Find a linear inequality with the following solution set. Each grid line represents one unit.
1 answer:
Answer:
-0.5x + y + 0.5 > 0
Step-by-step explanation:
Let the equation of the line is,
y - y' = m(x - x')
where (x', y') is a point lying on the line
m = slope of the line
Since two points (1, 0) and (3, 1) lie on the line,
Therefore, slope of the line 'm' =
m =
m =
Equation of line passing through (1, 0) and slope = will be,
y - 0 =
y = 0.5x - 0.5
Since, line given in the graph is a dotted line therefore, its an inequality having sign of (> or <).
In this inequality shaded region is above the dotted line therefore, inequality representing the solutions by the shaded region will be,
y > 0.5x - 0.5
-0.5x + y + 0.5 > 0
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The Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
<h3>What is Riemann sum?</h3>
Formula for midpoints is given as;
M = ∑0^n-1f((xk + xk + 1)/2) × Δx;
From the information given, we have the following parameters
- x0 = 0
- n = 6
- xn = 3
Let' s find the parameters
Δx = (3 - 0)/6 = 0.5
xk = x0 + kΔx = 0.5k
xk+1 = x0 + (k +1)Δx
Substitute the values
= 0 + 0.5(k +1) = 0.5k - 0.5;(xk + xk+1)/2
We then have;
= (0.5k + 0.5k + 05.)/2
= 0.5k + 0.25.
Now f(x) = 2x^2 - 7
Let's find f((xk + xk+1)/2)
Substitute the value of (xk + xk+1)/2)
= f(0.5k+ 0.25)
= 2(0.5k + 0.25)2 - 7
Put values into formula for midpoint
M = ∑05[(0.5k + 0.25)2 - 7] × 0.5.
To evaluate this sum, use command SUM(SEQ) from List menu.
M = - 12.0625
A Riemann sum represents an approximation of a region's area from addition of the areas of multiple simplified slices of the region.
Thus, the Riemann sum with n = 6, taking the sample points to be midpoints is - 12.0625
Learn more about Riemann sum here:
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