A simply supported beam carries a point load P(lb) at its midpoint. Determine the value of the constant in theequation formed as Y = a+bP using least square method with the given data corresponding to the relationshipbetween P and the maximum deflection Y (in).PY1070.541360.5931490.6221770.7421980.8232190.974

Answered: Image /qna-images/answer/4409ccee-aa87-43c6-be86-461f3b4ad48b.jpg

Answered: A simply supported beam carries a point…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the following data on the number of minutes (x) that 10 persons spent on social media during office hours and their productivity level (y): Xi 10 29 54 63 70 76 88 91 108 118 Yi 92 72 59 50 49 48 38 25 14 9 A linear model was fitted using the statistical software R, producing the following output: Coefficients: (Intercept) 98.81082 -0.75263 Estimate Std. Error t value Pr(>|t|) 29.8 1.74e-09 *** -17.6 1.1le-07 *** 3.31574 0.04277 Signif. codes: 0 ***' 0.001 **** 0.01 0.05 .' 0.1 1 Residual standard error: 4.304 on 8 degrees of freedom Multiple R-squared: 0.9748, F-statistic: 309.7 on 1 and 8 DF, Adjusted R-squared: p-value: 1.11e-07 0.9717 (a) Obtain the equation of the estimated regression line. (b) Interpret the slope coefficient. (c) Discuss whether the simple linear regression model obtained does a good job of explaining observed variation in productivity level. (d) Perform a model utility test using a = 0.01. Use an appropriate P-value from the output given. (Note: R uses…
Use the following equations to find the least square regression quadratic for the given points. Use the regression capabilities of a graphing utility to verify your results. Σ +b + C |= 1 i = 1 in 3 + b' 2 + a |= 1 i = 1 i = 1 n n a + cn = X; i = 1 i = 1 i = 1 (0, 10), (1, 9), (2, 6), (3, 0) y =
Sh44
Consider the point P=(1,2) on the graph of y = x + m= Let Q = (1+h, 1+h+ 1th) be another point on the same curve. What is the slope of the line passing through P and Q? What is the significance of this slope? m is the slope of the tangent line to y. m = m is the slope of the normal line to y. 1 m = x h² +2 h(h+1) ' m = h² +2 h(h+ 1) ' h (h+1) ' m is the slope of the tangent line to y at point P when h approaches 0. h (h+1) ' m is the slope of the tangent line to y at point P when h approaches 1. m is the slope of the secant line passing through P and Q, and has nothing to do with the tangent line.
The scatter plot shows the time spent texting, x, and the time spent exercising, y, by each of 24 students last week. 10 9- Time spent 7- exercising xx (in hours) 1- 10 1 Time spent texting (in hours) Use the equation of the line of best fit, v =-0.75x+8.65, to answer the questions below. Give exact answers, not rounded approximations. (a) What is the predicted time spent exercising for a student who doesn't spend any time texting? O hours (b) For an increase of one hour in the time spent texting, what is the predicted decrease in the time spent exercising? O hours (c) What is the predicted time spent exercising for a student who spends 6 hours texting? hours
pard Lear The following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year Retail Sales 0. 85.851 108.426 6. 141.781 6. 169.256 12 202.297 15 222.266 Let F(t) be the retails sales in billions of dollars in t years since 1995. A linear model for the data is F(t) 9.44t + 84.182. 220 210 200 190 180 170 160 150 140 130 120 110 100 90 6. 12 15 804 Use the above scatter plot to decide whether the linear model fits the data well. The function is not a good model for the data The function is a good model for the data.
A method sometimes used by pediatricians to calculate the dosage of medicine for children is based on the child's surface area. If a denotes the adult dosage (in milligrams) and if S is the child's surface area (in square meters), then the child's dosage is given by D(S) = Sa 1.7 . (a) Show that D is a linear function of S.Hint: Think of D(S) as having the form D(S) = mS + b. What is the slope m and the y-intercept b? m = b = (b) If the adult dose of a drug is 450 mg, how much should a child whose surface area is 0.4 m2 receive? (Round your answer to two decimal places.) mg
The speed of sound in a particular medium is f (T) = 344.51/1+ T meters/second 273.15 where T'is the temperature in degrees Celsius. Find a linear function that approximates the speed of sound for temperatures near O°C. Specifically, fill in the missing numbers below for the local linearization of f at T = 0. Round your answers to three decimal places. f(T) = •T meters/second
A group of children were asked to draw a circle the size of a nicket, without having a nickel to see. In the data below, x= Incomes (in thousands of $) of the the family and y= the diameter of the circle drawn. Test for a significant correlation between income and drawn nickel size. Income (thousands of $) Coin size (mm) 33 25 20 23 36 16 47 22 22 34 14 27 23 20 45 27 24 39 23 91 22 42 12 84 18 46 18 45 22 90 13 54 22 45 18 90 16 54 19 You can copy the data into StatCrunch, Excel, or Google Sheets, by highlighting the data, right-clicking, and selecting Copy (or Ctrl • c), then open a StatCrunch, Excel, or Google Sheets spreadsheet, click on the first cell, and right-clicking and selecting Paste (or Ctri + v). Test the claim that there is significant correlation at the 0.02 significance level. Retain at least 3 decimals on all values. a) Identify the correct hypotheses. Họ:r = 0 HA:r +0 Ho:4 = 0

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