{ c^{3}}[/tex]

The fraction is: [tex] \frac{27 c^{4} d^{5}}{9 c^{7} d^{4} } [/tex]
Let's rewrite it: [tex]\frac{27 c^{4} d^{5}}{9 c^{7} d^{4} }= \frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }[/tex]

Now, let's use the rule [tex] \frac{ x^{a} }{ x^{b}} = x^{a-b} = \frac{1}{ x^{b-a} } [/tex]:
[tex]\frac{27}{9}*\frac{c^{4}}{c^{7}}*\frac{d^{5}}{d^{4} }=3* \frac{1}{c^{7-4}} * d^{5-4} =3* \frac{1}{ c^{3} } *d^{1}= \frac{3d}{ c^{3} } [/tex]

$45.00 for 9 pounds what is the unit rate?

Answers

$45/9 pounds
$5 per pound
To find the unit rate, divide 45 by 9.

45/9 = 5

The unit rate is $5.

The total cost of gasoline varies directly with the number of gallons purchased. Gas costs $1.89 per gallon. Write a direct variation to model the total cost c for g gallons of gas.

Answers

If it costs $1.89 per gallon then it would be C = 1.89G

Answer:c=1.89g

Step-by-step explanation: gradpoint

Which of the following correctly expresses the number below in scientific notation? 0.00000765
A. 7.65 • 10-6
B. 7.65 • 10-7
C. 7.65 • 10-5
D. 76.5 • 10-7
E. 765 • 10-8
F. 765 • 10-6

Answers

Start with 7.65. Then count the zeros to the left of the decimal place.

Should be 7.65 * 10^-6
Final answer:

In scientific notation, 0.00000765 is written as 7.65 • 10-6. This represents the number of places to the right of the decimal point to the first non-zero digit.

Explanation:

The task is to express the number 0.00000765 in scientific notation. Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in standard decimal form. It is commonly used in science and mathematics.

We have to determine which of the given options correctly represents this number in scientific notation.

The number 0.00000765 can be written as 7.65 times ten to the negative sixth power. This is because there are six places to the right of the decimal point before we encounter the first non-zero digit. Therefore, the correct answer is 7.65 • 10-6.

Learn more about scientific notation here:

https://brainly.com/question/16936662

#SPJ2

Common factors of 32 and 40

Answers

32=2^5
40=2^3.5
common factors=2^3=8

A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.

x + y = 24

3x + 5y = 100

What does the solution of this system indicate about the questions on the test?

Answers

First we solve system to see what it indicates.

multiply first equation by 3 and subtract it from second.
it will become
3x + 3y = 72

after subtracting from second we get:
2y = 28
y = 14
x = 24 - 14 = 10

We can conclude that there are more 5 points question. there are 10 three point questions and 14 five point questions.

Graph x2 + 9y2 = 25. What are the domain and range?
Someone please help me !
(Picture below)

Answers

x^2 + 9y^2 = 25
x^2/5^2 + (3y)^2/5^2 = 1

This represent an equation of an ellipse with cente at the origin, the horizontal major axis running from -5 to 5 and vertical minor axis running from -5/3 to 5/3

The third graph is the correct answer.

Answer:

the third graph is correct.

Step-by-step explanation:

domain: -5 ≤ x ≤ 5

range: -1.67 ≤ y ≤ 1.67

What is the sum?
7/2+(-3/5)

Answers

Use pemdas. 7/2-3/5 Find common denominator and then solve. 35/10 - 6/10 = 29/10 = 2 9/10

If P(x) = 2x 4 - x 2 + 3x - 1, use synthetic division to find P (2).

17
21
33

Answers

Answer:  33

Step-by-step explanation:

P(x) = 2x 4 - x 2 + 3x - 1

To find the value of p(2) we simply substitute x = 2.

That is; wherever you see x, simply put 2

P(2)  =  2 [tex](2)^{4}[/tex]   -  [tex](2)^{2}[/tex]   +  3(2)  - 1

         =2(16) -  4  + 6 - 1

        = 32  - 4 + 6 -1

        =28 + 6 -1

         =34 - 1

         =33

Therefore the value of  P(2) is 33

Which of the points shown below are on the line given by the equation y = x - 1? Check all that apply.



A. Point A: (1, -2)

B. Point B: (2, 1)

C. Point C: (4, 3)

D. Point D: (-3, -4)


Answers

Final answer:

To find points on the line y = x - 1, substitute the x and y values of each point into the equation. Points B, C, and D satisfy the equation.

Explanation:

The equation given is y = x - 1. To determine which points lie on this line, you need to substitute the x and y values of each point into the equation and see if the equation holds true.

Point A: (1, -2) - Substitute x = 1, y = -2 into y = x - 1. -2 = 1 - 1 is false.Point B: (2, 1) - Substitute x = 2, y = 1 into y = x - 1. 1 = 2 - 1 is true.Point C: (4, 3) - Substitute x = 4, y = 3 into y = x - 1. 3 = 4 - 1 is true.Point D: (-3, -4) - Substitute x = -3, y = -4 into y = x - 1. -4 = -3 - 1 is true.

Therefore, Points B, C, and D lie on the line represented by the equation y = x - 1.

Given: x + y = 15. Which of the following are ordered pairs of this equation?

Answers

(0,5)(1,4)(2,3) I got those
The answer is most likely:

(0-5) (1-4) (2-3)

A Branliest or just a thanks would be terrific!

Fill in the blank:
To find the values of p, q, r and s, you should start by finding all factor ___ of the leading coefficiant and constant term. Then try them to determine which ones give you the correct product ...?

Answers

I can be wrong, but I think that the answer is: To find the values of p, q, r and s, you should start by finding all factor pairs of the leading coefficiant and constant term. 

at a local store you find the following prices listed:
Tape 2 rolls for $1.28
Notepads 3 pads for .87
Highlighters 1 for 1.59
Pens 2 for 1.98

How much would you pay for one roll of tape, two note pads, two highlighters, and two pens?

A. $8.07
B. $4.50
C. $6.38
D. $5.72

Answers

The answer is C. $6.38

four times daphne's age plus five times isaac's age adds up to 57. also, isaac's age is 11 less than twice daphne's age. how old is isaac?

Answers

4d + 5i = 57
i = 2d - 11

4d + 5(2d - 11) = 57
4d + 10d - 55 = 57
14d = 57 + 55
14d = 112
d = 112/14
d = 8 <== Daphne's age

i = 2d - 11
i = 2(8) - 11
i = 16 - 11
i = 5 <==Isaac's age

Quadrilateral MNOP is a rhombus. Find the measure of angle MRN.

a. 90
b. 45
c. 85
d. 60

Answers

Not sure but I think it should be 60.
Final answer:

Without further information or a diagram indicating the position of point R in the rhombus MNOP, we cannot accurately determine the measure of angle MRN. If R is at the intersection of the diagonals, angle MRN would be 90 degrees.

Explanation:

The student asks to find the measure of angle MRN in a rhombus named MNOP. Unfortunately, the information provided is insufficient to determine the measure of angle MRN directly. However, one property of a rhombus is that all sides are of equal length and opposite angles are equal. Additionally, the diagonals of a rhombus are perpendicular bisectors of each other and bisect the angles of the rhombus. Without a specific diagram or more information about the location of point R in relation to the rhombus, it's impossible to give an exact answer. If R is located at the center where the diagonals intersect, then angle MRN would be 90 degrees because the diagonals of a rhombus bisect each other at right angles. If R is not at the center, then we cannot determine the angle without additional information.


1) A comet that passes through the solar system just once has a path that is modeled by a conic section. Astronomers discover a comet whose path is modeled by the following equation, with the Sun at one focus. What type of conic section is the comet's path?
x^2/2,500-y^2/37,500=1

2) What are the vertices of the comet's path? (Hint: Examine the general formula for the path and identify the numbers that determine the vertices.)

3) At its closest point to the Sun, this comet is ____ million miles from the Sun. (Enter only the number.)
Hint: Subtract the vertex from the focus

Answers

The answers are as follows:

1) see the – in front of y, The answer would be hyperbola.

2) see 2500 under x²? √2500 = ±50 on the x axis are the vertices 

3) focus² = 2500 + 37,500 = 40,000 

focus = 200 

focus – vertex = 200 - 50 = 150 million miles

I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!

How many solutions are there to the equation below?

11x + 25 = 7x + 15







A.

0








B.

Infinitely many








C.

1

D a monky beats a man with a stick

Answers

the answer is c because ther is only one value for x which is -2.5

Answer:

D) A monky beats a man with a stick.

Step-by-step explanation:

Monky like stick. Monky like beat man.

70% of a number is 98.

What is 90% of that same number?



A.
63


B.
68.6


C.
88.2


D.
126

Answers

The solution is as follows:

Set up the proportion:

70% - 98
90% - x

70% / 90% = 98 / x

7 / 9 = 98 /x

(7 / 9) x = 98

x = 98 x 9/7

x = 14 x 9

x = 126

The answer is D. 126.


I hope my answer has come to your help. God bless and have a nice day ahead!

Which relation is a direct variation that contains the ordered pair (2, 7)?
Y=4x-1
y=2/7x
y=7/2x
y=7/x

Answers

Lets write equation of a function:

y = kx + n

Direct variation in simple is equation of a line which has n=0 or in other words which y to x ratio is k.

First option gets 7=7 but it isnt direct variation because n is not equal to 0

third option is indeed correct. once we implement coordinates (2,7) we get 7=7

Answer is 
y = 7/2x

Answer: The guy up above, is correct. The answer is D

Step-by-step explanation: Edge 2021

"In ABC, mBAC = 5x + 8, mABC = 6x + 22, and mBCA = 3x  25.
A.Find the value of x.
B.Find the measure of 3. Show your work."

Answers

Actually, the answer is 12.5

5x+8+6x+22+3x+25= 180

(5x+6x+3x)+(8+22-25)= 180

14x+5=180

14x+(5-5)=180-5

14x=175

14x/14=175/14

X=12.5

Double check:

(5*12.5)+8=70.5

(6*12.5)+22= 97

(3*12.5)-25=12.5

70.5+97+12.5=180 degrees.


So, x=12.5


Which is a secant of circle A?

(Points : 1)
segment AB

line DE

segment HG

line CD

Answers

Answer:

The correct option is line CD

Step-by-step explanation:

Given the diagram we have to find the secant of circle A.

Secant of a circle is a line intersecting the circle at exactly two different points and a chord is the line determined by these two.

In the circle A the only line intersect two different points is CD and the interval on a secant is the chord of circle.

Here, HG is only the chord of circle not secant.

Hence, the correct option is line CD

A 4 in. by 5 in. photo is enlarged so that its width (shorter dimension) is 5 in. What is the length of the enlarged photo? 5.25 in. 6 in. 6.25 in. 7 in.

Answers

6.25 in Answer:

6.25 in

Step-by-step explanation:

i took the text

Final answer:

The length of the enlarged photo is 6.25 inches.

Explanation:

The question asks for the length of an enlarged photo when its width, the shorter dimension, has been increased from 4 inches to 5 inches. This is a problem of similar rectangles where the aspect ratio must remain constant. In the original photo, the width is 4 inches and the length is 5 inches. As the photo is enlarged, and the new width becomes 5 inches, we must find the new length that keeps the aspect ratio the same.

To find the scale factor, you compare the new width to the original width:

Scale factor = new width / original width = 5 inches / 4 inches = 1.25

To find the new length, multiply the original length by the scale factor:

New length = original length × scale factor = 5 inches × 1.25 = 6.25 inches

Therefore, the length of the enlarged photo is 6.25 inches.

Which is not a property of all similar triangles

Answers

The corresponding side are congruent
The corresponding side are congruent is your answer.

The distance from the library to the park is 0.7 kilometers. how many meters is this?

Answers

the answer is 700 meters

Answer:

700 is the answer

Step-by-step explanation:

yuo multipy bye the 1000 over 1


WILL UPVOTE

This is all the info it gives me so sorry.



The formula for rate is r=dt.

Solve for d.

Enter your answer in the box.



Thanks!

Answers

divide both sides by t. answer is d=r/t
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