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- A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 9 miles down the shore from P in the least time? Let ?x be the distance between point P and where the boat lands on the lake shore.Using the equation f(x) = 3.14x2 – 10x + 2 and by using incremental search method, what is the interval of the root at the third iteration where the approximate value of the root was obtained? Start the procedure with the initial value of 0 and a step size of 0.1 (first iteration), then 0.01 (second), and lastly 0.01 (third). Group of answer choices [0.211, 0.212] [0.212, 0.213] [0.213, 0.214] [0.214, 0.215]What is meant by absolute, relative, percentage and round-off errors?If in the formula , the percentage error in R is not to exceed 0.3%, find the allowable percentage errors in r and h when r = 48 mm and h = 56 mm. In the evaluation of x4 - 3.17x3 + 5.29x - 1.173 at x = 5.12. Estimate the maximum rror assuming that all decimals are subject to maximum rounding off error.
- an epidemiological study of the spread of a certain influenza strain that hit a small school population found that the total number of students, p, who contracted the flu t days after it broke out is given by the model P+-t^2+13t+160, where 1 is less than or equal to t is less than or equal to 6. find the day that 200 students had the flu. recall that the restriction on t is at most 6.The function shown in the graph below is increasing on the interval [1, 6]. The interval will be divided into 20 subintervals. (a) What are the left endpoints of the first and last subintervals? (b) What are the right endpoints of the first two subintervals? (c) When using the right endpoints, do the rectangles lie above or below the graph of the function? (d) What can you conclude about the heights of the rectangles when the function is constant on the given interval? the grapg is on a separate attachmentA piece of cardboard measuring 12 inches by 9 inches is formed into an open-top box by cutting squares with side length xx from each corner and folding up the sides.Find a formula for the volume of the box in terms of xxV(x) = Find the value for xx that will maximize the volume of the box (round your answer to the nearest hundredth place).x =
- An open box is to be made from a 20-inch by 32-inch piece of cardboard by cutting outx-inch by x-inch squares from the four corners and bending up the sides. The largestpossible volume of the box is obtained by maximizing V (x) =_________ for x in the interval _________The function shown in the graph below is increasing on the interval [1, 4]. The interval will be divided into 12 subintervals. (a) What are the left endpoints of the first and last subintervals? (b) What are the right endpoints of the first two subintervals? (c) When using the right endpoints, do the rectangles lie above or below the graph of the function? (d) What can you conclude about the heights of the rectangles when the function is constant on the given interval?Suppose thatf(x)=x^3−6x^2+2.(A) Find all critical values of f. If there are no critical values, enter -1000. If there are more than one, enter them separated by commas. Critical value(s) =? (B) Use interval notation to indicate where f(x) is decreasing. Decreasing:? (C) Find the x-coordinates of all local maxima of f. If there are no local maxima, enter -1000. If there are more than one, enter them separated by commas. Local maxima at x =? (D) Find the x-coordinates of all local minima of f. If there are no local minima, enter -1000. If there are more than one, enter them separated by commas. Local minima at x =?
- q3.4 Find the following limits analytically or state that they do not exist.ANSWER THE PROBLEM WITH COMPLETE SOLUTION (INCLUDE A TABLE) Using Direct Search Method, estimate the root of the function f(x) = e -x - x in four decimal places with interval [0,1], and with tolerance limit 0.0002Consider the following. y = x4/5 − 1 Find the critical numbers. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) x = 0 Find the open intervals on which the function is increasing or decreasing. Use a graphing utility to verify your results. (Enter your answers using interval notation. If an answer does not exist, enter DNE.) increasing: decreasing: