Find the exact value for the expression under the given conditions.
cos(α+β), sin α= -8/17 for α in Quadrant lll and cosβ= -8/15 for β in Quadrant ll.

Answers

Answer 1

Answer:

[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]

Step-by-step explanation:

We are given the conditions:

[tex]\displaystyle \sin(\alpha)=-\frac{8}{17}\text{ and } \cos(\beta)=-\frac{8}{15}[/tex]

Where α is in QIII and β is in QII and we want to find the exact value of cos(α + β).

The first ratio gives us the opposite side and the hypotenuse with respect to α . Then the adjacent side is (we can ignore negatives):

[tex]a=\sqrt{(17)^2-(8)^2}=15[/tex]

The second ratio gives us the adjacent side and the hypotenuse with respect to β. Then the opposite side is:

[tex]o=\sqrt{(15)^2-(8)^2}=\sqrt{161}[/tex]

Therefore, for α, ignoring negatives, the adjacent side is 15, the opposite side is 8, and the hypotenuse is 17.

And for β, ignoring negatives, the adjacent side is 8, the opposite side is √(161), and the hypotenuse is 15.

We can rewrite our expression as:

[tex]\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]

Since α is in QIII, sin(α), cos(α) < 0, and tan(α) > 0.

And since β is in QII, cos(β), tan(β) < 0, and sin(β) > 0.

Using this information, substitute:

[tex]\displaystyle \cos(\alpha+\beta)=\left(-\frac{15}{17}\right)\left(-\frac{8}{15}\right)-\left(-\frac{8}{17}\right)\left(\frac{\sqrt{161}}{15}\right)[/tex]

Therefore:

[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]


Related Questions

The probability of buying a small car is 1. What does that mean?
It is unlikely.
It is impossible.
It is definite.
It is likely

Answers

Answer:

it is unlikely if it is one out of 5

Step-by-step explanation:

answer all of them please


easy math questions for 20 points ​

Answers

1) 18
2) 4
3) 60
4) 18
5) 6
6) 4
7) 9
8) 4
9) 4
10) $35
11) 8
12) 9
13) 56
14) 10000
15) 78
16) $50
17) 10
18) 1,2,3,4,6,12
19) 1,2
20) 1000
21) 8
22) 5
23) 12
24) 366
25) 35

PLZ RESPOND AS SOON AS POSSIBLE
What point is located at (-2, -6)
a. F
b. G
c. H
d. K

Answers

"Point K" is the correct answer!-2 means 2 left-6 means 6 down

The answer is for your question is letter k

What is the width of a rectangle with a length of 3/8 ft and and area of
4 square feet?

Answers

L: 3/8ft
A: 4
W: 10.6666666668881

Explanation: 3/8ft x 10.6666666668881 = 4ft

I need the surface area plz

Answers

Answer:

922

Step-by-step explanation:

(5x22)x2=220

(13x5)x2=130

(22x13)x2=572

220+130+572=922

Answer:

Length (l) = 22 ft

Breadth (b) = 13 ft

Height (h) = 5 ft

Surface Area of a cuboid

[tex] = 2(lb + bh + lh)[/tex]

[tex] = 2(22 \times 13 + 13 \times 5 + 5 \times 22) \\ = 2(286 + 65 + 110) \\ = 2(461) \\ = 2 \times 461 \\ = 922 \: ft ^{3} [/tex]

=> Surface area of the cuboid will be 922 ft³.

(8 – 10i) – (-16 + 2i)

Answers

Answer:

8-10i - -16+2i= 236

Step-by-step explanation:

I am brainliest

Answer:

-16

Step-by-step explanation:

(8-10i) - (-16+2i)

2i - (-14i)

-16

Arlie is on an airplane that has traveled 420 miles in 3/4 of an hour. At this rate, how far will the airplane travel in the next 1/2 hour?

Answers

The plane will travel miles in the next 1/2 hour. A total of 700 miles.

A trapezoid with a height of 19 meters has a base of 26 meters and another base of 46 meters. What is the area of the trapezoid?


the area of the trapezoid is

A 342m2 B 598m2 C 684 m2D 1,368m2

Answers

Answer:684

Step-by-step explanation:

A= 1/2 h (b1+b2)

A= 1/2 19 (46+26)

A= 9.5 (72)

A=684

The answer is C... 684

The Edward James Toy Company uses a Kanban system to make plastic wheels that are a component of several toys. The waiting time for a container of the wheels during production is 0.25 day; average processing time is 0.15 day per container. Each container holds 200 wheels. The company uses 2,000 wheels a day in the production of its products. Use the information in Case 6.1. Using a policy variable of 5%, calculate the number of Kanban containers needed for the wheels.

Answers

Answer:

[tex]N_c \approx 5.0[/tex]

Step-by-step explanation:

From the question we are told that:

Waiting time for a container of the wheels during production [tex]T_w=0.25day[/tex]

Average processing time is [tex]T_a=0.15 day per container[/tex]

Wheel per container [tex]N_w=200[/tex]

Total wheel per day [tex]D=2000[/tex]

Policy variable of [tex]X=5%[/tex]  

Generally the equation for Total number of container [tex]N_c[/tex] is mathematically given by

[tex]N_c=DT(\frac{1+X}{N_w} )[/tex]

Where

Total time [tex]T=T_w+T_a[/tex]

[tex]T=0.15+0.25[/tex]

Therefore

[tex]N_c=DT(\frac{1+X}{N_w} )[/tex]

[tex]N_c=2000*0.40(\frac{1+0.5}{200} )[/tex]

[tex]N_c=(\frac{840}{200} )[/tex]

[tex]N_c=4.2[/tex]

[tex]N_c \approx 5.0[/tex]

Therefore the number of Kanban containers needed for the wheels is

[tex]N_c \approx 5.0[/tex]

Jelpppsldkdhjdisjsjxjxjzjdjz

Answers

Answer:

28716.35 mm³

Step-by-step explanation:

The formula of volume of sphere

[tex] = \frac{4}{3} \pi {r}^{3}[/tex]

The volume of the sphere

[tex] = \frac{4}{3} \times 3.14 \times {(38 \div 2)}^{3} [/tex]

[tex] = \frac{4}{3} \times 3.14 \times {19}^{3} [/tex]

[tex] = \frac{86149.04}{3} [/tex]

[tex] = 28716.34667...[/tex]

= 28716.35 mm³ (rounded to the nearest hundredth)

Dr. Victory is a psychologist studying the effects of high-level classes, bullying, and music classes on the anxiety levels of middle school students. He has previously determined that the effects from class levels, bullying experiences, and music classes are independent. It has been determined that the probability that a student is taking a high-level English class is 0.23, the probability that a student has been bullied is 0.36, and 1/3 of students are in music classes.
(a) What is the probability that a randomly selected student is in a high-level English class and has been bullied?
(b) What is the probability that a randomly selected student is in a music class and has been bullied?
(c) What is the probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class?

Answers

Answer:

a) 0.0828 = 8.28% probability that a randomly selected student is in a high-level English class and has been bullied

b) 0.12 = 12% probability that a randomly selected student is in a music class and has been bullied

c) 0.0276 = 2.76% probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class

Step-by-step explanation:

Probabilities of independent events happening together:

The probabilities of independent events happening together is the multiplication of the probabilities of each event happening.

In this question:

0.23 probability that a student is taking a high-level English class.

0.36 probability that a student has been bullied.

1/3 = 0.3333 probability that a student is in music class.

(a) What is the probability that a randomly selected student is in a high-level English class and has been bullied?

0.23*0.36 = 0.0828

0.0828 = 8.28% probability that a randomly selected student is in a high-level English class and has been bullied

(b) What is the probability that a randomly selected student is in a music class and has been bullied?

0.36*1/3 = 0.12

0.12 = 12% probability that a randomly selected student is in a music class and has been bullied

(c) What is the probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class?

0.23*0.36*1/3 = 0.23*0.12 = 0.0276

0.0276 = 2.76% probability that a randomly selected student is in a music class, has been bullied, and is in a high-level English class

Area 15 cm 12 cm 19 cm triangle

Answers

Answer:

not clear

Step-by-step explanation:

what is the height and base? need an image

Which histogram correctly displays the information above

Answers

Answer:  The answer is c

Pls solve the 2nd q fast. Best answer will be marked brainliest

Answers

Step-by-step explanation:

[tex] \frac{ - 16}{11} + \frac{ - 3}{9} = \frac{ - 48 - 11}{33} = \frac{ - 59}{33} [/tex]

these are the answers in different forms

need help asap i have no clue how to solve this

Answers

Answer:

c and

28.57%

Step-by-step explanation:

count how many number fall into each category

50-59 has 1

60-69 has 2

70-79 has 4

80-89 has 4

and 90-99 has 3

So the last histogram fits this data

to find the % of those that are between 70-79, take the total number of items that fit into that category (4) and divide by the total number of items (14)

4/14=.2857 --> turn to a percent .2857*100=  28.57%

Would greatly appreciate the help with both A and B

Answers

the answers are a, c, and f

SOME HELP HERE PLEASE?!!

Solve for x:
x+2 / x+5 = 2/3
A. -11
B. - 3
C. 2
D. 3
E. 4

Thanks!!​

Answers

Step-by-step explanation:

Your answer is 4. Hope you like my answer.

Answer:

x+2 / x+5 = 2/3

2x + 10 = 3x + 6

•°• x =4

correct option → E

Hope it helped :)

A zoo has 15 toucans and 75 parrots What is the ratio of the number of toucans to the number or parrots in the zoo

Answers

Answer:

Since there is 15 toucans and 75 parrots the ratio would be written as

15/75

Step-by-step explanation:

As of 15 to 75. Then write out with a colon between the too! 15:75

Hope this helped and have a wonderful day!! <33

If ax+b=3 and a=0, then x=

Answers

Answer: the answer is e

Step-by-step explanation:

If ax + b = 0, is x > 0

(1) a + b > 0

(2) a - b > 0

Please help. I NEED GOOD GRADES

Answers

Answer:

The circle should be open and the arrow should go the other way.

This is the correct answer your welcome

Final Question!!!! College Math! I also did half of it!

Answers

Answer:

15π/4

9π /4

Step-by-step explanation:

[tex]5 \int\limits^4_1 {f(x)} \, dx[/tex]  = 5 ((-π/4)+ π) = 5 (π-π/4) = 5(3π/4) = 15π/4

[tex]5 \int\limits^6_1 {|f(x)|} \, dx[/tex] =  5(π/4 + 2π)  = 5(9π /4) = 45π/4

I need help I need the answer

Answers

Answer:

(4,4)

Step-by-step explanation:

because it's right in between the school and bank therefore equal distance to both

Answer:

(6,8)

Step-by-step explanation:

the same distance from bank to school (sorry if im wrong)

Find the surface area of the rectangular prism:​

Answers

Answer: 430 cm²

Step-by-step explanation:

1) Front x Back=  15 x 7  x 2= 210 (We do time 2 because there are two of the same shapes ex. there are two squares that are both 16 ft so just do 16 x 2)

2) Right x Left=  7 x 5 x 2 = 70

3) Top x Bottom=  15 x 5 x2 = 150

4) Add. 150 + 210 + 70 = 430 cm²

Hope that helped! :)

Which of the following represent the numerical expression 2p? (c (Select all that apply.) 1: The product of 2 and p 2: Two more than p 3: Two less than p 4: Two groups of p 5: The quotient of 2 and p 6: Two multiplied by p​

Whoever answer this question Get Mark Brainiest

Answers

Answer:

(1) The product of 2 and p (6) Two multiplied by p​.

Step-by-step explanation:

The given numerical expression is 2p.

Here, 2 is a variable and p is a constant. 2 and p are getting multiplying. The multiplication of two numbers is called their product.

The product of 2 and p is equal to 2p.

Also, product of 2 and p.

Hence, the statement that represents 2p are : (1) The product of 2 and p (6) Two multiplied by p​.

Gina will pay $14 for fabric at a crafting store. The tax rate is 8.5%. How much will she pay for her fabric including tax?

Answers

Answer:

$15.19

Step-by-step explanation:

8.5% = 0.085

0.085 x 14 = $1.19

1.19+14= $15.19

Help Please!! Struggling with this for a while

Answers

Answer:

Area of triangle ABC = 6 square units

Step-by-step explanation:

By applying Pythagoras theorem in right triangle ADC,

AC² = AD² + CD²

3² = (1.8)² + CD²

9 - 3.24 = CD²

CD = √5.76

CD = 2.4 units

By applying mean ratio theorem,

[tex]\frac{AD}{CD}=\frac{CD}{DB}[/tex]

CD² = AD × DB

(2.4)² = 1.8 × DB

DB = [tex]\frac{5.76}{1.8}[/tex]

DB = 3.2 units

AB = AD + DB

AB = 1.8 + 3.2

AB = 5 units

Since, area of a triangle ABC = [tex]\frac{1}{2}(\text{Base})(\text{Height})[/tex]

                                                = [tex]\frac{1}{2}(\text{AB})(\text{CD})[/tex]

                                                = [tex]\frac{1}{2}(5)(2.4)[/tex]

                                                = 6 square units

What is the measure of angle A? How do you know this?

HELPPP QUICK ANSWER BOTH PARTS

Answers

Answer:

x = 20 degrees

Step-by-step explanation:

We know this because angles next to each other in parallelograms add up to 180 degrees, so if we create an equation, 3x + 120 = 180 meaning that 3x = 60, which means that x = 20 degrees.

please help me how to get the answer for this one

Answers

Answer:

i say c sorry if im wrong

Step-by-step explanation:

The correct answer is each term in patter A is 8 times more than pattern B.
So the answer is D

Graph triangle JKL and its image after a reflection in the line x=2 J(1,-1), K(3,0), L(0,-4)

Answers

Answer:

I need more information to help you on this question.

Step-by-step explanation:

The points after image reflection in the line x = 2 will be k'(1, 0), L'(4, -4) and J'(3, -1).

What is a graph?

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given information in the question,

Here mirror (x = 2) is vertical, hence only x-coordinate changes vertical distance from x-axis will not change.

For point k(3, 0)

It is one unit right side or x  = 2. So, its  image point will be one unit left side that is k'(1, 0).

For point L(0, -4)

It is two unit left side, so L' will be 2 unit right side of x = 2, so the point will be L'(4, -4)

Similarly, point J(1, -1) will become J'(3, -1).

To know more about Graph:

https://brainly.com/question/17267403

#SPJ2

E = (2a + 3b + 2) + (3a + 5b - 1) + (2a - 2b)

Answers

Answer:

7a+6b+1

...............

Answer:

7a+6b+1

Step-by-step explanation:

2a+3b+2+3a+5b-1+2a-2b=7a+6b+1

Combine like termsUse this fact:

(+)×(+)=+ (-)×(-)=+

(+)×(-)=- (-)×(+)=-

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