Question

Determine if the following answers are true or false. If false, justify why it’s not true and find the correct answer(s). If true, justify why they are correct.

Answer 1

FALSE because the solutions of 3 cos x + 4 = 6 at the interval (0, 2π] is x = 0.841 and x = 5.442.

Step-by-step explanation:

Let's solve for the value of x. Here are the steps.

a. Subtract 4 on both sides of the equation.

`3cosx+4-4=6-4`
`3cosx=2`

b. Divide both sides of the equation by 3.

`(3cosx)/(3)=(2)/(3)`
`cosx=(2)/(3)`

c. Take the inverse of the cosine function.

`x=cos^(-1)(2)/(3)`
`x=0.841`

One of the solutions is 0.841.

To get the other solution, subtract 0.841 from 2π.

`2\pi-0.841=5.442`

The other solution within the interval (0, 2π) is 5.442 and not 3.983.

Hence, the statement is false.