prove that; tan20+4sin20= square root of3

Answers

Answer 1

tan( 20 ) + 4 Sin( 20 ) =

( Sin( 20 ) / Cos( 20 ) ) + 4 Sin( 20 ) =

Sin( 20 ) + 4 Sin( 20 ).Cos( 20 ) / Cos( 20 ) =

Sin( 20 ) + 2 × 2 Sin(20).Cos(20)/ Cos(20) =

Sin( 20 ) + 2 × Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Sin( 40 ) / Cos( 20 ) =

Sin( 20 ) + 2Cos( 50 ) / Cos ( 20 ) =

Sin( 20 ) + 2Cos( 20 + 30 ) / Cos( 20 ) =

________________________________

2 × Cos( 30 + 20 ) =

2 × [ Cos(30).Cos(20) - Sin(30).Sin(20) ] =

2 × [ √3/2 × Cos(20) - 1/2 × Sin(20) ] =

√3 Cos(20) - Sin(20)

_________________________________

Sin( 20 ) + 2Cos ( 20 + 30 ) / Cos( 20 ) =

Sin( 20 ) + 3 Cos(20) - Sin(20) / Cos(20) =

Sin(20) - Sin(20) + √3 Cos(20) / Cos(20) =

0 + √3 Cos(20) / Cos(20) =

√3 Cos(20) / Cos(20) =

Cos(20) simplifies from the numerator and denominator of fraction

√3 × 1 / 1 =

√3

And we're done ....


Related Questions

Dany has 15 toys. This morning Mrs. Bahr woke up to see that Dany ruined one of her toys, so Mrs. Bahr threw it away. If now half of Dany's toys have squeakers, how many of her toys do not have squeakers?

Answers

Answer:

7 ?

Step-by-step explanation:

if im correct the total amount of toys was 15, dany broke one so thats 14. HALF of danys toys have speakers so

14 divided by 2 is 7

the answer is 7.

Answer:

7

Step-by-step explanation:

in total they were 15 toys , but 1 was thrown away. which means only 14 toys were left .

now half of the 14 toys have squeakers

so it can be calculated as :

14 ÷ 2 = 7

Item 3 Which measurement is equivalent to 1 kilometer? 10 meters 100 centimeters 1,000 meters 1,000 centimeters

Answers

Answer:

1,000 meters

Step-by-step explanation:

Kendra started making jewelry to sell. She spent $12 for supplies to make four bracelets. She will sell the
bracelets for $5 each. If each bracelet takes two hours to make, how much money will Kendra earn per
hour?

Answers

Answer:

$1

Step-by-step explanation:

4 x 5 = 20

20 - 12 = 8

4 x 2 = 8

8/8=1

The coordinates for three vertices of a rectangle are (0٫4)٫(8٫4) and (8٫1). What is the coordinates of the fourth vertex ? A : (1٫0) B : (8٫0) ٫ C : (0٫1) D : (0٫8)

Answers

Answer:

(0, 1):  Answer D

Step-by-step explanation:

The three given vertices are (0٫ 4)٫(8٫ 4) and (8٫ 1).  Note that the x-coordinates of two of these are both 8.  The remaining x-coordinate of the fourth vertex is 0.  Since the figure is a rectangle, there are two sets of parallel sides.  If one side is x = 8, the opposite vertical side must be x = 0, since the remaining coordinate is 0.  This side is a vertical line segment.  The fourth and last vertex is at the intersection of x = 0 and y = 1;  (0, 1):  Answer D.

extend pattern 1,4,9​

Answers

Answer:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100......

Step-by-step explanation:

This is a list of perfect squares.

1 is the square of 1. ( 1 x 1 = 2)

4 is the square of 2. (2 x 2 = 4)

9 is the square of 3. (3 x 3 = 9)

So, the next number would be the square of 4 which is 16 ( 4 x 4)

And so on.

Which product is represented by the model below

Answers

Answer:

A. 3/8*2=6/8

Step-by-step explanation:

Think about a whole number as (whole number)/1

(2/1)

Then multiply

3/8*2/1=6/8

Hope that helps!

a T-shirt increased in price by 1/7 after the increase it was a priced at £56. what was the original price?​

Answers

Answer: £48

Explanation: divide £56 by 7. each of the seven parts is equal to £8. Subtract £8 from £56 and the original price is £48.

find the radian measure of the angle 55°​

Answers

Answer:

[tex]55 degree= \frac{\pi }{180}\times55=\frac{11\pi }{36} =0.9599 radians[/tex]

Step-by-step explanation:

[tex]180 degree= \pi radian\\1 degree= \frac{\pi }{180}\\55 degree= \frac{\pi }{180}\times55=\frac{11\pi }{36} =0.9599 radians[/tex]

Find the area and the circumference of a circle with diameter 10 m.

Write your answers in terms of pi, and be sure to include the correct units in your answers.

Answers

Step-by-step explanation:

area of a circle= πr²

and r= half diameter

therefore we have r=10/2=5

area= 5² x π

area= 25π

circumference=2πr

circumference= 2xπx5

circumference=10π

The cost of cleaning up pollution in a stream is given by C = 37000 100−p, where C is the cost in dollars to clean p percent of the stream. Find and interpret C(20)

Answers

Answer:

$462.5

Step-by-step explanation:

Given the cost function expressed as;

C = 37000/100−p

To get C(20), we will substitute p = 20 into the expression and get C as shown;

C(20) = 37000/100-20

C(20) = 37000/80

C(20) = 462.5

Hence the cost needed to clean 20% of the stream is $462.5

4(q-5) = 16
help pleaseee

Answers

Answer:

q = 9

Step-by-step explanation:

the key thing to understand in this problem is the distributive property. which basically means we can muliply what's on the interior of the parenthestes ( in this case q-5) by what's on the outside (4).

so 4 will distrubute to both the q and the -5

4q - 20 = 16

add 20 to both sides

4q = 36

divide both sides by 4

q = 9

The following dot plots describe the test scores on Mr. Santos’s final exam.

The second-period class is represented on a number line where the numbers fifty-five to ninety-five are plotted at intervals of five. There is one bullet each plotted above fifty-five, seventy, and ninety-five. Six bullets each are plotted above seventy-five and eighty. Two bullets are plotted above eighty-five and three bullets are plotted above ninety.

The sixth-period class is represented on a number line where the numbers fifty-five to ninety-five are plotted at intervals of five. There is one bullet plotted above sixty-five and two bullets above ninety-five. Three bullets each are plotted above seventy-five and ninety, five bullets above eighty, and six bullets are plotted above eighty-five.

Form a valid inference based on the means of the data sets. Use the drop-down menu to show your answer.

On average, students in the sixth-period class scored
Choose... (Higher, Lower)
as compared to students in the second-period class.

Answers

Answer:

It is higher I have no time to explain. Hope it's right!

you want to create a 99 confidence interval with a margin of error of 25 assuming that the population standard deviation is equal to 1.5 what's the minimum size of the Rams Tampa

Answers

Answer:

The minimum sample size is 239.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Population standard deviation is equal to 1.5

This means that [tex]\sigma = 1.5[/tex]

Margin of error of 0.25

This means that [tex]M = 0.25[/tex]

What's the minimum size of the sample?

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.25 = 2.575\frac{1.5}{\sqrt{n}}[/tex]

[tex]0.25\sqrt{n} = 2.575*1.5[/tex]

[tex]\sqrt{n} = \frac{2.575*1.5}{0.25}[/tex]

[tex](\sqrt{n})^2 = (\frac{2.575*1.5}{0.25})^2[/tex]

[tex]n = 238.7[/tex]

Rounding up:

The minimum sample size is 239.


HELP ASAPPPP!!!!You are making a picture frame in the craft cabin at summer camp. The frame measures 9 inches by 12
inches. You measure the diagonal and it is 17 inches Is the frame rectangular? Explain your reasoning.

Answers

Answer:

yes

Step-by-step explanation:

euhm ... did u just asked if a figure with h=9inches and b=12inches is rectangular???

Does it matter what the diagonals are etc?

if the frame has angles of 90° and it has two different lengths then it has to be rectangular. The sides of a square would have the same lengths.

Mr. Assan had 492 tickets left after the movie. He started with 2,009 tickets. How many tickets did Mr. Assan sell?

Answers

Answer:

1,517

Step-by-step explanation:

2,009 - 492 = 1,517

2,009-492=1,575
He started out with 2,009 he had 492 left over so subtract that from the amount he started out with and you get the answer

3. Find the volume of the following figure. 62 units 58 units 60 units) 64 units3​

Answers

Answer:

60 units

Step-by-step explanation:

Its a 5 × 3 × 4 cube

To find volume multiply the dimensions and you will get 60

Answer:

60 units

Step-by-step explanation:

I did the test.

What is the surface area of the prism?

Answers

Step 1: Find the area of the bases (triangles)

A = 1/2 * base * height

A = 1/2 * 16 * 6

A = 48

48 + 48 = 96

Area of the triangles = 96 cm^2

Step 2: Find the area of the sides (rectangles)

A = base * height

A1 = 16 * 12

A1 = 192

A2 = 10 * 12

A2 = 120

120 + 120 = 240

240 + 192 = 432 cm^2

Step 2: Add the areas together

96 + 432

528 cm^2

Hope this helps!! :)

8 divided by two -thirds of x. PLS SOLVE THIS FOR ME ASAP​

Answers

Answer:

12 [tex]x[/tex]

Step-by-step explanation:

8 divided by two-thirds of x is

⇒ 8/2/3 × [tex]x[/tex]

⇒ 8 × (3/2) [tex]x[/tex]

⇒ 8×3 [tex]x[/tex] / 2

⇒ 24 [tex]x[/tex]/ 2

∴ 12 [tex]x[/tex]

Which point is the image of point R(4, -7) first reflected across the x-axis and then across the y-axis?

Answers

Answer:

(-4, 7)

Step-by-step explanation:

It would be the exact opposite of point R because it was rotated about 180 degrees from it's original location

Put the following equation of a line into slope-intercept form, simplifying all
fractions.

18y – 3.x = -90

Answers

Answer:

The equation of the line in slope-intercept formula is [tex]y = \frac{x}{6} - 5[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line, in slope-intercept formula, is given by:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept(value of x when y = 0).

In this question:

[tex]18y - 3x = -90[/tex]

Isolating y:

[tex]18y = 3x - 90[/tex]

[tex]y = \frac{3x}{18} - \frac{90}{18}[/tex]

Simplifying the fractions:

[tex]y = \frac{x}{6} - 5[/tex]

The equation of the line in slope-intercept formula is [tex]y = \frac{x}{6} - 5[/tex]

% of 400,000 = 100,000

Answers

Answer:

25%

Step-by-step explanation:

100,000/400,000 x 100

= 1/4 x 100

= 25%

Hence, 100,000 is 25% of 400,000

Feel free to mark this as brainliest :D

Answer:

x/100 x 400,000 = 100,000

x100                            x100

400,000x = 10,000,000

Divide by 400,000 on both sides:

X = 25%

the perimeter of a rectangle is 90m. The length is three less than five times the width. What is the length and the width of the rectangle?

Answers

Answer:

length : 37 m

width : 8 m

Step-by-step explanation:

perimeter = 2×l(ength) + 2×w(idth) = 90

l = 5w - 3

=> 2×(5w-3) + 2w = 90

10w - 6 + 2w = 90

12w = 96

w = 8

=> l = 5w - 3 = 5×8 -3 = 40-3 = 37

A bag contains four red marbles and eight
blue marbles. You randomly pick a marble and then pick a second marble without returning the marbles to the bag.Both marbles are red.

Answers

Answer:

B is most credible for this problem. :-D

Hi I am so happy that I have had to

Seven hundred twenty -one thousandths as a decimal

Answers

Answer:

0.721

Step-by-step explanation:

the last digit (the number '1') must be in the thousandths place; then work backward so the '2' would be in the hundredths and the '7' would be in the 'tenths'

A certain smart phone game app allows the player, once a day, to spin a wheel with 8 different sections. Seven of the sections contain a small prize and one of the sections is the grand prize, in which the player wins all of the other seven prizes. The makers of the game claim that the wheel has an equally likely probability of landing on each section. Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.

Required:
What would be appropriate hypotheses for the Andraya to test?

Answers

Answer:

The appropriate hypothesis set for Andraya to test is:

[tex]H_0: p = 0.125[/tex]

[tex]H_1: p < 0.125[/tex]

Step-by-step explanation:

The makers of the game claim that the wheel has an equally likely probability of landing on each section.

That is, the makers claim that the probability of earning the grand prize is:

[tex]p = \frac{1}{8} = 0.125[/tex]

Andraya has played the game for several months and believes that the grand prize occurs less often than the game makers claim.

At the null hypothesis, we test if it happens as often as the makers claim, that is, the proportion is 0.125. So

[tex]H_0: p = 0.125[/tex]

At the alternate hypothesis, we test if it happens less ofter than the makers claim, that is, the proportion is less than 0.125. So

[tex]H_1: p < 0.125[/tex]

The appropriate hypothesis set for Andraya to test is:

[tex]H_0: p = 0.125[/tex]

[tex]H_1: p < 0.125[/tex]

What are the equation and slope of the line shown on the grid ?

F y = 6; slope is zero
G x = 6; slope is zero
H y = 6; slope is 6
J x = 6; slope is undefined

Answers

Answer:

The answer is J x= 6; slope is undefined

Step-by-step explanation:

iTS undefined because it's a line

The answer is J

The reason the line is unidentified is because it is going straight up and the slope is unable to be determined.

Estadística: Luego de entrevistar a diez de los pasajeros que viajaba en el bus que chocó intempestivamente contra un poste, se concluyó que el chofer era inocente. Identifica la población, la muestra, variable y el tipo de variable.

Answers

Respuesta:

Población = Todos los pasajeros en el autobús

Muestra = los 10 pasajeros entrevistados

Variable = inocencia del conductor; por tanto es una variable cualitativa

Explicación paso a paso:

La población se refiere a todo el conjunto de observaciones que están relacionadas con un evento o experimento en particular. Aquí, todos los pasajeros del vehículo constituyen la población, ya que nuestra investigación se basa en el vehículo.

La muestra es un subconjunto de la población que generalmente se elige al azar de manera que sea representativa de la población.

La variable que pretendemos medir es si el conductor es inocente o no. Por lo tanto, llamamos a esto la variable medida. Debido a que la culpa o la inocencia no es numérica, se considera una variable cualitativa.

Find the missing side. X is the hypotenuse 12 and 5 are the legs

Answers

Answer:

10.9

Step-by-step explanation:

Given that,

Hypotenuse = 12

One leg = 5

We need to find the another leg. Let it is b. We can solve it using Pythagoras theorem as follows :

[tex]H^2=h^2+b^2\\\\b^2=H^2-h^2\\\\b^2=12^2-5^2\\\\b=10.9[/tex]

So, another leg is 10.9.

If 30 men can do a work in 8 days how many men can do the same work in 12 days ​

Answers

Answer:

Step-by-step explanation:

Identify which property is used for: 62 x (-10) = (-10) x 62 *​

Answers

Answer:

Commutative property of multiplication

Step-by-step explanation:

Properties of Multiplication:

Commutative:

Multiplying two or more factors in a different order.

ex: 2 x 4 x 5 = 2 x 5 x 4

Associative:

Multiplying factors in parenthesis with different grouping. usually to make the problem simpler.

ex: (13 x 4) x 25 = 13 x (4 x 25)

Distributive:

Distributing a multiplicand to factors in parenthesis.

ex: 2(4 - 1) = 2(4) - 2(1)

ex: 2(8+7) = 2(8) + 2(7)

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

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