Answer:
1) No represent the water weed. 2)The amplitude of the function is 2.
Explanation:
To find the area of the water weed after 480 hours, we need to convert the given time into days. Since there are 24 hours in a day, 480 hours is equal to 480/24 = 20 days.
Given A(t) = 100t (10/(1.5)), we can substitute t = 20 into the equation to find the area after 20 days:
A(20) = 100 * 20 * (10 / 1.5)
= 100 * 20 * 6.6667
= 13333.33 square meters
Therefore, none of the provided options (a), b), c), d)) accurately represents the area of the water weed after 480 hours.
Moving on to the next set of questions:
The interval of y = -2sin(2x + π/4) + 2 is π/2. The sine function completes one full period in 2π, and the coefficient of x in the argument is 2, so the period of the function is 2π/2 = π.
The period of y = -4cos(2x - π/3) + 2 is also π. Similar to the previous function, the cosine function completes one full period in 2π, and the coefficient of x in the argument is 2, so the period remains the same as π.
The horizontal shift of y = 2 - 4cos(2x - π/3) is π/6. The horizontal shift of a cosine function is given by (phase shift coefficient) * (period). In this case, the phase shift coefficient is π/3, and the period is π. Multiplying these values gives us the horizontal shift of π/6.
The range of y = 5 - 2sin(2x - π/3) is [-3, 7]. The sine function oscillates between -1 and 1. The coefficient of 2 in the argument affects the amplitude of the function but doesn't change the range. Adding and subtracting values to the sine function shifts the range vertically, so the range becomes [-2 - 1, 5 + 1] = [-3, 7].
The amplitude of y = 2 - 2sin(x + π/4) is 2. The coefficient in front of the sine function, which is 2, represents the amplitude. So, the amplitude of this function is 2.