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
aleksandrvk [35]
3 years ago
11

How many solutions does the equation sin(5x) = 1/2 have on the interval (0, 2PI]

Mathematics
1 answer:
Darina [25.2K]3 years ago
4 0

Answer:

Step-by-step explanation:

Given the equation

Sin(5x) = ½

5x = arcSin(½)

5x = 30°

Then,

The general formula for sin is

5θ = n180 + (-1)ⁿθ

Divide through by 5

θ = n•36 + (-1)ⁿ30/5

θ = 36n + (-1)ⁿ6

The range of the solution is

0<θ<2π I.e 0<θ<360

First solution

When n = 0

θ = 36n + (-1)ⁿθ

θ = 0×36 + (-1)^0×6

θ = 6°

When n = 1

θ = 36n + (-1)ⁿ6

θ = 36-6

θ = 30°

When n = 2

θ = 36n + (-1)ⁿ6

θ = 36×2 + 6

θ = 78°

When n =3

θ = 36n + (-1)ⁿ6

θ = 36×3 - 6

θ = 102°

When n=4

θ = 36n + (-1)ⁿ6

θ = 36×4 + 6

θ = 150

When n =5

θ = 36n + (-1)ⁿ6

θ = 36×5 - 6

θ = 174°

When n = 6

θ = 36n+ (-1)ⁿ6

θ = 36×6 + 6

θ = 222°

When n = 7

θ = 36n + (-1)ⁿ6

θ = 36×7 - 6

θ = 246°

When n =8

θ = 36n + (-1)ⁿ6

θ = 36×8 + 6

θ = 294°

When n =9

θ = 36n + (-1)ⁿ6

θ = 36×9 - 6

θ = 318°

When n =10

θ = 36n + (-1)ⁿ6

θ = 36×10 + 6

θ = 366°

When n = 10 is out of range of θ

Then, the solution is from n =0 to n=9

So the equation have 10 solutions in the range 0<θ<2π

You might be interested in
In a small town 15 out of every 26 people voted for the current mayor. His opponents reveived a total of 440 votes. How many peo
Fittoniya [83]

I'm sorry, but there is not enough information for me to correctly answer this question, please provide more information.


3 0
3 years ago
NEED HELP ASAP!!!
azamat
The answer is B f(x)= -3(x+1)^2+2
6 0
3 years ago
PLEASE HELP QUICKLY!!! A student's parents offer him one of two options to receive scholarship money for college.
emmainna [20.7K]

Answer:

A = $47,500.00, B = $65,536.00; B, because he receives $18,036.00 more

Step-by-step explanation:

Option A Versus Option B

Option A                                                Option B

Day Amount Deposited                        Day Amount Deposited

0     $40,000.00                                    0       $1.00

1      $40,250.00                                     1        $2.00

2      $40,500.00                                    2       $4.00

...

30   $47,500                                          16      $65,536.00

Answer:

A = $47,500.00, B = $65,536.00; B, because he receives $18,036.00 more

7 0
3 years ago
Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work
Bingel [31]

Given that we Jenny wants to equivalent fraction of 45% then convert into reduced fraction and then convert into decimal equivalent.

She has already shown her work. We just need to find the error if any.

to convert any percent value we just divide that number by 100 because percent itself means divide by 100.

Hence first step 45%=45/100 is correct.


Then she needed to convert into reduced fraction. To do that she divided numerator and denominator both by 5 and got 9/20.

step 2 is also correct.


Now she needs to convert into decimal equivalent so she divided 9 by 20 and got 4.5 while the correct answer should be 0.45

Hence she did error when converting fraction form into decimal form.

8 0
3 years ago
Read 2 more answers
Which rule represent the reduction of a figure?
vazorg [7]

Answer:

Correct option: second one

Step-by-step explanation:

Let's check each option to find the correct one.

First option: x and y increase by 2.3 times, so the figure expands. So this is not the correct option.

Second option: x and y decrease 0.52 times, so the figure is reduced. So this is the correct option.

Third option: x and y are translated by 1/3 of their position, so the figure is not reduced.

Fourth option: x and y increase by 7/2 times, so the figure expands. So this is not the correct option.

Correct option: second one

5 0
3 years ago
Other questions:
  • PLEASE HELP!! I WILL NAME THE BRAINLEST!!!!
    7·1 answer
  • If y=3x+1 were changed to y=x+1 how would the graph of the new function compare with the original?
    13·1 answer
  • Given the measure of arc AC is 114, what is the measure of angle ADC
    11·2 answers
  • True or False: the sum of any two consecutive prime numbers is also prime?
    15·2 answers
  • |a-5|, if a&gt;5<br><br> Please help me
    11·2 answers
  • HELP PLEASE I DONT KNOW WHAT TO DO
    10·1 answer
  • Help please will give brainlyest
    6·2 answers
  • Type the correct answer in each box.
    14·1 answer
  • Leia needs to make at least 40 necklaces to sell at a craft show. So far, she has made 7. Which inequality shows the
    11·2 answers
  • HEY CAN ANYONE PLS ANSWER DIS MATH PROBLEM!!!
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!