2. (5 points) The formula h(t) = 125 sin (2pit ? pi/2) + 125 represents the height above the ground at time t, in minutes, of a person who is riding a Ferris wheel. During the first turn, at what time does the reach 200 feet? At what time during.
2. A power plant treats 2 ML dr of feedwater to remove total organic carbon (TOC). The source water contains 30 mg L' of TOC. The treatment system consists of a square coagulation and flocculation tank that with a removal efficiency of 30% TOC (because organic matter sticks to floc)..
2. A steady water jet in the figure is deflected along a cart. The angle of deflection is 50 degree. And a spring that has spring constant (k) of 1500 N/m is fixed with solid stick in the cart. The velocity of the jet is v = 2S m/s. Denote.
2. For each of the following sampling situations, identity the populations as exactly as possible. a. An opinion poll contacts 1161 adults and then asks them, "which political party do you think has better ideas for leading the country in the 21st century? b. A sociologist wants to know the.
2. Let X is an exponential random variable with mean=1, then the pdf is f(x) = e^-x, x > 0. (a) Find the cdf, F(x), for all - infinity < x infinity, and sketch its graph. (b) Let p be a real number between 0 and 1, i.e., 0 <.
2. If you have a family of independent rv?s, any subfamily is also independent Let X1,. . . , X be independent random variables, i.e., their joint pmf/pdf f : R^n arrow R is equal to the product of the marginals: f (x1,. . . , xn) = i= 1.
2. As part of the planning for a major office development project, it is necessary to install telephone lines to the buildings. Information about the project is given below. The distances are provided in feet. What is the total length of this?
Buildings
Distances.
2. Paramagnetism. Find the equilibrium value at temperature t of the frac tional magnetization MINm of the system of N spins each of magnetic moment m in a magnetic field B. The spin excess is 2s. Take the entropy as the logarthithm of the multiplicity g(N,s) as given in (1.35):.
2.
3.
A company finds that there is a linear relationship between the amount of money that it spends on advertising and the number of units it sells. If it spends no money on advertising, it sells 200 units. For each additional $3000 spent,.
2. How many incongruent solutions do each of the following congruences have? a. 5r sa 100(mod 110). b, r2 m 1(mod 88). 3. Find the exact value of each of the following. a. T(6!) b, o (210)
.
2. Answer all the questions.
2. Answer all the questions. Solve and check the linear equation 3(x-3)-13 = 2(x+4) The solution set is {[]}. (Simplify your answer.)
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2. O -2 points stitzPrecalc1 5.1.001 k. 0/100 submissions used Let f(x) 3x g(x) Ixl, hox) x and k(x) Find and simplify the indicated composite function (f o g o h)(x) State the domain. (-co, co) [3, co) (-00, -7] O [0, 00) oo, oj.
2. f(x) = 4x^3 5x^2 + 1.
a. Prove that B = {f, f, f, f} is a basis for P_4.
b. Find the change of basis matrix from this basis B to the basis C = {x^3 1, x^3 +x^2 +1, x^2 x+1,.
2. A highway makes an angle of 6 o with the horizontal. This angle is maintained for a horizontal distance of 5 miles. To the nearest hundredth of a mile, how high does the highway rise in this 5-mile section? Show the steps you use to find the distance. 3..
2. [2 marks] Consider the set A = : m/n N} of positive rational numbers. Which of the following statements are true? 1. The set A has an upper bound. 2. The set A has a least upper bound. 3. For every R, > 0 there is a number a.
2. The following rational function describes concentration in blood of a certain
medicine taken once depending on time, find
a. the horizontal or oblique asymptote(s), if any,
b. the vertical asymptote(s), if any,
c. describe their possible meanings.
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2. A chicken farmer surveyed his flock with the following results. The farmer has: 9 fat red roosters 7 thin brown hens 2 fat red hens 18 thin brown roosters 26 fat roosters 6 thin red roosters 37 fat chickens 5 thin red hens
[ Hint: You.
2. For each of (a)-(c) below, either draw a graph with the specified properties or else explain why no such graph exists. (a) Graph with six vertices of degrees 1, 1, 2, 2, 2, and 3. (b) Graph with four vertices of degrees 1, 2, 2, and 5. (c) Simple.
2. In Gothic structures, builders used very heavy pinnacles to redirect the line of thrust (force) downward toward the ground. Without the added weight of the pinnacle, the structure would fail. What is the required magnitude of the weight, W, such that the resultant force is oriented 20 degree CW.
2. Suppose the product AB of two square matricies is invertible. Prove that A is invertible. [Hint: Let C be the inverse of AB. Multiply AB on the left by C. See if you can tell what the inverse of A would be. ]
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2. A hot-water stream at 80 Degree C enters a mixing chamber with a mass flow rate of 0.5 kg/s where it is mixed with a stream of cold water at 20 Degree C. If it is desired that the mixture leave the chamber at 45 Degree C, determine the.
2. (15 points) If the construction worker exerts 25 lb, on the 'tag line: how much does the crate weigh? 3 (10 points) Given force vector F = 10.5 i - 6.2 j Newton?s. Find a distance vector r that is perpendicular to F..
2. Ohio Pick 4 In Ohio's Pick 4 game, you pay $1 to select a sequence of four digits, such as 7709. If you buy only one ticket and win, your prize is $5000 and your net gain is S4999. a. If you buy one ticket,.
2. (25) Let A a1.a2.aa) be a 3 x 3 matrix where aj are the column vectors of A. Suppose that a 2a2 3aa (zero column vector) Is A non-singular? Explain why..
2. [10 marks] Consider the vectors v1 (1,2,3), v2 (2,-1,0) and v3 (-3,1,0) in Rs. encourage you to use
a mathematics solver, such as Wolfram Alpha, to check that the solution of your sets of linear equations is correct.) (a) Show that the three vectors are linearly.
2.) A MSW landfill is being designed to handle solid waste generated by Binford at a rate of 50 Mg/d. It is expected that the waste will be delivered by compactor truck on a 5d/week basis. the density as spread is 122 kg/m^3. it will be spread in 0.50 m.
2. Algorithm implementation: Write a MATLAB program to compute the square root using the following algorithm: y(n) = x(n) - y^2(n - 1) + y(n - 1). Show that the output y(n) of this system for an input x(n) = alpha u(n) with y(-1) = 1 converges to as n.
2. In each case, determine which value is larger. (Hint: This can be done without using the tables by sketching the graph. a) X0.08,5,X0.94,5 b) x80316, xa02.16.
2. (25 points) A typical mass-spring system is governed by the second order differential equation:
mx?? + cx? + kx = F(t). (1)
To simplify, let F (t) = 0.
(a) Compute the critical damping value ccr in terms of m.
2. A positive integer x is called odd if and only if there exists k Element of N such that x = 2k + 1. A positive integer x is called divisible by 3 if and only if there exists k Element of N such that x = 3k. Using.
2. In class Monday Jan 12th, we were trying got prove this biconditional (goes both ways) statement: If n is a positive integer, then n is even if and only if 3n2+8 is even James proved: if n is even then 3n2+8 is even and if n is odd, then.
2. Let F(r, y) be the proposition that r is the father of y, and let M (r, y be the proposition that r is the mother of y. Express each of the following propositions symbolically. (a) Fred is Ann's father. (b) A is the child of B..
2. A manufacturer estimates his production function as Q hat = 50 + 10 L + 25 K where Q is output, L is labor in people and K is capital (units of machinery). a. If the manufacturer employs 400 workers and uses 17 units of capital, what should output.
2. Given the following single-input single-output functions input ok, output y, y f(x), determine if they are linear A y e B. y- 3x +5 C, y x D. y 3 sin x x(t).
2. Find the derivatives of the following functions. State what di?erentiation
rules you use.
(a) f(x) = x cos x
(b) f(x) = sin(sin x)
(c) f(x) = x^2 / 1 + x^2.
2. -3 points scalcet7 14.7.013.nva My Notes Ask Your Teacher Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the important aspects of the function. (Enter your answers as.
(20 5+8+7 points) Consider the sequence of fractions 1 4 10 28 an 1 2 6 16 where a and bm are defined by the formulae a1 b1 1 and an +1 an 3bn am (a) Model the process of approximation as a discrete time system evolution. In particular, specify.
2. (4 points) a. Prove that A * B = Trace(AB) defines an inner product on the space S^n of symmetric n x n matrices. b. Find an orthonormal basis for S^n in this inner product..
