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
Will a 11.5-inch x 18-inch rectangular tray fit in<br> the box shown? Explain.
pychu [463]

Answer:

Option D

Step-by-step explanation:

From the picture attached,

In the parallelogram ABCD,

Length of diagonals AC and BD are equal.

By the property,

"If the lengths of the diagonals of a parallelogram are equal, parallelogram will be a rectangle".

Therefore ABCD is a rectangle.

That means all interior angles of the given rectangle will be 90°.

Now we apply Pythagoras theorem in right triangle ΔABC,

AC² = AB² + BC²

(22)² = (12)² + (BC)²

484 - 144 = (BC)²

BC = √340

BC = 18.44 inches

Dimensions of the given box are 12 inches by 18.44 inches.

Dimensions of the rectangular tray is 11.5 inches by 18 inches.

Since, dimensions of the box are larger than the dimensions of the tray, tray can be adjusted in the box.

Therefore, Option D will be the answer.

3 0
2 years ago
Find the value of angle BAC​
julsineya [31]

Answer:

The value of angle BAC = 75°

Step-by-step explanation:

=> Angle BAC + 105° = 180°

=> Angle BAC = 180° - 105°

=> Angle BAC = 75°

7 0
2 years ago
A rental truck cost $48 plus $0.40 per mile.
Natalija [7]
(a) If we let x be the number of miles and y be the total cost, the equation for relating the number of miles and the total cost would be,
                                y = 0.4x + 48

(b) If the rental cost is 60,
                               60 = 0.4x + 48
The value of x from the equation is 30.

(c) You may prepare the table of values by allowing x be any number and then solve for y until we arrive with an answer for y being equal to 60. 
3 0
3 years ago
Sustituir. 20c + 15r + 75p + 50e​
AVprozaik [17]

Answer:

8c - 7r + 10p - 20e

Step-by-step explanation:

Subtract (20c + 15r + 75p + 50e) - (12c + 22r + 65p + 70e)

(20c + 15r + 75p + 50e) - (12c + 22r + 65p + 70e)

Open bracket

20c + 15r + 75p + 50e - 12c - 22r - 65p - 70e

Collect like terms

= 20c - 12c + 15r - 22r + 75p - 65p + 50e - 70e

= 8c - 7r + 10p - 20e

3 0
3 years ago
Someone plz help me with These questions :u have to solve for x and show work
irakobra [83]
Ok so the first one is 
1.x=135
2.x=-23
3.x=3
4.x=70

5 0
3 years ago
Other questions:
  • You earn $100 plus 1/5 of your sales each week. What dollar amount of sales do you need this week to earn $600?
    8·1 answer
  • Write a real world problem for 5/6 divided by 1/12. Use a model to solve.
    15·1 answer
  • Triangle ABC is an equilateral triangle with side lengths of 10 inches.
    13·2 answers
  • Please I need help. Don’t understand
    12·1 answer
  • Can you check my question please?Thanks for your help. 12 points.
    12·1 answer
  • Simplify –3(x + 3) + 4x and do a step by step
    6·1 answer
  • For the school play 205 students buy tickets and 232 adults buy tickets all tickets cost 16 how much did the school make in tick
    11·1 answer
  • Lisa watches the vehicles that passes buy in front of he apartment building.she has counted 15 vans and 30 cars. what is the app
    6·1 answer
  • Marco randomly pulled a marble out of a bag then returned the marble to the bag. He did this 10 times. Three times the marble wa
    6·1 answer
  • a golden padlock weighs 4/5 of a pound, but only 3/4 of the padlock is real gold. How many pounds of real gold are in the padloc
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!