COS(α+β); SINα=- 1/3, α IN QUADRANT IV, TANβ=7/3, β IN QUADRANT III

PLEASE, I HAVE BEEN TRYING TO FIND THE ANSWER FOR 3 HOURS, AND I HAVE SPENT LIKE 1000 POINTS

Answers

Answer 1

Recall the angle sum identity for cosine,

cos(α + β) = cos(α) cos(β) - sin(α) sin(β)

Then given sin(α) = -1/3, we have

cos(α + β) = cos(α) cos(β) + 1/3 sin(β)

α is in quadrant IV, so 3π/2 < α < 2π, and so sin(α) is negative and cos(α) is positive. Then from the Pythagorean identity, we get

sin²(α) + cos²(α) = 1

⇒   cos(α) = √(1 - sin²(α)) = 2√2/3

β is in quadrant III, so π < β < 3π/2, so both sin(β) and cos(β) are negative. If we multiply both sides of the previous identity by 1/cos²(α) and replace α with β, we get

sin²(β)/cos²(β) + cos²(β)/cos²(β) = 1/cos²(β)

⇒   tan²(β) + 1 = 1/cos²(β)

⇒   1/cos(β) = -√(tan²(β) + 1) = -√58/3

⇒   cos(β) = -3/√58

Also recall that by definition,

tan(β) = sin(β)/cos(β)

⇒   sin(β) = tan(β) cos(β) = 7/3 • (-3/√58) = -7/√58

Putting everything together, we find that

cos(α + β) = 2√2/3 • (-3/√58) + 1/3 • (-7/√58) = -(6√2 + 7)/(3√58)

or more clearly,

[tex]\cos(\alpha + \beta) = -\dfrac{6\sqrt2 + 7}{3\sqrt{58}}[/tex]


Related Questions

pls help fast

brainlest to enyone who helps

Answers

Answer:

B STEP 2

Step-by-step explanation:

5/8 is not more than 1

Consider an economy made up of 100 people, 50 of whom hold jobs, 10 of whom are
looking for work, and 15 of whom are retired. The unemployment rate is approximately:

17 percent

10 percent

25 percent

20 percent

12 percent

Answers

Answer:

20 por cento de cada um , que colocar

The unemployment rate is approximately 17 per cent. The correct option is A.

To calculate the unemployment rate, we need to consider the number of unemployed individuals (those looking for work) divided by the total labour force (those employed plus those looking for work).

Given:

Total population = 100

Employed individuals = 50

Individuals looking for work (unemployed) = 10

Total labour force = Employed + Unemployed

Total labor force = 50 + 10 = 60

Unemployment rate = (Unemployed / Total labour force) x 100

Unemployment rate = (10 / 60) x 100 ≈ 16.67 percent

Rounding to the nearest whole number, the unemployment rate is approximately 17 per cent.

Therefore, the correct answer is option A.

To know more about an expression follow

https://brainly.com/question/31462319

#SPJ2

Adult men have heights with a mean of 69.0 inches and a standard deviation of 2.8 inches. Find the z-score
of a man 72.4 inches tall. (to 2 decimal places)

Answers

Answer:  1.21

Work Shown:

z = (x - mu)/sigma

z = (72.4 - 69.0)/(2.8)

z = (3.4)/(2.8)

z = 1.2142857 .... which is approximate

z = 1.21

Z-score of a man who is 72.4 inches tall is 0.45.

Understanding the concept of the z-score helps us gauge how far a value is from the mean in terms of standard deviations.

A z-score, denoted as , measures the deviation of a data point from the mean in terms of standard deviations. It's calculated using the formula:

= ( - ) /

Where:

- is the value we want to find the z-score for (72.4 inches in this case).

- is the mean of the dataset (69.0 inches).

- is the standard deviation of the dataset (2.8 inches).

Plugging in the values:

= (72.4 - 69.0) / 2.8 = 1.25 / 2.8 ≈ 0.446

Rounded to two decimal places, the z-score is approximately 0.45.

This means that a man who is 72.4 inches tall is roughly 0.45 standard deviations above the mean height of adult men.

In other words, his height is a bit taller than the average height by about 0.45 times the standard deviation.

This positive value indicates that the man's height is above the mean. If the z-score were negative, it would mean the height is below the mean. By using z-scores, we can compare data points from different distributions and understand how unusual or typical a particular value is within its dataset.

Z-scores help us quantify the relative position of a data point, providing a standardized way to interpret its significance in the context of the dataset's characteristics.

In summary, the z-score of a man who is 72.4 inches tall is approximately 0.45, indicating that his height is slightly above the average height of adult men.

To know more about Z-Score here

https://brainly.com/question/33665002

#SPJ3

Find the surface area of the square pyramid below.

Answers

Answer:

Step-by-step explanation:

Answer:

96 cm or B

Step-by-step explanation:

Base-l*w, 6*6, 36

Side 1-(h*w)1/2, (30)1/2, 15

Side 2-Same as 1

Side 3-Same as 1

Side 4-Same as 1

15+15=30, 15+15=30, 30+30=60, 60+36=96

96 cm

evaluate x-2y when x =0.75 and y =0.96

Answers

Step-by-step explanation:

x = 0,75

y = 0,96

= x - 2y

= 0,75 - 2.0,96

= 0,75 - 1,96

= -1,21

What are the roots of the equation 4x^2+24x+45=0 in simplest a+bi form?

Answers

Answer:

X=(-1.5, 7.5)

Step-by-step explanation:

Simplifying

4x2 + -24x + -45 = 0

Reorder the terms:

-45 + -24x + 4x2 = 0

Solving

-45 + -24x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.

(-3 + -2x)(15 + -2x) = 0

 

Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying

-3 + -2x = 0

Solving

-3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.

-3 + 3 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -2x = 0 + 3

-2x = 0 + 3

Combine like terms: 0 + 3 = 3

-2x = 3

Divide each side by '-2'.

x = -1.5

Simplifying

x = -1.5  

Set the factor '(15 + -2x)' equal to zero and attempt to solve:

Simplifying

15 + -2x = 0

Solving

15 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-15' to each side of the equation.

15 + -15 + -2x = 0 + -15

Combine like terms: 15 + -15 = 0

0 + -2x = 0 + -15

-2x = 0 + -15

Combine like terms: 0 + -15 = -15

-2x = -15

Divide each side by '-2'.

x = 7.5

Simplifying

x = 7.5

Solution

x = {-1.5, 7.5}

Which of the following sets of ordered pairs is not a function?

{(-1, 2), (1, 3), (1, 5), (-3, 4)}
{(0, 2), (1, 4), (2, 5), (3, 6)}
{(-4, 3), (-1, 1), (-2, 5), (3, 7)}
{(0, 2), (1, 2), (2, 2), (3, 2)}

Answers

Answer:

1

first choice

Step-by-step explanation:

in a function, the x-value never repeats.

(found in brainly)

combine like terms and solve x


12x + 3 - 4x - 6 = 5

5x - 4 + 7 + 6x - 4x = 24

Answers

Answer:

12x + 3 - 4x - 6 = 5

x=1

5x - 4 + 7 + 6x - 4x = 24

x=3

Please help with this question

Answers

Answer:

The question or equation is not clear.....

7 6/10= ?/? please help

Answers

Answer:

7.6

Step-by-step explanation:

Answer:

76/10

Explanation

7 × 10 is 70 + the 6 is 76/10

you can look up fractions on yt

to get a better explication.

line j passes through the point (-4,10) and (2,-8). Line k passes through the point (1,2) and is parallel to line j. Find an equation for line k.

Answers

Answer:

344444444433333338694

Step-by-step explanation:

Answer: y = -3x+5

Step-by-step explanation:

what is 916 divied by 320

Answers

Answer:

2.8625

This is 916 divided by 320

Answer:

Full Answer - 2.8625

Rounded - About 3

Nearest Tenth - 2.9

Nearest Hundredth - 2.86

Step by Step:

Shown Below  

Hope this Helps

Use a calculator . Round to the nearest tenth of a degree given cos 0=0.8458

Answers

0.8458 rounded to the nearest tenth is 0.8 given cos is 0.696706709347

Draw an ordered stem and leaf diagram to show this information.



245, 250, 251, 253, 258, 264, 267, 269, 273, 276



Key:24|5 means 245.

Answers

Answer:  The filled out diagram is shown below

=========================================================

Explanation:

The key tells us how to set up the stem and leaf diagram. It says that [tex]24|5[/tex] represents the value 245.

This means that "24" is one of the stems. In fact, it's the smallest stem possible since there's nothing smaller than 240 on this given list of values.

The only leaf associated with this stem is 5. The stem 24 and the leaf 5 combine to form the number 245 as the key indicates.

--------------------------

In the next row is the stem 25. For this stem, we'll have the leaves of: 0, 1, 3, 8. The stem 25 and those leaves mentioned combine to form 250, 251, 253, 258 in that exact order. This time we'll use up four boxes for this row. The last box in this row is blank.

The remaining rows (stems 26 and 27) are handled in pretty much the same fashion. Let me know if you have questions how the boxes are filled in. It helps to start with sorted data from smallest to largest. Luckily, that's already been done for us.

The filled out chart is shown below. I replaced the stems 0,1,2,3 with 24,25,26,27.

the shown bellow question answer

Answers

Answer:

The area of the shape can be divided into the area of the rectangle, and the area of the semi-circle.

The area of the rectangle can be found by [tex]11*4=44[/tex]

The area of a semi-circle can be found with the formula [tex]\frac{1}{2} \pi r^2[/tex] where r is the radius.

Since we know the diameter of the semi-circle is 4,

the radius will be 4 ÷ 2 = 2.

Therefore, the area of the semi-circle is [tex]\frac{1}{2}\pi 2^2=\frac{1}{2}\pi*4=2\pi[/tex]

Therefore, the area of the shape is [tex]44+2\pi[/tex] or [tex]50.283cm^2[/tex] (3 decimal places)

The 1st one was doable, but I don't understand the 2nd Question.

Answers

Answer: ? What are you talking about?

Step-by-step explanation:

tim gtri nguyen cua x de bthuc B=x+2/can(x) - 1

Answers

Answer:

sorry di ko alam

Step-by-step explanation:

Given f(x)=-x-4f(x)=−x−4, find f(4)f(4).

Answers

Answer:

1/4 or .25

Explanation

As for this specific question algebra is something I do in my head and skip many steps for however if you want to proof my answer it would be this.

-0.25-16*.25=-0.25-4

-0.25-4=-0.25-4

-4.25=-4.25

For the function  f(x) = -x-4 the value of f(4) is -8.

The given function is f(x) = -x-4.

We need to find the value of f(4).

To find this we have to replace the x value with 4.

Substitute x=4 in the function:

f(4)=-4-4

f(4)=-8

Hence, the value of f(4) is -8.

To learn more on Functions click:

https://brainly.com/question/30721594

#SPJ3

1.what is the y-intercept f (x) = 3x+8/x-4?
a.-2
b.0
c.2
d.4
2.the horizontal asymptote of f (x) = 2x+5/x^2-3x+2?
a. y = -1
b. y = 0
c. y = 1
d. y = 2
3. what is the x - intercept of f (x) = 2x+6/x-1?
a.-5
b.-3
c.-1
d.0
4.what is the vertical asymptote of f (x) = x^2+5x+6/x-5?
a.x = -6
b.x = 0
c.x = 5
d.x = 6
5. what is the zero of f (x) = x^2-25/x+5?
a.-5
b.0
c.5
d.25
6.the oblique asymptote of f (x) = x^2=3x-5/x+2?
a.y = x + 1
b.y = x + 2
c.y = x + 3
d.y = x + 5

Answers

The Eubanks Answer:

Step-by-step explanation:hehus

A Distributive Property and GCF

56+42

Answers

Answer:

98

Step-by-step explanation:

you at 56 in to 42

Answer:

98

pa brainless

Step-by-step explanation:

please brainless

Express in vertex form

Y=2x^2 - 2x - 5

Answers

Answer:

y = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex]

Step-by-step explanation:

y = 2x² - 2x - 5 ← factor out 2 from the first 2 terms

 = 2(x² - x) - 5

Using the method of completing the square

add/subtract (half the coefficient of the x- term)² to x² - x

y = 2(x² + 2(- [tex]\frac{1}{2}[/tex] ) x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² + 2(- [tex]\frac{1}{4}[/tex] ) - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{1}{2}[/tex] - 5

  = 2(x - [tex]\frac{1}{2}[/tex] )² - [tex]\frac{11}{2}[/tex] ← in vertex form

 

7⅕-2⅔x0,5 explain step by step

Answers

Step-by-step explanation:

7/5 - 2×2/3 × 0.5 = 1.4 - 2×0.5×2/3

= 1.4 - 1 ×2/3

=1/4 × 2/3

=1.5 - 0.6

Express 2x2 + 16x +11 in the form a (x + b)2 + c, where a, b and c are
numbers.
What are the values of a, b and c?

Answers

Step-by-step explanation:

I assume the original expression is

2x² + 16x + 11

we need to get this into the form of a(x + b)² + c

let's do the generic multiplication and compare the result to the given expression :

a(x² + 2bx + b²) + c = ax² + 2abx + ab² + c

when we compare this with the original equation, we only need to look at terms with the same variable exponents.

2x² is the only term with "x²".

and ax² is the only term with "x²" in the generic form.

so ?

2x² = ax²

=>

a = 2

16x is the only term with "x" (exponent 1).

2abx is the only term with "x" in the generic form.

16x = 2abx

8x = abx = 2bx

4x = bx

=>

b = 4

11 is the only pure number (constant).

ab² + c is the only constant term in the genetic form.

11 = ab² + c = 2×4² + c = 2×16 + c = 32 + c

-21 = c

so, the solution is

2(x + 4)² - 21

Which numbers are solutions to the equation 30=x2?

Answers

If you meant 2x, x is 15; if you meant x^2, the answer is the square root of 30

i need the answer for


3-3 Mini Assessment | Constant of Proportionality in Graphs




Question
POSSIBLE POINTS: 1
The relationship between the number of ounces of tea purchased and the total cost of the tea is proportional as shown in the graph.



Which equation models this relationship?


y = 7/4x

y = 4/7x


y = 4/1x


y = 1/4x

Answers

Answer:  y= (7/4)x

Step-by-step explanation:

Build a table of representative values and then calculate the slope between any 2 of the points.   I'll pick (2,3.5) and  (8,14)    [See attachment. ]

The slope is the Rise/Run:

Rise = (14 - 3.5) = 10.5

Run = (8-2) = 6

Slope = Rise/Run:  (10.5/6) = 1.75

The equation should read y = 1.75x.  

None of the options works, as written, but note that 7/4 looks close to 1.75.  In fact, 7/4 = 1.75.

Use the equation y = 1.75x and enter several values of x (the ounces purchased) and y (the total cost of the purchase).  The attachment summarizes the results (Predicted), along with the actual values (Actual) taken from the graph.  Excellent correlation, considering the difficulty in making precise graph readings.

Therefore y = (7/4)x

pls help ill give brainliest ​

Answers

Answer:

4

Step-by-step explanation:

-5g -6

Let g= -2

-5 (-2) -6

Multiply

10 -6

4

Answer:

A. 4

Step-by-step explanation:

So, we have an equation with a variable (g), and they've given us the value of g to be -2. All we have to do at this stage is plug in the value of g into the equation.

-5g-6 (g=-2)

-5(-2)-6

10-6=4

Doing the math by plugging in -2, you would get your answer to be 4. Let me know if you see any errors, and if you have any further questions at all.

help please i need it

Answers

Answer:

42m + 12

Step-by-step explanation:

6 ( 7m + 2 )

= 6 ( 7m ) + 6 ( 2 )

= ( 6 * 7m ) + ( 6 * 2 )

= 42m + 12

Answer:

a

Step-by-step explanation:

do distributive property and u get 42m+12

Class 10R sat a test.
The mean mark for the class was 70%.

There are 30 students in class 10R, 20 of whom are boys.
The mean mark for the boys in the test was 62%.

Work out the mean mark for the girls.

Answers

Answer:

86%

Step-by-step explanation:

30 students in the class with a mean average of 70% can be expressed as:

total class percent / 30 = 70%

Rearranged, this gives that the class achieved a total of 30x70 or 2100%.

20 boys in the class with a mean average of 62% can be expressed as:

total boys percent / 20 = 62%

Rearranged, this gives that the boys achieved a total of 20x62 or 1240%.

This means that the girls achieved 2100 - 1240 so 860%.

Because there are 30 students and 20 boys, there are 10 girls.

Then work out the mean with a total of 860% and 10 girls.

860/10 = 86%.

A researcher wants to estimate the likelihood that the baseball player will hit 2 home runs in a single game, given that the player hits a home run once in every 13 times at bat. Which type of study is most suitable for data collection in this situation?


A. experimental


B. census


C. survey


D. simulation

Answers

a its it hope it is okkkkkkk

Question 13 of 20
If fx) = 5x- 4 and g(x) = 4x+1, find (f- g)(x).

Answers

Answer:

Step-by-step explanation:

x-5

Other Questions
please help with statistic 20 (2x+1)(x+5)6x-4xy16x^2-25 Subtract: 3/4y-(1/2y+1/3) how the brochures helped to attract more tourists? I need 3-5 sentence A local car rental business charges an upfront fee of $25 plus an additional charge per mile. When Steven drove 200 miles, his bill came to $45. Which equation represents this relationship?A) y = 10x + 25B) y = 0.10x + 25C) y = 45x + 25D) y = 25x + 45 at the time of creation of cui material the authorized holder Write the equation of the following parabolae in their canonical form and hence find their vertices, foci and directrix.1.[tex] {y}^{2} - 6y - 2x + 19 = 0[/tex]2.[tex] {x}^{2} + 4x + 4y + 16 = 0[/tex] what is the solution to the system of equations COMPOSITION:Vos vacances d'hiver. Describe your winter vacation in 5 sentences or more. An informative essay and an expository essay the same thing Elijah has 4 new dogs and wants to build a square fence in his backyard for them. He wants the sides to each measure (x + 6) feet. Which expression below would he use to find the perimeter of the fence? The author says that writing "cooled my head: like water over a smallburn in the pit of my mind. What does this simile explain about why Yangbecame a writer Explain what types of sports injuries for which it is appropriate to use over-the-counter medications and why. If A(2, 3) and B(-4, -6), find AB.-- Find the equation for g What is the interview about? A store owner has 65.5 pounds of candy. If he splits the candy equally into 5 boxes, how many pounds of candy will each box contain? The year is 1930. You are a middle class man/woman living in New York City. Your savings bank has closed and your money is gone. You have lost your job. Describe your life in terms of economic, political and social welfare. Pls answer questions 1-4 on this pic (must include the math work)i will give brainlist for the most helpful answer How do I make my new hamster calm down she is trying to climb her tank walls, she doesnt have a wheel yet and it comes in on Saturday!