1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
klemol [59]
3 years ago
12

Given: cos a = -3/5, sin b = 5/13, and a and b are second-quadrant angles; find sin(a - b).

Mathematics
1 answer:
Vladimir79 [104]3 years ago
7 0

Answer:

63/65

Step-by-step explanation:

Recall that sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

Therefore, we have:

sin(a-b) = sin(a)cos(b) - (-3/5)(5/13)

sin(a-b) = sin(a)cos(b) + 3/13

Since sin(x) = opposite/hypotenuse and cos(x) = adjacent/hypotenuse, then if cos(a) = -3/5, sin(a) = 4/5. Likewise, if sin(b) = 5/13, then cos(b) = 12/13.

Therefore, sin(a-b) = (4/5)(12/13) + 3/13 = 48/65 + 3/13 = 48/65 + 15/65 = 63/65

You might be interested in
A string passing over a smooth pulley carries a stone at one end. While its other end is attached to a vibrating tuning fork and
nasty-shy [4]

Answer:

correct option is C)  2.8

Step-by-step explanation:

given data

string vibrates form =  8 loops

in water loop formed =  10 loops

solution

we consider  mass of stone = m

string length = l

frequency of tuning = f

volume = v

density of stone = \rho

case (1)  

when 8 loop form with 2 adjacent node is \frac{\lambda }{2}

so here

l = \frac{8 \lambda _1}{2}      ..............1

l = 4 \lambda_1\\\\\lambda_1 = \frac{l}{4}

and we know velocity is express as

velocity = frequency × wavelength   .....................2

\sqrt{\frac{Tension}{mass\ per\ unit \length }}   =   f × \lambda_1

here tension = mg

so

\sqrt{\frac{mg}{\mu}}   =   f × \lambda_1     ..........................3

and

case (2)  

when 8 loop form with 2 adjacent node is \frac{\lambda }{2}

l = \frac{10 \lambda _1}{2}      ..............4

l = 5 \lambda_1\\\\\lambda_1 = \frac{l}{5}

when block is immersed

equilibrium  eq will be

Tenion + force of buoyancy = mg

T + v × \rho × g = mg

and

T = v × \rho - v × \rho × g    

from equation 2

f × \lambda_2 = f  × \frac{1}{5}  

\sqrt{\frac{v\rho _{stone} g - v\rho _{water} g}{\mu}} = f \times \frac{1}{5}     .......................5

now we divide eq 5 by the eq 3

\sqrt{\frac{vg (\rho _{stone} - \rho _{water})}{\mu vg \times \rho _{stone}}} = \frac{fl}{5} \times \frac{4}{fl}

solve irt we get

1 - \frac{\rho _{stone}}{\rho _{water}}  = \frac{16}{25}

so

relative density \frac{\rho _{stone}}{\rho _{water}} = \frac{25}{9}

relative density = 2.78 ≈ 2.8

so correct option is C)  2.8

3 0
4 years ago
Solve the following system of equations by graphing.
never [62]

Answer:

(x,y)=(3,1)

Step-by-step explanation:

8 0
3 years ago
A total of 243 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student t
alina1380 [7]

Answer:

81 adult tickets

Step-by-step explanation:

Step 1:

Set up a system of equations

Since the adult tickets and student tickets add to 243, we can do

a+s=243

and the student tickets sold were 2x the adult tickets, we can do

s=2a

We can replace s in the first equation adding to 243 with 2a

a+s(2a)=243\\3a=243\\

Step 2:

Solve for a. We can divide both sides by 3.

a=81

Therefore, there were 81 adult tickets sold.

Step 3:

We can check our work! Since we learned earlier the student tickets are 2x adult tickets, we can multiply 81 by 2 and add that to 81 to see if it equals 243!

s=2a\\s=2(81)\\s=162

And...

162+81=243

So, 81 must be the answer!

8 0
3 years ago
Read 2 more answers
What statements are true about the ordered pair (7,19) and the system of equations?
Tju [1.3M]

Answer:C


Step-by-step explanation:


3 0
4 years ago
The seventh-grade class is building target areas for a PE activity. The bases for the game will be circular in shape. The diamet
murzikaleks [220]
19.6 would be the area of a single base circle πr² is the area formula
5 0
3 years ago
Read 2 more answers
Other questions:
  • Model each two-step operation by solving.<br> -2x-3=5
    10·2 answers
  • Can anyone tell me how to do 28% of 32
    13·2 answers
  • Simplify (2x+7)-(6x-8)
    5·2 answers
  • {8} ⊆ {7,8,9} true or false
    15·2 answers
  • What are the factor pairs of 38
    8·2 answers
  • What is the measure of an angle that is the complement of angle A?
    10·1 answer
  • Can y’all help me on question 40?!
    11·1 answer
  • Which of the following are square roots of the number below? Check all that
    14·1 answer
  • Wesley willed his estate to Margaret,
    14·2 answers
  • A circle has a radius r which is a positive integer. If the circumference of the circle divided by the area of the circle is a p
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!