Prove that cos (12/13) + sin (3/5) = sin (56/65)

Answer:See below Step-by-step explanation:We need to prove : cos [tex]\frac{12}{13}[/tex] + sin [tex]\frac{3}{5}[/tex] = tan [tex]\frac{56}{65}[/tex]Let's simplify the LHS.cos [tex]\frac{12}{13}[/tex] + sin [tex]\frac{3}{5}[/tex]Convert the inverse cos and sin functions into inverse tan functionstan [tex]\frac{5}{12}[/tex] + tan [tex]\frac{3}{4}[/tex][This can be found taking a right triangle and labeling the sides, and then using Pythagorean Theorem, we can find the missing side and take the ratio of tan]Identitytan x + tan y = tan [tex]\frac{x+y}{1-xy}[/tex]Using this identity, we can simplify our earlier equation! tan [(5/12 + 3/4)/(1 - (5/12 x 3/4))] tan [(20 + 36) / (48 - 15) tan (56/65) RHS Proved

Mathematics High School

Prove that cos⁻¹ (12/13) + sin⁻¹ (3/5) = sin⁻¹ (56/65)

Answers

Answer 1

Answer:

See below ↓

Step-by-step explanation:

We need to prove :

⇒ cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex] = tan⁻¹ [tex]\frac{56}{65}[/tex]

Let's simplify the LHS.

cos⁻¹ [tex]\frac{12}{13}[/tex] + sin⁻¹ [tex]\frac{3}{5}[/tex]

Convert the inverse cos and sin functions into inverse tan functions

tan⁻¹ [tex]\frac{5}{12}[/tex] + tan⁻¹ [tex]\frac{3}{4}[/tex][∴This can be found taking a right triangle and labeling the sides, and then using Pythagorean Theorem, we can find the missing side and take the ratio of tan]

Identity

tan⁻¹ x + tan⁻¹ y = tan⁻¹ [tex]\frac{x+y}{1-xy}[/tex]

Using this identity, we can simplify our earlier equation!

⇒ tan⁻¹ [(5/12 + 3/4)/(1 - (5/12 x 3/4))]

⇒ tan⁻¹ [(20 + 36) / (48 - 15)

⇒ tan⁻¹ (56/65)

⇒ RHS

⇒ Proved ∴√

Answer 2

[tex]\text{L.H.S}\\\\=\cos^{-1} \dfrac{12}{13} + \sin^{-1} \dfrac 35\\\\=\sin^{-1} \dfrac 5{13} + \sin^{-1} \dfrac 35\\\\[/tex]

[tex]=\sin^{-1}\left[\dfrac 5{13}\sqrt{1- \left(\dfrac 35 \right)^2} + \dfrac 35\sqrt{1-\left(\dfrac 5{13} \right)^2} \right]\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{1-\dfrac 9{25} }+\dfrac 35 \sqrt{1-\dfrac{25}{169}} \right)\\\\=\sin^{-1} \left(\dfrac 5{13} \sqrt{\dfrac{16}{25}}+\dfrac 35 \sqrt{\dfrac{144}{169}} \right)\\\\=\sin^{-1} \left(\dfrac{5}{13} \cdot \dfrac 45 + \dfrac 35 \cdot \dfrac{12}{13} \right)\\[/tex]

[tex]=\sin^{-1} \left(\dfrac 4{13} +\dfrac{36}{65}\right)\\\\=\sin^{-1} \left(\dfrac{20}{65} + \dfrac{36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{20+36}{65} \right)\\\\=\sin^{-1} \left(\dfrac{56}{65} \right)\\\\=\text{R.H.S}[/tex]

Related Questions

A fuel tank is in the shape of a right circular cylinder. The radius of the base and height of the tank are

10

feet and

25

feet, respectively. Due to safety measures, the tank can be filled to only

80

%

of its capacity.

If

100

cubic feet of fuel are equal to

2. 78

gallons, what is the maximum number of whole gallons of fuel the tank can contain due to safety measures?

Answers

The maximum number of whole gallons of fuel the tank can contain due to safety measures is 174.584 gallons

Volume of a cylinderv = πr²h

r = radius

h = height

Therefore,

r = 10 ft

h = 25 ft

The tank can only be 80% filled due to safety measures. Therefore,

v = 3.14 × 10² × 25

v = 3.14 × 100 × 25

v = 3.14 × 2500

v = 7850 ft³

80% capacity of 7850 ft³ is as follows:

80 / 100 × 7850 = 628000 / 100 = 6280 ft³

100 ft³ = 2.78 gallons

6280 ft³ = ?

cross multiply

maximum number of whole gallons = 6280 × 2.78 / 100 = 17458.4 / 100 = 174.584 gallons

Therefore, the maximum number of whole gallons of fuel the tank can contain due to safety measures is 174.584 gallons

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find the sum of the interior angle measures of a regular polygon with 22 sides

Answers

Answer:

Step-by-step explanation:

We can split this into 20 triangles, each with an angle sum of 180 degrees.

So 180(20) = 3600 degrees.

PLEASE PLEASE PLEASE HELP ME YALL‼️‼️‼️‼️‼️

There are four boys in a class of ten students. Four students are to be randomly selected
(without replacement) to help in the lunch line. Determine the probability that all four
students are boys.

Answers

Answer:

Hi .. im happy to help

answer is 0.033

Step-by-step explanation:

P = C(4,4)÷C(10,4)

P = 1 ÷ 30

[tex]p = \frac{1 }{30} [/tex]

p = 0.033

yo can i get a hand here just so i dont get it wrong

Answers

ALGEBRAIC EXPRESSIONS

[tex]__________________________[/tex]

B. 72 IS THE QUOTIENT OF THE EXPRESSION72 is an addend in the expression and not the quotient.

please someone help i will give brianliest

Answers

Answer:

the answer is 16

Step-by-step explanation:

look at the photo

Write x=2 in slope intercept form

Answers

When x=a the slope is undefined . And when y is b the slope is zero

Pls help I need to know how much the penny will be by the end

Answers

Answer:

Day 1: $.01

Day 2: $.02

Day 3: $.04

Day 4: $.08

Day 5: $.16

Day 6: $.32

Day 7: $.64

Day 8: $1.28

Day 9: $2.56

Day 10: $5.12

Day 11: $10.24

Day 12: $20.48

Day 13: $40.96

Day 14: $81.92

Day 15: $163.84

Day 16: $327.68

Day 17: $655.36

Day 18: $1,310.72

Day 19: $2,621.44

Day 20: $5,242.88

Day 21: $10,485.76

Day 22: $20,971.52

Day 23: $41,943.04

Day 24: $83,886.08

Day 25: $167,772.16

Day 26: $335,544.32

Day 27: $671,088.64

Day 28: $1,342,177.28

Day 29: $2,684,354.56

Day 30: $5,368,709.12

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no te vallas :(

Answers

Answer:

n=5 x=6

Step-by-step explanation:

2n+1 +n = 16

3n+1 =16

3n=15

n=5

2x+x+x+1 =25

4x+1=24

4x=24

x=6

Which person is not living within their means?
A. Joyelle set aside money for emergency funds by limiting her thing
entertainment costs for a few months.
B. Bill earns a high salary, so he contributes the maximum allowed to
his IRA each year.
C. Ella maxed out all three of her credit cards but pays the minimum
balance each month.
O D. Dmitri earns $1000 a month and spends $800 on rent, groceries,
and other expenses.

Answers

The person that is not living within their means is Ella who has maxed out all three of her credit cards but pays the minimum balance each month.

What does it mean when a person is living above their means?

If a person is living above their means, the person is spending more money than they have. A person living above their means would most likely borrow in order to afford their lifestyle. A person living above their means would have no amount of savings.

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Rachel has half the amount of money that Melanie has.

Melanie has $12 less than 3 times the amount that Kim has.

Let k represent the amount. of money kim has.

(A) write an expression that represents the amount of money that Melanie and Kim has. (two separate expressions)

(B) if kim has $20, how much money does Melanie and Rachel have?

EXPLAIN UR WORK

Answers

Given↷Rachel has half the amount of money that Melanie has.

Melanie has $12 less than 3 times the amount that Kim has. To find↷

expression that represents the amount of money that Melanie and Rachel has.

If kim has $20, how much money does Melanie and Rachel have?Answer↷Melanie: 3k - $12 & Rachel : 1.5k - $6Melanie: 48 & Rachel:24Solution ↷

Let the amount of money Kim has be k then,

ATQ,

The amount of money Melanie has

⇢3k - $12

The amount of money Rachel has

⇢3k-$12/2 = 1.5k - $6

Given that,

Kim has $20,

so,

The amount of money Melanie has

⇢3k - $12 = 3 x $20 -$12 = $48

The amount of money Rachel has

⇢ 1.5k - $6 = 1.5 x $20 -$6 = $24

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the lengths of the prisms vary. It cost $0.04 per square centimeter to fabricate the prisms and the factory owner has set a limit of $11 per prism. What is the maximum length of each prism?

Answers

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

How to determine the maximum length of each prism?

The surface area of the hexagonal prism is calculated using:

A = 6al + 3[tex]\sqrt[/tex]3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3[tex]\sqrt[/tex]3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3[tex]\sqrt[/tex]3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48[tex]\sqrt[/tex]3]

Divide both sides by 0.04

275 = 24l + 48[tex]\sqrt[/tex]3

Subtract 48[tex]\sqrt[/tex]3 from both sides

24l = 275 - 48[tex]\sqrt[/tex]3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Answers

Answer:

For two different equations:

(3x+9)

x = -3

(4x+3)

x = -3/4

Finding x using both equations:

plug x = -3 into the other equation

4(-3) + 3 = -9

x = -9

plug x = -3/4 into the other equation

3(-4/3) + 9 = 27/4

x = 27/4

Set the equations equal to each other:

3x+9=4x+3

3x-4x = 3-9

-x = -3

x=3

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

help me pleaseeeeeeeeee

Answers

for 2 points A(xa;ya) and B(xb;yb)

the slope is (yb - ya) / (xb - xa)

here

the slope = 4 = (17-r) / (4-(-1))

(17-r) / 5 = 4

17 - r = 20

r = 17 - 20

r = - 3

point (-1 ; -3)

Abby practiced her horn for 3/4 of an hour every day for 12 days?
a) How many hours did she practice in those 12 days?

b) How many minutes did she practiced in those 12 days?

Answers

Answer:

9 hours, 540 minutes

Step-by-step explanation:

12 x 0.75 = 9

Elsa drove 737 miles in 11 hours.
At the same rate, how many miles would she drive in 13 hours?

Answers

Answer:

871 miles

Step-by-step explanation:

737/11= 67

67 x 13= 871

A triangle has two sides of length 14 and 19. What is the largest possible whole-number length for the third side?

Answers

its 33 I checked it mark the one above me brainiest

A house on the market was valued at $418,000. After several years, the value increased by 9 percent. By how much did the house’s value increase in dollars? What is the current value of the house?

Answers

$455,620

First you would find 9% of the original price.
418,000x0.09=37,620
Then add that total to the original price.
418,000+37,620=455,620

Jacob had a cube. When Jacob made a cross section parallel to the base, what shape did the cross section form? trapezoid square parallel triangle

Answers

Answer: Square

Step-by-step explanation:

A cross section cut parallel to a base will be the same shape as the base itself, and the base of a cube is a square. :)

Answer:

A square because it is not diagonal.

Step-by-step explanation:

A dartboard is divided into 20 sectors. Each sector is worth a point value from 1 to 20 and has shaded regions that double or
triple this value. A sector is shown below. Find the areas of the entire sector, the double region, and the triple region. Round
your answers to the nearest hundredth.
in
triple
double
The area of the entire sector is about
square inches.
The area of the double region is about
square inches.
square inches.
The area of the triple region is about

Answers

The area of each sector is the amount of space on the sector

The area of the entire region is 6.89The area of the double region is 0.75The area of the triple region is 0.46

The area of the entire sector

The area of a sector is calculated as:

A = (1/2) × r^2θ

For the entire sector, we have:

θ = π/10

r = 6.625

So, we have:

A = (1/2) × 6.625^2 × π/10

Evaluate the product

A = 6.89

The area of the double region

For the double region, we have:

θ = π/10

r = 6.25

So, we have:

A = Complete sector - (1/2) × r^2θ

A = 6.89 - (1/2) × 6.25^2 × π/10

Evaluate the difference

A = 0.75

The area of the triple region

For the triple region, we have:

θ = π/10

R = 4.125

r = 3.75

So, we have:

A = (1/2) × R^2θ - (1/2) × r^2θ

A = (1/2) × 4.125^2 × π/10 - (1/2) × 3.75^2 × π/10

Evaluate the difference

A = 0.46

Hence, the area of the triple region is 0.46

Answers

Step-by-step explanation:

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Identify the population and the sample. Lena wants to open a new restaurant in a mall and needs to determine what kind of food to serve to attract the most customers. Out of 1200 mall visitors, 200 are asked their food preference.

Answers

The total mall visitors is the population parameter of the experiment

The sample of the experiment is 200, while the population is 1200

How to identify the sample and the experiment?

From the question, we have the following parameters:

Total mall visitors = 1200Visitors interviewed = 200

The total mall visitors is the population while the visitors that were asked of their food preference are the sample

Hence, the sample of the experiment is 200, while the population is 1200

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https://brainly.com/question/9910540

Triangle ABC was transformed to create triangle DEF.

2 triangles are shown. Triangle A B C has point A at the top, B on the bottom right, and point C on the bottom left. Triangle D E F has point D at the top, E on the bottom right, and F on the bottom left. The triangles are identical.
Which statement is true regarding the side in the image that corresponds to Side length B A?

Side length B C corresponds to Side length B A because they are about the same length.
Side length E D corresponds to Side length B A because they are in the same position.
Side length E F corresponds to Side length B A because the transformation is isometric.
Side length F D corresponds to Side length B A because the length is not preserved.

Answers

Answer: Side length E D corresponds to Side length B A because they are in the same position.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

Using the Fibonacci sequence of numbers a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15. Find the 3rd ration. Do not forget to change to %. a 423.6% b 161.8% c 261.8% d 50%

Answers

Answer: I'm sorry is this a real question

Joel has 24 sports trophies. Of the trophies 1/8 are soccer trophies. How many soccer does Joel have ?

Answers

Answer:

We are given that Joel has 24 sports trophies, of the 24 trophies there are 1/8 soccer trophies.

1/8 of 24 is 3.

24 divided by 8 = 3 soccer trophies

There are 3 soccer trophies all the rest of the trophies, which is 21 trophies, will be other sports. 21 trophies + 3 soccer trophies = 24 trophies in total

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Please help me with this please and thank you

Answers

Answer:

so i wrote the steps but not the answers, if you want i can write the answers too

Step-by-step explanation:

hello! so here all you have to do is substitute the given points of x to the equation. then you put two points on the graph. (two points on each graph) i can write the answers if you want, but please try first! if you cant ill help some more and show how to do it.

In the drawing, what must be the coordinates of D to show ABCD is a square?

Answers

The coordinates must be (4, 7), bc if you look at the graph closely, all you need is one more coordinate at the top to make a square.

Hi please help me out and add an explanation if u can!

Answers

Question 1: Find the perimeter of the baseDefinition of Perimeter: it is all the side lengths of the shape added up

What do we know

-the pentagon is a regular pentagon meaning all its side lengths

are equal since all the sides have one tick mark which says all

the side lengths are equal

2. Solve:

Perimeter: 6 + 6 + 6 + 6 + 6 = 30cm

Question 2: Find the height of the prismHeight of the prism

⇒ distance between the base pentagon and the top pentagon

⇒ Height is 6 cm

Question 3: Find the Lateral AreaDefinition of Lateral Area: it is only the area of the non-base faces

⇒ the non-base faces are the squares on the side of the figure

⇒ there are 5 squares

⇒ Lateral Area = 5 * (Area of Square) = 5 * (6 * 6) = 180 square cm

Question 4: Find the area of the base

The formula for the pentagon's area ⇒ [tex]\frac{5}{2}*s*a[/tex]

s --> length of the sides of the pentagon --> 6cma --> apothem length --> 4.1 cm

*apothem is the distance from the center of the pentagon to any

one of the sides

Area = [tex]\frac{5}{2} *6*4.1 = 15 * 4.1 =[/tex] 61.5 square centimeters

Question 5: Find the surface areaDefinition of Surface Area: all the areas of different sides added up

Surface Area = 2 * (Area of Base) + (Lateral Area)

= 2 *61.5 + 180 = 123 + 180 = 303 square centimeters

Hope that helps!

Will give
BRAINLY AND FIVE STARS and A THANKS

Answers

Answer:

k = 12h

Step-by-step explanation:

Since each of the inputs of h can be mutiplied by 12 to get the output k, the equation is k = 12h
Hope this helps :)

What is the missing numerator?

A: 1
B: 2
C: 3
D: 4

Answers

Answer:

C. 3

is the answer :)

hopefully this helps

Answer:

D: 4

Step-by-step explanation:

1) Make the 1/4 into 5/20 by multiplying top and bottom by 5/5

x/5 - 5/20 = 11/20

2) Move the 5/20 to the other side

x/5 = 11/20 + 5/20

3) Add the 2 fractions on the right

x/5 = 16/20

4) Make the fraction on the right have a denominator of 5 by dividing top and bottom by 4/4

x/5 = 4/5

5) Multiply both sides by 5

x = 4

The missing numerator is 4.

Pick the biggest number.
A0.193 B0.26 C0.6 D0.308

Answers

Answer:

Hello fellow Human! ^ω^

The answer is option D. 0.308

Step-by-step explanation:

We are going to Compare the digits starting with the greatest place value.

The Number 0.193 Is not the biggest number. However, 0.193 is bigger than 0.26 and 0.60.

The number 0.193 is smaller than the number 0.308.

Therefore, the answer is Option D. 0.308

Hope this helps!

Have an Awesome Friday!

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