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Q: 3. Find the points of inflection: y = x-2cosx
A: Explanation of the answer is as follows
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Q: 2 5. Write the equation of the line tangent to y=4-x when x=-1.
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- The curve y = a x 2 + b x + c passes through the point ( 1 , 2 ) . The line y = 2 x + 1 is tangent to the curve when x = 0 . What are the values of a , b and c ?Suppose a researcher collects data on the bacterial contamination, measured in colony-forming unit per milliliter, for both upstream and downstream sections of 35 rivers. The data is plotted with upstream bacterial contamination on the horizontal axis and downstream bacterial contamination on the vertical axis. The Scioto River is an outlier in the ?y‑direction. What must be true about this river? The upstream bacterial contamination for this river is much higher or lower than the rest of the rivers in the data set. The downstream bacterial contamination for this river is much higher or lower than other rivers in the data set that have similar upstream bacterial contamination. This river is an influential observation. The downstream bacterial contamination for this river is much higher or much lower than the rest of the rivers in the data set. The absolute value of the residual of this river is large.What is the length of the curve y= x3/2+4 from the point (1,5) to (4,12)?
- The following graph shows the approximate value of the United States Consumer Price Index (CPI) from December 2006 through July 2007. On the graph titled "CPI Dec 2006-July 2007," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 202), goes up and right becoming more steep, passes through the approximate point (3.5, 205.5), goes up and right becoming less steep, and ends at the approximate point (7, 208.7). The approximating curve shown on the figure is given by I(t) = −0.04t3 + 0.4t2 + 0.1t + 202 (0 ≤ t ≤ 7), where t is time in months since the start of December 2006. (a) Use the model to estimate the monthly inflation rate in January 2007 (t = 1). Recall that the inflation rate is I′(t) I(t) . (Round your answer to three decimal places.)The following graph shows the approximate value of the United States Consumer Price Index (CPI) from December 2006 through July 2007. On the graph titled "CPI Dec 2006-July 2007," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 202), goes up and right becoming more steep, passes through the approximate point (3.5, 205.5), goes up and right becoming less steep, and ends at the approximate point (7, 208.7). The approximating curve shown on the figure is given by I(t) = −0.04t3 + 0.4t2 + 0.1t + 202 (0 ≤ t ≤ 7), where t is time in months since the start of December 2006. (a) Use the model to estimate the monthly inflation rate in January 2007 (t = 1). Recall that the inflation rate is I′(t) I(t) . (Round your answer to three decimal places.) (b) Was inflation slowing or speeding up in January 2007? slowing downspeeding up (c) When was inflation speeding up? When was inflation…What is the slope of the curve y= 2 over √x at the point (4,1)?
- The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from September 2004 through November 2005. On the graph titled "CPI Sep 2004-Nov 2005," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 190), goes up and right becoming more steep, passes through the approximate point (8, 195), goes up and right becoming less steep, and ends at the approximate point (14, 199.9). The approximating curve shown on the figure is given by I(t) = −0.005t3 + 0.12t2 − 0.01t + 190 (0 ≤ t ≤ 14), where t is time in months since the start of September 2004. (a) Use the model to estimate the monthly inflation rate in July 2005 (t = 10). Recall that the inflation rate is I′(t) I(t) . (Round your answer to three decimal places.) % (b) Was inflation slowing or speeding up in July 2005? slowing downspeeding up (c) When was inflation speeding up? When was inflation slowing?…The intercept is 0, the autoregressive coefficient is 0.2 and the moving average coefficient is 0.5 in an ARIMA(1,1,1) model. What is the one-step ahead forecast if the shock for the current period is -2 and the current and one-period lagged values of the forecast variable are 110 and 105?Find the distance between the line x + y + 2 = 0 and the point (1, 1).