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
Naily [24]
2 years ago
9

For what values of x∈[0,2π] does the graph of y=x+2cosx have a horizontal tangent?

Mathematics
1 answer:
Katen [24]2 years ago
3 0

Answer: x = pi/6 and x = pi/3.

Step-by-step explanation:

We have the function:

y = x + 2*cos(x)

It will have a horizontal tangent at the point where it's derivate is equal to zero.

Then first let's differentiate y.

y' = dy/dx = 1 - 2*sin(x).

Then we must find the value of x between 0 and 2*pi (or 0° and 360°)

y'(x) = 1 - 2*sin(x) = 0.

Let's solve that:

2*sin(x) = 1

sin(x) = 1/2.

We know that:

sin(30°) = 1/2.

and

Sin(120°) = 1/2

Then let's convert 30° into radians.

We know that:

pi = 180°.

Then:

pi/180° = 1.

30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6

120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.

Then the two values of x are: pi/6 and pi/3.

You might be interested in
-2<3 multiple each side by -5 what is the resulting inequality
fgiga [73]

Answer:

\boxed{10>-15}

Step-by-step explanation:

-2

Multiply each side by -5.

-2 \times -5

Switch signs when multiplying or dividing by a negative integer.

10>-15

8 0
2 years ago
Read 2 more answers
What the equation and he abwser
strojnjashka [21]
6lbs divided by 4, x 16 = 24oz is your answer
7 0
3 years ago
Read 2 more answers
Which equation below and solution for X does the model represent??
VMariaS [17]

Answer:

D) 4x=85, x=21.25

Step-by-step explanation:

If the total is 85$, and every shirt costs the same amount, then you would divide 85 by 4.

That will leave you with 21.25 per shirt.

8 0
2 years ago
Read 2 more answers
What is the volume of the prism?
mezya [45]

Answer:

40 \frac{5}{8} cm^{3}

Step-by-step explanation:

The figure is a rectangular prism, so the formula would be Volume = length x width x height.

length =  6 \frac{1}{2} cm

width  =  2 \frac{1}{2} cm

height  =  2 \frac{1}{2} cm

If you plug everything you have in the problem into the volume equation, you would get : Volume = 6 \frac{1}{2} cm x 2 \frac{1}{2} cm x 2 \frac{1}{2} cm.

Without a calculator, I would first turn the mixed numbers into improper fractions.

  • 6 \frac{1}{2}  = \frac{13}{2}
  • 2 \frac{1}{2} = \frac{5}{2}

Volume = \frac{13}{2} x  \frac{5}{2} x  \frac{5}{2}

When you multiply everything together you should get \frac{325}{8}.

As a mixed number, that would be 40 \frac{5}{8} cm^{3}.

7 0
2 years ago
At a bake sale there were 90 items sold total. If 42 of the items sold were cookies and the rest were brownies what is the ratio
kari74 [83]
Firstly, you do 90 - 42 to get the amount of brownies sold, which is 48. Then, you put 42 and 48 into a ratio like 42:48. After that, all you need to do is simplify to get 7:8.
5 0
3 years ago
Other questions:
  • PLATO
    11·2 answers
  • Solve the following equation. Then place the correct number in the box provided.
    11·1 answer
  • Kathy's internet company charges a connection fee of $0.21 for each call she makes from her computer. The company also charges $
    12·1 answer
  • What is the area of the following circle <br> R=7
    13·2 answers
  • (PLEASE HELP ) A falcon flies 800,000 meters in 4 hours. Use the formula d = rt, where d represents distance, r represents rate,
    7·1 answer
  • WILL GIVE BRAINLIEST!!! DONT GUESS!!! EASY MATH PROBLEM FOR SMART PEOPLE!!!!
    13·1 answer
  • If G is the circumcenter of triangle ABC, AG = 6x + 1, GC = 9x – 11, and BC = 38, find GF.
    5·1 answer
  • 1 أعط ثلاثة أمجلة
    15·1 answer
  • Aight. I know the answer but tell me how to get it if I were to get it again? (It would help me ALOT.)
    11·2 answers
  • Tuto
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!