<h3>
Answer:</h3>
30 ft; 0.4 min
<h3>
Step-by-step explanation:</h3>
The mnemonic SOH CAH TOA reminds you ...
... Sin = Opposite/Hypotenuse
Here, the angle of elevation is opposite the triangle side representing the distance between floors. The hypotenuse is the length of the conveyor belt. Rearranging the formula (by muliplying by Hypotenuse/Sin), we get ...
... Hypotenuse = Opposite/Sin
Filling in the values from this problem, we have ...
... length of conveyor = (26 ft)/sin(60°) ≈ 30 ft
The time it takes to travel that distance is given by ...
... time = distance/speed
... time = (30 ft)/(75 ft/min) = 2/5 min = 0.4 min
For the first 60 positive integers, a = 1, n = 60, l = 60.
Sn = n/2(a + l)
s = 60/2(1 + 60) = 30(61)
For the next 60 positive integer, a = 61, n = 60, l = 120
Sum = 60/2(61 + 120) = 30(61 + 120) = 30(61) + 30(120) = s + 3600
Sum of first 120 positive integers = s + s + 3600 = 2s + 3600
The point-slope form of the equation of the line is:
(y - y1) = m (x - x1)
So, (y + 2) = - 1/3 (x - 4) in the point-slope form is:
[y - (-2) ] = (-1/3) [ x - 4 ]
You must, then realize that the line passes through the point (4,-2) and its slope is - 1 /3.
That slope, -1 / 3, means that the function is decresing (because the slope is negative), and it decreases one unit when x increases 3 units.
Now you can fill in the blanks in this way:
Plot the point (4, -2), move 1 unit down, and 3 units over to find the next point on the line.
Answer:
The answer is 7,200...........
