Xand R charts are to be used to control a critical dimension on a certain product using a subgroup size of 5 units. After 30 subgroups, EX = 574.5 mm, ER = 1.44 mm. (a) Calculate the values of the centre line and control limits for the X and R charts
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- Consider the graph of the cubicy = x(x - a)(x - b), where 0 < a < b. Verify that the graphbounds a region above the x-axis, for 0 < x < a, and bounds aregion below the x-axis, for a < x < b. What is the relationshipbetween a and b if the areas of these two regions are equal?Determine the exact area of the region bound by the graph of f(x) = −x^2 + 5 and the x-axis on [−1,1] using a right-endpoint Riemann sum.Find the are of the region under the graph of f on [a,b] f(x)=e-x/2 ; [-1,14]
- Consider the region bounded between the graphs of y= sin(x) and y = cos(x) with x between 0 and 2 pie, illustrated belowFind the are of the region: y=9cos(pi*x) , y=8x^2-2In the given equation , use the limit process to find the area of the region bounded by the graph of the function and the x-axis over the given interval. Sketch the region y = 27 - x3 , [1, 3]
- Use the limit process to find the area of the region between the graph of the function and the y-axis over the given y-interval. g(y) = 4y2 − y3, 1 ≤ y ≤ 3 (Show on the graph)Consider the region bounded by the graphs of y = x2 and y = b, where b > 0. Sketch a graph of the region.Consider the following equations whose graphs enclose a region. f(x) = x3; g(x) = x2 + 6x Find the x-coordinates of the points of intersection of the graphs. (Enter your answers as a comma-separated list.) x = Which is the top curve on the left-most interval enclosed by the graphs? f(x) = x3 g(x) = x2 + 6x Which is the top curve on the right-most interval enclosed by the graphs? f(x) = x3 g(x) = x2 + 6x Find the area of the region enclosed by the graphs. (Give an exact answer. Do not round.)