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
Lady bird [3.3K]
3 years ago
6

Solve the equation by first using a Sum-to-Product Formula. (Enter your answers as a comma-separated list. Let k be any integer.

Round terms to three decimal places where appropriate.) sin(5θ) − sin(3θ) = cos(4θ)
Mathematics
1 answer:
schepotkina [342]3 years ago
5 0

Answer:

Solutions of the equation are 22.5°, 30°.

Step-by-step explanation:

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos(\frac{5\theta+3\theta}{2})sin(\frac{5\theta-3\theta}{2})

= 2cos(4\theta)sin(\theta) [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = \frac{90}{4}

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = \frac{1}{2}

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

You might be interested in
In a highway building project, 32 miles of a new highway have been
pychu [463]

Answer: 105 miles

Step-by-step explanation:

You can write an equation for this problem and solve it.

32 miles=1/3x-3, where x is equal to the total length of the highway.

35=1/3x, and then you multiply by 3, to get x=105

7 0
3 years ago
What is the center of the circle for this equation:<br> (x + 3)² + (y - 2)² = 25
Ksju [112]

The formula for the equation of a circle is (x - h)² + (y - k)² = r²

where (h, k) is the center of the circle and <em>r</em> is the radius.

So we need to find the values of (h, k) in order to find the center of the circle.

If we simply line up the equation of our given circle with our formula,

we can see that -h = 3 or h = -3 and -k = -2 so k = 2.

So now we have our answer.

center ⇒ (-3, 2)

8 0
3 years ago
F(x)=23x−1 and g(x)=−4x+6.
USPshnik [31]

The transformation occurs from function g is a vertical translation 6 units down.

<h3>What is Transformation?</h3>

A function f, usually with some geometrical underpinning, that maps a set X to itself, i.e. f : X → X.

Given:

g(x) = 4x + 6

g(x) = 0

4x + 6=0

x= -6/4

Now,

f(-6/4) = 2 - 1

=-1

By seeing g(x), we can say that  function g is a vertical translation 6 units down.

Learn more about transformation here:

https://brainly.in/question/29403318

#SPJ1

3 0
2 years ago
A bicycle shop sells only bicycles and tricycles. Altogther there are 23 seats and 50 wheels. How many bicycles and tricycles ar
slamgirl [31]

Answer:

The number of bicycles is 19.

and the number of tricycles is 4.

Step-by-step explanation:

As we know that the number of seats in bicycles as well as in tricycles is 1.

The number of wheels in bicycles is 2

and the number of wheels in tricycles is 3.

Let the number of bicycles be x.

and the number of tricycles be y.

Thus using the given information we can make equation as,

x + y = 23

and, 2x + 3y = 50

Solving these two equations:

We get, x = 19 and y = 4

Thus the number of bicycles is 19.

and the number of tricycles is 4.

8 0
3 years ago
A square picture with a side length of 4 inches needs to be enlarged. The final area needs to be 81 square inches.
gizmo_the_mogwai [7]

Answer:20.25

Step-by-step explanation:

If you do 81 divided by 4

I think Im not sure

8 0
3 years ago
Other questions:
  • The side lengths of a right triangle are 18 cm, 24 cm, and 30 cm. You are asked to find the area of the triangle by using A = 1/
    12·1 answer
  • There are 84 players on a football team. The ratio of offensive players to defensive players is 4 to 3. How many offensive playe
    12·1 answer
  • Baseball fans can buy tickets for seats in the lower deck or upper deck of the stadium. Tickets for the lower deck cost $42 each
    5·2 answers
  • Expand <br> (–5a^2+2a+3)(4a^2–2a+1)
    12·1 answer
  • If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (cd)(x)?
    11·1 answer
  • What is the value of x in the following proportion? 7/x-5 = 15/x+4
    14·1 answer
  • Which shows a difference of squares?
    7·2 answers
  • Please help me I asked like 2 times and no one has helped :/
    6·1 answer
  • My question: 23% of $52 is $
    13·1 answer
  • 2. choosing rye or Bermuda grass and 3 different mixtures of fertilizer<br> Please help :(
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!