Answer:
y = 0.5cos(4(x+π/2)) -2
Step-by-step explanation:
The centerline of the oscillation is at -2, so only the 2nd and 4th choices are viable.
The multiplier of x is computed from (2π)/period. One period is π/2, so the multiplier of x is ...
... 2π/(π/2) = 4 . . . . . matching the 2nd selection.
The horizontal offset in the second equation (π/2) is of no consequence, as it is one full period of the function.
The peak-to-peak amplitude of the oscillation is 1 unit, so the multiplier of the cosine function (which usually has a peak-to-peak value of 2 units) is 0.5. Every offered answer has that characteristic.
The appropriate choice is the 2nd one:
... y = 0.5cos(4(x+π/2)) -2
Number of large boxes:
50
Number of small boxes: 65
Answer:
The line passing through the given points is:
in its slope-intercept form
Step-by-step explanation:
Start by finding the slope of the segment that joins the two given points using the slope formula:
which for our case renders:
Now we can find the y-intercept by using any one of the given points in the general slope-intercept form of a line with this slope:
Therefore, the equation of the line becomes:
Answer:
24.5 cubic inches
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
A can with a diameter of 2.5 inches has a radius of 1.25 inches. Filling in the given values, the volume is ...
V = π(1.25²)(5) = 7.8125π ≈ 24.54 . . . . cubic inches
The approximate volume is 24.5 cubic inches.
