If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA

Answers

Answer 1

Answer:

Step-by-step explanation:

Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA

Starting with the expression

4sinB= 3sin(2A+B)

Let us re write angle B = (A + B) - A

and 2A + B = (A + B) + A

Substituting the derived expression back into the original expression ww will have;

4Sin{(A + B) - A } = 3Sin{(A + B)+ A}

From trigonometry identity;

Sin(D+E) = SinDcosE + CosDSinE

Sin(D-E) = SinDcosE - CosDSinE

Applying this in the expression above;

4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}

Open the bracket

4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA

Collecting like terms

4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA

Sin(A+B)CosA = 7Cos(A+B)sinA

Divide both sides by sinA

Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA

Since cosA/sinA = cotA, the expression becomes;

Sin(A+B)cotA = 7Cos(A+B)

Finally, divide both sides of the resulting equation by sin(A+B)

Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)

CotA = 7cot(A+B) Proved!


Related Questions

a car traveling at 87 km/h and a bus leave a toll booth at the same time. twenty minutes later the bus is 3 km farther from the toll booth than the car. what is the average speed of the bus

Answers

Answer:

96 km/h

Step-by-step explanation:

Speed of car = 87 km/h

Time = 20 minutes = [tex]\frac{20}{60} = \frac{1}{3}\ hrs[/tex]

Distance traveled by bus = 3 km more than that of traveled by car

To find

Average speed of bus = ?

Solution:

Formula for distance traveled is given as:

[tex]Distance = Speed \times Time[/tex]

So, distance traveled by car in 20 minutes = 87 [tex]\times \frac{1}3[/tex] = 29 km

As per given statement, distance traveled by bus = 29 + 3 = 32 km

Time taken = [tex]\frac{1}{3}\ hrs[/tex]

Using the formula:

[tex]Speed = \dfrac{Distance}{Time}[/tex]

Speed of the bus =

[tex]\frac{32}{\frac{1}3} = \bold{96\ km/h}[/tex]

Solve for x. PLZ ANSWER FAST

Answers

Answer:

No solutions.

Step-by-step explanation:

7(2) + 39 > 53 and 16(2) + 15 > 31

14 + 39 > 53 and 32 + 15 > 31

53 >_ 53 but, 47 > 31 :/

So even with one the first equation is smaller.

CAN SOMEONE PLEASE HELP ME !!!!

Answers

Answer:

k = 29

29 + 6 = 35

-3 + 5 = 2

35 + 2 = 37

I am an odd two-digit number. The sum of my two digits is 10 and the difference of my two digits is 0. What number am I?

Answers

The answer is 55 I know this because 5 + 5 is 10 and 5 - 5 is 0. Therefor the answer is 55. HOPE THIS HELPS!

Complete the statements. f(4) is . f(x) = 4 when x is

Answers

Answer:

x=4

Step-by-step explanation:

it's a identity function because it is in the form of f(x)= x ,so the value of x is 4.

NEED HELP!

Create a table of points from the equation f (x)= 3x^2 -8x + 2

Answers

Answer:

The second table

Step-by-step explanation:

To create table of points using the function, [tex] f(x) = 3x^2 - 8x + 2 [/tex], substitute the value of x in each case.

Thus,

For x = -1,

[tex] f(-1) = 3(-1)^2 - 8(-1) + 2 = 3(1) + 8 + 2 = 3 + 8 + 2 [/tex]

[tex] f(-1) = 13 [/tex]

For x = 0

[tex] f(0) = 3(0)^2 - 8(0) + 2 = 3(0) - 0 + 2 = 0 - 0 + 2 [/tex]

[tex] f(0) = 2 [/tex]

For x = 1,

[tex] f(1) = 3(1)^2 - 8(1) + 2 = 3(1) - 8 + 2 = 3 - 8 + 2 [/tex]

[tex] f(1) = -3 [/tex]

For x = 2,

[tex] f(2) = 3(2)^2 - 8(2) + 2 = 3(4) - 16 + 2 = 12 - 16 + 2 [/tex]

[tex] f(2) = -2 [/tex]

For x = 3,

[tex] f(3) = 3(3)^2 - 8(3) + 2 = 3(9) - 24 + 2 = 27 - 24 + 2 [/tex]

[tex] f(3) = 5 [/tex]

The second table is the correct answer.

Al’s Produce Stand Al’s Produce Stand sells 6 ears of corn for $1.50. Barbara’s Produce Stand sells 13 ears of corn for $3.12. Write two equations, one for each produce stand, that model the relationship between the number of ears of corn sold and the cost. Then, use each equation to help complete the tables below.

Answers

Answer:

5.9998

Step-by-step explanation:

because thats the answer

Given the equation 4x−8y=32, a second equation that forms a system with no solution is: 1. x−2y=8 2. x−2y=32 3. x+2y=8 4. 2x−y=32

Answers

Answer:

2. x−2y=32.3

Step-by-step explanation:

Given 4x - 8y = 32, a second equation that forms a system with no solution is most easily found by reducing the given equation to x - 2y = 8; we can then easily compare this x - 2y = 8 to x - 2y = 32.3.  These two lines are parallel and thus do not intercept, and thus the system has no solution.

it is 4km from Martina house to the nearest mailbox. how far is it in meters?

Answers

Answer:

4,000

Step-by-step explanation:

1 kilo = 1,000 meters.

Y = 0.2(0.35)^t decay rate

Answers

Answer:

Step-by-step explanation:

At 1 year old it is: e1 = 2.7 mm high ... really tiny!

At 5 years it is: e5 = 148 mm high ... as high as a cup

At 10 years: e10 = 22 m high ... as tall as a building

At 15 years: e15 = 3.3 km high ... 10 times the height of the Eiffel Tower

At 20 years: e20 = 485 km high ... up into space!

find the slope of the line that contains (-1,2) and (2,2)

Answers

Answer:

[tex]slope=0[/tex]

Step-by-step explanation:

Use the slope formula:

[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}[/tex]

Rise over run is the change in the y-axis over the change in the x-axis from one point to the other. This is also known as the "slope".

Insert the values:

[tex](-1_{x1},2_{y1})\\\\(2_{x2},2_{y2})\\\\\frac{2-2}{2-(-1)}\\\\\frac{2-2}{2+1}\\\\[/tex]

Simplify:

[tex]\frac{2-2}{2+1}=\frac{0}{3} =0[/tex]

The slope of the line is 0. This means that the two points lie on the same horizontal line.

:Done

Find the missing probability: P(B)=7/20, P(A|B)=1/4, P(A∩B)=?

Answers

Answer:

P(A∩B) = 7/80

P(A∩B) = 0.0875

Step-by-step explanation:

Given

P(B)=7/20

P(A|B)=¼

Required

P(A∩B)=?

The given probability shows conditional probability and the relationship between the given parameters is as follows.

P(A∩B) = P(B) * P(A|B)

Substitute ¼ for P(A|B) and 7/20 for P(B)

The expression

P(A∩B) = P(B) * P(A|B) becomes

P(A∩B) = 7/20 * ¼

P(A∩B) = 7/80

P(A∩B) = 0.0875

Hence, the calculated P(A∩B) is 7/80 or 0.0875

Please solve.
Essie likes plants. She never misses a chance to go to the nursery section in Home Depot. Essie has a total of $65.50 to spend on her trips to the store over the next three days. On her second trip to the nursery she spent $15.50 dollars more than what she spent on the first trip to the store. On her third trip to the nursery she spent two times much as what she spent on her first trip to the nursery. How much did she spend on her first trip to the nursery? Create a linear equation to model a real-world situation and solve the equation to find the solution


Answers

Answer:

Step-by-step explanation:

Let $ x = the amount spent on the first day

The amount spent on the second day = x + 15.50

The amount spent on the third say = 2*x = 2x

Total amount Essie spent on 3 days = $65.50

x + (x +15.50) + 2x = 65.50

x + x + 15.50 + 2x = 65.50

Add like terms

4x + 15.50 = 65.50

Subtract 15.50 from both sides

4x = 65.50 - 15.50

4x = 50

Divide both sides by 4

x = 50/4

x = $ 12.50

The amount spent on the first day = $ 12.50

The amount spent on the second day = 12.50 + 15.50 = $ 28

The amount spent on the third day= 12.50 * 2 = $ 25

The following frequency table shows the number of fish caught by each of Igor's family members. What was the maximum number of fish that a family member caught? _____ fish

Answers

Answer:

4

Step-by-step explanation:

The values on the left of the table represent the number of fish caught, and the number of the right of the table represents how many family members caught that amount of fish.

Therefore, the first row means that 0 family members caught 0 fish.

The second row means that 3 family members caught 1 fish.

The third row would mean 1 family member caught 2 fish.

The next row would mean 0 family members caught 3 fish.

And the final row would mean 4 family members caught 4 fish.

The question does not ask for the total amount of fish caught; rather is ask for the maximum number of fish that a single family member caught.

Therefore, the maximum amount of fish that a single family member catches is 4. (And 4 family members did so. But individually, the maximum amount of fish one person caught is 4).

Answer:

it's 1 fish

Step-by-step explanation:

i took the test

2
3
4
5
Which expression is equivalent to (f + g)(4)?
f(4) + g(4)
f(x) + g(4)
f(4 +
| + g(4))
4(f(x) + g(x))

Answers

Answer:

  (f + g)(4) = f(4) + g(4)

Step-by-step explanation:

  (f + g)(4) = f(4) + g(4)

___

The notation (f+g)(x) means that the value of f(x) is added to the value of g(x).

What is x
I dont get it

Answers

Answer:

x = 35

Step-by-step explanation:

The angles of a triangle add to 180 degrees

103+ 42 + BCA = 180

BCA = 180 -103 -42

BCA =35

BCA and x are corresponding angles and corresponding angles are equal if the lines are parallel

PLEASE ANSWER QUICKLY ASAP
READ THE QUESTION CAREFULLY PLEASE ​

Answers

Answer:

140°

Step-by-step explanation:

total angle of a hexagon is 720. We know already 510°. That leaves 210°. The ratio between the two angles is 2:1, therefore angle CDE is 140° and angle DEF is 70 °

Answer:

140°

Step-by-step explanation:

We know that all of these angles here are part of a hexagon, meaning that their angle measures will all add up to 720°.

We can use what we already know and find what CDE and DEF will add up to.

[tex]145+90+160+115=510\\720-510=210[/tex]

Now, assuming x is the measure of DEF, we can create an equation for this.

[tex]x + 2x = 210\\3x = 210\\x = 70[/tex]

This is the measure of DEF, but it asks for CDE, which is twice the size of DEF. So

[tex]70\cdot2=140[/tex]

We can double check this is right by adding up all the measures.

[tex]145+90+160+115+140+70=720[/tex]

Hope this helped!

the length of a basketball pitch can be divided into 12 parts which 25 centimetres on how much parts it's 20 centimetres long can be obtained from the pitch​

Answers

Answer:

the number of parts is going to be

= 15 parts

Step-by-step explanation:

A basketball pitch can be divided into twelve(12) parts , each part of equal length of twenty five (25) centimeters.

The initial and total length of the basketball pitch = 12*25

The initial and total length of the basketball pitch = 12*25

The initial and total length of the basketball pitch = 300 cm

So if it's now divided into parts of each 20 cm ,

the number of parts is going to be

= 300/20

the number of parts is going to be

= 15 parts

Compute the value of each expression: |−12|−2|−6|

Answers

Answer:

12, 2, 6

Step-by-step explanation:

67.77759 rounded to nearest meter

Answers

Answer:

68

Step-by-step explanation:

0.7 rounds to 1 so add 1 to 67 to get 68

sbajsbisws hsbwks hawk sisswiajaa s

7. The annual interest rate is 20%. The balance after the grace period was $15,000. A payment of $2,500 was made on the 3rd day. What is the interest for the month?

Answers

Answer:

Interest (I) = $18

Step-by-step explanation:

$15,000 by the end of grace period

$2,500 payment was made by the 3rd day

$15,000/$2500=6

6×3=18

I = PRT/100

I = (15,000 × 20% × 18 days)/100

I = {15,000 × 0.2 × (18/30)}/ 100

I= {15,000 × 0.2 × 0.6}/ 100}

I= {1800}/ 100}

I= {18}/ 1}

Interest (I) = $18

The projected worth (in millions of dollars) of a large company is modeled by the equation w = 236(1.06) t. The variable t represents the number of years since 2000. What is the projected annual percent of growth, and what should the company be worth in 2011? A. 6%; $448.00 million B. 16%; $474.88 million C. 16%; $250.16 million D. 6%; $422.64 million

Answers

Answer:

  A.  6%, $448 million

Step-by-step explanation:

a) The base of the exponential term is 1.06, so the projected annual growth is 1.06 -1 = .06 = 6%

__

b) Filling in 11 for t, we find the projected worth to be ...

  w = 236(1.06^11) ≈ $448 . . . million

Which expression is not equivalent to the other expressions?

-6(2x-4)
-(12x-6)+18
-3(4x-3)+15
-4(3x+6)

Answers

It’s -4(3x+6) because if you solve it you get a different answer then all of them all over them were the same answer except -4(3x-6)

Michael is trying to hang Christmas lights on his house. His house is 17 ft tall and the ladder leaning is 34 degrees above the ground. How long must the ladder be to reach the house? a 24 feet b 17 feet c 34 feet d 30 feet

Answers

Answer:

34 feet

Step-by-step explanation:

let length of ladder be x

[tex] \ \sin(34) = \frac{17}{x} [/tex]

[tex]x \sin(34) = 17[/tex]

[tex]x = \frac{17}{ \sin(34) } [/tex]

x = 32.131083564

The map of a biking trail is drawn on a coordinate grid. The trail starts at P(−2, 1) and goes to Q(6, 1). It goes from Q to R(6, −3) and then to S(9, −3). What is the total length (in units) of the biking trail? 11 15 18 19

Answers

Answer:

19

Step-by-step explanation:

Answer:

Hey there!

We use the distance formula to find the distances between each of these points.

From -2, 1 to 6, 1 is a total of 8 units.

From 6, 1 to 6, -3 is a total of 4 units.

From 6, -3 to 9, -3 is a total of 3 units.

8+4+3=15 units.

Let me know if this helps :)

Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.

Answers

Answer:

x = 12.5

Step-by-step explanation:

Since the figure above is a right angled triangle we can use trigonometric ratios to find x

To find x we use cosine

cos∅ = adjacent / hypotenuse

From the question

The hypotenuse is x

The adjacent is 10

Substitute these values into the above formula and solve for x

That's

[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]

Divide both sides by cos 37

[tex]x = \frac{10}{ \cos(37) } [/tex]

x = 12.52135

We have the final answer as

x = 12.5 to the nearest tenth

Hope this helps you

Answer:

probably 16.5

Step-by-step explanation:

please help. pls show workings ​

Answers

Answer:

≈ 10.52 cm²

Step-by-step explanation:

The unshaded area is calculated as area of square subtract area of quarter circle, thus

A = 7² - [tex]\frac{1}{4}[/tex]πr²

   = 49 - ( 0.25π × 7²)

   = 49 - (0.25π × 49)

   = 49 - 12.25π

   ≈ 10.52 cm² ( to 2 dec. places )

 

Answer:10.5cm^2

Step-by-step explanation:

Area of the square = L^2 =(7) ^2=49cm^2

Radius of quadrant = 7cm

Area of the quadrant =1/4 x πr^2

1/4 x 22/7 x (7) ^2

1/4 x 22/7 x 49

=38.5cm^2

Area of unshaded part= area of square - area of quadrant

49cm^2 - 38.5cm^2

=10.5cm ^2

Square root & simplifying radicals
√30

Answers

Answer:

√30 =

5.4772255751

It can be simplified as this only, not more

At an elite baseball camp, 60% of players can bat both right-handed and left-handed. If 25% of the players who bat left-handed do not bat right-handed, what is the probability that a player selected at random does not bat left-handed?

Answers

Answer:

The probability that a player selected at random does not bat left-handed is 20%.

Step-by-step explanation:

Assume that there are a total of 100 baseball players at an elite baseball camp.

The information provided is:

60% of players can bat both right-handed and left-handed. 25% of the players who bat left-handed do not bat right-handed.

That is, the number of players can bat both right-handed and left-handed is,

n (L and R) = 60.

Now, if 25% of the players who bat left-handed do not bat right-handed, then 75% of all left-handed players can also bat right-handed.

⇒ n (L and R) = n (L) × 75%

            60     = n (L) × 0.75

           n (L)    =  60/0.75

           n (L)    = 80

So there are 80 left handed batters.

Compute the number of only left handed batters as follows:

n (Only L) = n (L) × 25%

                = 80 × 0.25

                = 20

So there are 20 only left handed batters.

Compute the number of only right handed batters as follows:

Total = n (Only L) + n (Only R) + n (L and R)

 100 = 20 + n (Only R) + 60

n (Only R) = 20

Thus, the probability that a player selected at random does not bat left-handed is 20%.

In a test (+5) marks are given for every correct answer and (-2) marks are given for every incorrect answer. Radhika answered all the questions and scored 30 marks though she got 10 correct answers. How many incorrect answers had they attempted?

Answers

Answer:

10 incorrect answers

Step-by-step explanation:

From the information given, you can say that 5 marks for the number of correct answers minus two marks for the number of incorrect answers is equal to 30 that is the score that Radhika got:

(5*10)-2x= 30, where x is the number of incorrect answers.

Now, you can solve for x:

50-2x=30

50-30=2x

20=2x

x=20/2

x=10

According to this, the answer is that they attempted 10 incorrect answers.

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