Answered: As indicated in the notes, what…

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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The volume of water in a cylindrical tank is given by: V = лr²h where V is the volume of water in m³, r is the radius of the tank in metres, and h is the height of the water in metres. For a certain tank, the radius is 3.0 m. This is a property of the tank, so it is a constant. Water is filling the tank, so the height and volume are constantly changing hence h and V are variables. At a certain point in time, the height of the tank is increasing by 0.21 metres/hour and the height is 29 metres. Determine the rate of change of volume (in units of m³/h) at this point in time. Give your answer to three decimal places. Hint 1: You are being asked to find dv/dt. Hint 2: dh/dt = 0.21 m/h
Let f(z) be the height of a maple tree in inches and z the number of years since 2000. A linear model for the data is f(z)= 9.44r +84.182. %3D 220 210 200 190 180 170 160 150 140 130 120 10 100 90 80 70 60 50 12 15 A) To the nearest inch, estimate the height of the maple tree in 2015. inches B) Use the equation to find the year in which the tree will be 232 inches tall. Question Help: Message instructor Submit Question hp
The following table represents collected data from literature regarding the inelastic axial capacity (Pn) of Aluminum symmetric profiles as a function of the Area of the section and the Slenderness Ratio (SR) of the bar. Produce a linear model for the capacity in the form Pn= C1 X Area + C2 X SR, show the statistics of the linear model on this paper. Use your linear model to predict Pn for the case of Area= 200 and SR = 35. Produce a 95% confidence interval for your expected value of Pn at Area=200mm2 and SR=35. Find the maximum possible Pn and the minimum possible Pn based on 95% confidence limits of the parameters. Suggest how to improve your model by saying which one of the two factors must be treated nonlinearly and show why you think so! (give at least one direct reason) Area (mm2) SR (-) Pn (kN) 198.3 16 1273 216.3 89 136.5 228 94 129 184.3 83 133.8 220.1 99 112.3 166.7 33 765.4 201.5 70 205.6 219.8 53…
Is Assumption MLR1. Linear in Parameters satisfied for the following model? Explain. y = Bo + B1x1 + B,x² + Bzx² +
1. Use the provided graph of y = f(x) to draw a sketch of each equation. Draw the sketches on the same provided graph. 4 a) y = f(x + 1) + 1 b) y = f(2x) 0 I
1. Consider f(x, y) = (x² + 2y²) a. Sketch cross sections (at least two) off by keeping y fixed and then x fixed. b. Sketch a contour diagram for f with at least four labeled contours. 2. Does the following table represent a linear function? Justify your answer. y 012 xo0 5 10 127 12 24914 3. Find the equation a linear function z = c + mx + ny whose graph contains the points (0,0,0), (0,2,-1) and (-3,0,-4). 4. Find a formula for a function f(x, y, z) whose level surface f = 1 is an ellipsoid (tri-axial) with center at (2,3,4) and the length in x, y, z axes are given by a, b, c respectively.
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
For the DDS given by 1 -(Pn-1)² +4, P₁₁ find the equilibrium values. Write your answers as a list, separated by commas. Pe=

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As indicated in the notes, what functional form is the following model? Q = β1+ β2sin(T) a.Roller Coaster b.Cyclical c.Quadratic d.Trimetric e.Hypotenuse