Split up the interval [2, 5] into
equally spaced subintervals, then consider the value of
at the right endpoint of each subinterval.
The length of the interval is
, so the length of each subinterval would be
. This means the first rectangle's height would be taken to be
when
, so that the height is
, and its base would have length
. So the area under
over the first subinterval is
.
Continuing in this fashion, the area under
over the
th subinterval is approximated by
, and so the Riemann approximation to the definite integral is
and its value is given exactly by taking
. So the answer is D (and the value of the integral is exactly 39).
Answer: 18 quarts for Part a
9 gallons for part b
Step-by-step explanation:
<h3>
Answer: y = (-1/2)x + 2</h3>
This is the same as y = -0.5x+2
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Explanation:
Refer to the diagram below.
The blue line is the graph of y = 2x+8, which is the left bank of the river.
For now, ignore the y = (-1/2)x+2 in the diagram and pretend we don't know that just yet. The red line is the bridge and it's some linear equation in the form y = mx+b. We're told the bridge is perpendicular to the river, so the bridge must also be perpendicular to the riverbank.
The blue line has slope m = 2. Apply the negative reciprocal to this to end up with -1/2. This is the perpendicular slope, and the slope of the red line. Note how the two slopes (2 and -1/2) multiply to -1. Any two perpendicular lines will have their slopes multiply to -1, as long as neither line is vertical or horizontal.
Since we want the bridge to pass through (0,2), this must mean the y intercept is b = 2.
So with m = -1/2 and b = 2, we go from y = mx+b to y = (-1/2)x + 2 which is the equation of the bridge shown in red.
This is the same as y = -0.5x + 2 since -1/2 = -0.5
The correct answer would be -21.63 and +21.63
Answer:
t = 1.75(s)
Step-by-step explanation:
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