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Charra [1.4K]
3 years ago
10

∠1 is decomposed into two nonoverlapping angles, ∠2 and ∠3.

Mathematics
1 answer:
AVprozaik [17]3 years ago
5 0
Angle 3 is and acute angle (60°)
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<img src="https://tex.z-dn.net/?f=%20express%20%5C%3A%20%20%5C%3A%20%5Csin%282x%29%20%20-%20%20%5Csqrt%7B3%7D%20%20%5Ccos%282x%2
gizmo_the_mogwai [7]

Answer:

α = π/3

γ = 2

x = -3π/4, -5π/12, π/4, 7π/12

Step-by-step explanation:

Easiest way to do this is in reverse.

γ sin(2x − α)

Angle sum/difference formula:

γ (cos α sin(2x) − sin α cos(2x))

Distribute:

γ cos α sin(2x) − γ sin α cos(2x)

Matching the coefficients:

γ cos α = 1

γ sin α = √3

Solve the system of equations.  Divide to eliminate γ:

tan α = √3

α is between 0 and π/2, so:

α = π/3

γ = 2

sin(2x) − √3 cos(2x) = 1

Using the identity from before:

2 sin(2x − π/3) = 1

Solving:

sin(2x − π/3) = 1/2

2x − π/3 = π/6 + 2kπ or 5π/6 + 2kπ

2x = π/2 + 2kπ or 7π/6 + 2kπ

x = π/4 + kπ or 7π/12 + kπ

x is between -π and π, so:

x = -3π/4, -5π/12, π/4, 7π/12

7 0
3 years ago
If a ∝ b and a = 18 when b = 3, then find a when b = 5.
Elden [556K]

"a ∝ b" means "a is proportional to b", which in turn means there is some constant k such that

a = kb

We're given that a = 18 and b = 3, so that

18 = 3k   ⇒   k = 6

Then when b = 5, we would have

a = 6 × 5 = 30

4 0
2 years ago
Please help on number 2?!?!?
Rainbow [258]
Basically, the higher the price an item is the more you will be taking off of it if it is 10 percent off. For example, at $50, 10 percent off is $5, but at $55, it’s $5.50. There is more to take away, making the final price less than the original. Hope that make sense!
8 0
3 years ago
Factor the expression completely by first taking out a common factor<br> 3x^2 + 27x +24
Mrac [35]
The answer to this is
3(x+1)(x+8)

4 0
3 years ago
If 50 × a = 50, then what is the value of 50 − a ?
Paraphin [41]

Answer: 50 - a = 49

Step-by-step explanation:

50 x a =50

50 x 1 = 50

a=1

50 - a = 50 - 1

50 - 1 = 49

5 0
3 years ago
Read 2 more answers
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