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
IceJOKER [234]
4 years ago
12

How many solutions does the equation sin(4x)=1/2 have on the interval (0 2pi)?

Mathematics
1 answer:
andre [41]4 years ago
8 0
The angle < pi/2  and whose sine is 1/2 is pi/6

so let 4x = pi/6 and we have x = pi/24   which is one solution.

angle in second quadrant = 5pi / 6  so x = 5pi/24 is another solution.

Each of these  will give new angles as we revolve around the circle in steps of pi/2  so for x = pi/24 next one will be 13pi/24  and for x = 5pi/24 next one will be 17pi/24    This will be true for all angles less than  48pi/24  (ie 2pi)

so there will be 8 solutions 
You might be interested in
Write an equation for the following line.<br> 10<br> -10<br> 10<br> -101
mestny [16]
Y= 4

How to:
Using the y axis it hits the line at 4
8 0
3 years ago
. If you saved $2.00 on january 1, $4.00 on february 1, $8.00 on march 1, $16.00 on april 1, and so on. how much money would you
SIZIF [17.4K]
=2+4+8+16+32+64+128+256+512+1024+2048+4096
=8190
4 0
4 years ago
Read 2 more answers
Find the slope.
puteri [66]

Answer:

2/4

Step-by-step explanation:

6 0
3 years ago
Which subject should u study first when there are loads of subjects?
il63 [147K]

Answer:

All that you can!

Step-by-step explanation:

Try studying all the subjects that you can because it will give you more information. Do Biology before chemistry, and Pre-calculus (if your school has it).

7 0
3 years ago
Express the given quantity as a single logarithm and simplify: 3logx+2log(y-2)-5logx
storchak [24]
Simplify each term<span>.</span>
Simplify <span>3log(x)</span><span> by moving </span>3<span> inside the </span>logarithm<span>. 
</span><span>log(<span>x^3</span>)+2log(y−1)−5log(x)</span><span> 
</span>
Simplify <span>2log(y−1)</span><span> by moving </span>2<span> inside the </span>logarithm<span>. 
</span><span>log(<span>x^3</span>)+log((y−1<span>)^2</span>)−5log(x)</span><span> 
</span>
Rewrite <span>(y−1<span>)^2</span></span><span> as </span><span><span>(y−1)(y−1)</span>.</span><span> 
</span><span>log(<span>x^3</span>)+log((y−1)(y−1))−5log(x)</span><span> 
</span>
Expand <span>(y−1)(y−1)</span><span> using the </span>FOIL<span> Method. 
</span><span>log(<span>x^3</span>)+log(y(y)+y(−1)−1(y)−1(−1))−5log(x)</span><span> 
</span>
Simplify each term<span>. 
</span><span>log(<span>x^3</span>)+log(<span>y^2</span>−2y+1)+log(<span>x^<span>−5</span></span>)</span><span> 

</span>Remove the negative exponent<span> by rewriting </span><span>x^<span>−5</span></span><span> as </span><span><span>1/<span>x^5</span></span>.</span><span> 
</span><span>log(<span>x^3</span>)+log(<span>y^2</span>−2y+1)+log(<span>1/<span>x^5</span></span>)</span><span> 
</span>
Combine<span> logs to get </span><span>log(<span>x^3</span>(<span>y^2</span>−2y+1))
</span><span>log(<span>x^3</span>(<span>y^2</span>−2y+1))+log(<span>1/<span>x^5</span></span>)

</span>Combine<span> logs to get </span><span>log(<span><span><span>x^3</span>(<span>y^2</span>−2y+1)/</span><span>x^5</span></span>)</span><span> 
</span>log(x^3(y^2−2y+1)/x^5)

Cancel <span>x^3</span><span> in the </span>numerator<span> and </span>denominator<span>. 
</span><span>log(<span><span><span>y^2</span>−2y+1/</span><span>x^2</span></span>)</span><span> 

</span>Rewrite 1<span> as </span><span><span>1^2</span>.</span> 
<span><span>y^2</span>−2y+<span>1^2/</span></span><span>x^2</span>

Factor<span> by </span>perfect square<span> rule. 
</span><span>(y−1<span>)^2/</span></span><span>x^2</span>

Replace into larger expression<span>. 
</span>
<span>log(<span><span>(y−1<span>)^2/</span></span><span>x^2</span></span>)</span> 
3 0
3 years ago
Other questions:
  • Lucy is shipping 5 boxes that all weigh the same, and 1 envelope that weighs 7.5 pounds. The total weight of the shipment is 65
    6·2 answers
  • PLEASE HELP!
    8·2 answers
  • I really need help with this in less than 10 min please
    5·1 answer
  • R,S, and T are collinear, and S is betrween R and T. If RS=x+1, ST=2x-2, and RT=5x-5, find RT.
    12·2 answers
  • the angle between two radii of a circle is 130°. then the angle between the tangents at the end points of radius at their point
    13·2 answers
  • Solve for x in the triangle. round your answer to the nearest tenth
    7·1 answer
  • I'LL GIVE BRAINLIEST<br><br> A or D
    6·1 answer
  • What is the answer can someone explain it
    7·1 answer
  • The calculator screen shows a linear regression. Write the equation for the line of best fit for the data. Round values to the n
    8·1 answer
  • PLEASE :(, 25 points!
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!