Final answer:
The equation 2sin(x) = 14 has no solutions in the interval [0, 2π) because the sine of an angle cannot have a value of 7, which is outside the range of the sine function [-1, 1]. b) 1 is correct answer.
Step-by-step explanation:
The equation given is 2sin(x) = 14. To solve for the number of solutions on the interval [0, 2π), we must first isolate sin(x) by dividing both sides of the equation by 2, resulting in sin(x) = 7.
However, the sine function has a range of [-1, 1], meaning that it cannot have a value of 7. Consequently, the equation 2sin(x) = 14 has no solutions within the given interval, since the sine of an angle cannot exceed 1 or be less than -1 in value.
The equation 2sin(x) = 14 can be rewritten as sin(x) = 7. To find the number of solutions to this equation on the interval [0, 2π), we need to find the values of x that satisfy sin(x) = 7. However, the sine function only takes values between -1 and 1, so there are no solutions to this equation.