Calculus

Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)
18 + 9 cos(2x) = 27 cos(x)

  1. 👍
  2. 👎
  3. 👁
  4. ℹ️
  5. 🚩
  1. 9cos2x - 27cosx + 18 = 0
    9(2cos^2x-1)-27cosx+18 = 0
    18cos^2x - 27cosx + 9 = 0
    2cos^2x - 3cosx + 1 = 0
    (2cosx-1)(cosx-1) = 0
    cosx = 1/2 or 1

    Take it from there.

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩
  2. x=0, pi/3, 5pi/3

    1. 👍
    2. 👎
    3. ℹ️
    4. 🚩

Respond to this Question

First Name

Your Response

Similar Questions

  1. math

    Let f be the function with f(0) = 1/ (pi)^2, f(2) = 1/(pi)^2, and the derivative given by f'(x) = (x+1)cos ((pi)(x)). How many values of x in the open interval (0, 2) satisfy the conclusion of the Mean Value Theorem for the

  2. Trig

    On the same set of axes, sketch and label the graphs of the equations y = cos 2x and y = –2 sin x in the interval 0 ≤ x ≤ 2π. How many values of x in the interval 0 ≤ x ≤ 2π satisfy the equation –2 sin x – cos 2x =

  3. Calculus 1

    Consider the following. B(x) = 3x^(2/3) − x (a) Find the interval of increase.(Enter your answer using interval notation.) Find the interval of decrease. (Enter your answer using interval notation.) (b) Find the local maximum

  4. Calculus

    Find all numbers c that satisfy the conclusion of Rolle's Theorem for the following function. If there are multiple values, separate them with commas; enter N if there are no such values. f(x)= x^2-10x+3, [0,10]

  1. Math

    An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) Find the solutions in the interval:

  2. Calc AB

    Suppose that y = f(x) = x^2-4x+4 Then on any interval where the inverse function y = f^–1(x) exists, the derivative of y = f^–1(x) with respect to x is: a) 1/(2x-4) b) 1/(2y-4), where x and y satisfy the equation y=x^2-4x+4

  3. Calc

    Given function f defined by f(x) = ( 1- x)³. What are all values of c, in the closed interval [0,3], that satisfy the conditions of the Mean Value Theorem?

  4. math

    Find all the values of x in the interval [0,2π] that satisfy the equation: 8sin(2x)=8cos(x)

  1. math

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 5 −

  2. Math

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f

  3. Calc 1

    Consider the function below. f(x) = (x^2)/(x−9)^2 (a) Find the vertical and horizontal asymptotes. x=? y=? (b) Find the interval where the function is increasing. (Enter your answer using interval notation.) Find the interval

  4. Calculus

    Consider f(x)=x^3-x over the interval [0,2]. Find all the values of C that satisfy the Mean Value Theorem (MVT)

View more similar questions or ask a new question.