Basic Math question and answers for July 09, 2023
- Q A computer aided drafting (CAD) instructor at a communitycollege wants to use his rapid prototype machine to produce demoitems for a seminar on engineering technology. He plans to bringtwo different...
- Q Consider a solid object with the base in the first quadrantbounded by y(x) = 1-( x^2/16) , x-axis, and y-axis. If the crosssection that perpendicular to the x-axis is in...
- Q Evaluate the line integralCF · dr,where C is given by the vector functionr(t).F(x, y, z) = sin(x) i + cos(y) j + xz kr(t) = t5 i ? t4 j...
- Q Theorems need to know a) The fundamental Thm of Algebra. b) TheRational Zero Thm. c) The intermediate Value Thm. d) The ConjugateThm.
- Q What can you say about the following three sequences?1 ) sequence = range [0, 100, 7]{0, 7 ,14 ,21 ,28 ,35 ,42 ,49 ,56 ,63 ,70 ,77 ,84 ,91 ,98]2...
- Q Find the tangential and normal components of the accelerationvector. ? (?) = ? ? ??+ ?2 ? ??+ ? ????
- Q Given: f(x) = x 2?36 x 2?7x+6 Find the followinga. V.A.b. Domainc. H.A.d. X-intercepte. Y-interceptf. Graph
- Q find the general solution to the second order linearnon-homogeneous differential equation(y"/2)-y' +y = cos x
- Q . Let ? be a finite incidence geometry. Prove that, if everyline in ? has exactly n points and every point in ? lies on exactlyn + 1 lines, then...
- Q Express the following systems of equations in matrix form as A x= b. What is the rank of A in each case (hint: You can find therank of a matrix...
- Q Determine an example of a vector field that would yield apositive value for a line integral around a circle that istraversed once clockwise for any nonzero radius and explain how...
- Q csc beta = 2/3. What is the beta to the nearest degree?
- Q For f(x)=x^2+x-2/x^2-4, determine the equation for any verticalasymptotes, the equation for any horizontal asymptotes, and thex-coordinates of any holes
- Q -Let O (0,0,0) be the origin and A(a+1,b,c) where a,b and c arethe last three digits of your student ID. Find, describe and sketchthe set of points P such that...
- Q Which option below provides the best description of the relationship between a quadratic parent function and a square root parent function? A. The square root function is the quadratic function reflected...
- Q why are the domain and range of square root function restrictedto [0,?) ?
- Q Find the domain of the function g(x) = square root of 3x+3
- Q Explain how to solve the following problems step by step, andreason it should be solved that way:1) Find domain for each problem and explain in brief in eachcase. How do...
- Q A ball is thrown vertically upward from a height of 5 ft with aninitial velocity of 40feet per second. Note that the acceleration of the ball is given bya(t) =...
- Q 239.Brett and Jordan are out driving in the coordinate plane,each on a separate straight road. The equations Bt = (?3, 4) + t[1,2] and Jt = (5, 2) + t[?1,...
- Q Graph the square root of the following function. State the domain and range of the square root of the function.y = -2x + 4
- Q a)f(u,v) fuction is provide f(6,-2)=2020, fu(6,-2)=2,fv(6,-2)=3 equations.g(x,y,z)=f(3yz+x2,2x+2y2-z2)so,find tangent plane of g(x,y,z)=2020 at the point (0,1,2).b)Find the tangent line ,which is parallel to question a)tangent plane, ofr(t)=<t2+1,2t+7,4t-t2>(-?<t<?)
- Q 1. x2/3 + 3x1/3 and y = 10. What are the values of X?A) -2, 5B) -5, 2C) -125, 8D) -8, 125E) None of the above2. When a number is...
- Q What path might a basketball travel if you shot from the foulline to a 10 foot hoop?Steve races down the basketball court, then stops and shoots --HE SCORES!!! The ball...
- Q a.Express y in terms of x given that dy/dx = (y + 2)(2x + 1)given that y = 2 at x = 0.b. Solve (x^2 + 1)dy/dx + 3xy =...
- Q Find the solutions of the equation4x^2 + 3 = 2x
- Q using these axioms ( finite affine plane ) :AA1 : there exists at least 4 distinct points , no there ofwhich are collinear .AA2 : there exists at least one...
- Q (a) Determine the inverse Laplace transform of F(s) =(2s?1)/s^2?4s + 6(b) Solve the initial value problem using the method of Laplacetransform. d^2y/dx^2 ?7dy/dx + 10y = 0, y(0) = 0,...
- Q 1.) Let f?(x) = 3x^2 ? 8x. Find a particular solution thatsatisfies the differential equation and the initial condition f(1)= 12.2.) An object moving on a line has a velocity...
- Q Consider the following differential equations:?3?/??3 + 9 ?2?/??2+ 20 ??/?? + 12? = 15?(0) = ??(0) = ??(0) = 0a) Find the solutions to the equation using Laplacetransform.b) Use the...
- Q Use the Laplace Transform method to solve the followingdifferential equation problem: y 00(t) ? y(t) = t + sin(t), y(0) =0, y0 (0) = 1Please show partial fraction steps to...
- Q Among all triangles with a perimeter of 2s=9 units, find thedimension of the triangle with the maximum area. (Hint: Heron'sFormula for the area of a triangle may be useful -A=Sqrt(s(s-a)(s-b)(s-c).
- Q Q: In the questionsbelow, nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, andIda) are in a room. Five of them stand in a row for a picture. Inhow...
- Q Two towns had a population of 12,000 in 1990. By 2000, thepopulation of town A had increased by ?13??% while the populationof town B had decreased by ?13??%. Assume these...
- Q Given that h(x) = x.sinx . Find the root of the function h(x) =1, where x is between [0, 2] using substitution method.
- Q Find the mass of the solid, moment with respect to yz plane, andthe center of mass if the solid region in the first octant isbounded by the coordinate planes and...
- Q 1-: ?(?) = ln (3 ? ?2? + 1) ? ?(0) =?2-Passing through the point x = 1 and ? = 2?Perpendicular to the straight line tangent to 3 +...
- Q Darla purchased a new car during a special sales promotion bythe manufacturer. She secured a loan from the manufacturer in theamount of $25,000 at a rate of 8%/year compounded monthly....
- Q Find the vertex and the x-intercepts (if any) of theparabola. (If an answer does not exist, enter DNE.)f(x) = 3x2 - 8x -3
- Q Consider the following planes.x + y + z = 7, x + 3y + 3z = 7(a) Find parametric equations for the line of intersection ofthe planes. (Use the parameter t.)(x(t),...
- Q Problem: Prove that every polynomial having real coefficients and odd degree has a real rootThis is a problem from a chapter 5.4 'applications of connectedness' in a book 'Principles of...
- Q 2-Find the critical numbers of the function. (Enter your answersas a comma-separated list. Use n to denote any arbitraryinteger values. If an answer does not exist, enter DNE.)f(?) = 6...
- Q Solve differential equation by using undetermined coefficientmethody^''+2y^'+y= 4 sin2x
- Q Suppose the first and second derivatives of f(x) are: f' (x) =4x(x^2 ? 9) f''(x) = 12(x^2 ? 3).(a) On what interval(s) is f(x) increasing and decreasing?(b) On what interval(s)...
- Q The business manager of a 90 unit apartment building is tryingto determine the rent to be charged. From past experience withsimilar buildings, when rent is set at $400, all the...
- Q Let S be the set of natural numbers which can be written as anon-empty string of ones followed by a non-empty string of zeroes.For example, 10, 111100 and 11100000 are...
- Q A rectangular storage container with an open top is to have avolume of 8 m3. The length of this base is twice the width.Material for the base costs $6 per...
- Q Q1)(a) Write implicit equations for two parallel planes, P1 containingthe line <?3,?5,3>+t<3,?4,?5> and P2 containing theline <?1,?2,1>+t<5,4,1>(b) Let n = <16,-28,32>The set of vectors w = <x,y,z> such that <3,?4,?5> x...
- Q The polynomial equation x^3?5x^2+11x?15=0 is known to have aninteger solution. Complete the following table listing in the firstcolumn the candidate integer solutions (there are eight) ofx^3?5x^2+11x?15=0 supplied by the Rational...
- Q Four numbers have a sum of 9900. The second exceeds the first by1/7 of the first. The third exceeds the sum of the first two by300. The fourth exceeds the...
- Q Solve differential equation by using undetermined coefficientmethody^''+9y=x^2e^x+6 , y(0)=1 and y^'(0)=1
- Q Find the second-order Taylor polynomial for f(x,y)=8y^2e^(?x^2)at (1,1).(Use symbolic notation and fractions where needed.)p(x,y)p(x,y) = .
- Q Laplace Transform : y ' - y = e^-3t cos3t , y(0) =3and, Show that, Differential Form ?dU = Tds - Pdv , dH=Tds-Vdp , dF= -sdT-Pdv , dG= -sdT+VdP
- Q solve the following initial value problem y''+4y'=g(t),y(0)=0,y'(0)=1 if g(t) is the function which is 1 on [0,1) and zeroelsewhere
- Q Find the general power series solution to the following ode:y"-4xy'+(4x2-2)y=0
- Q Give examples of sets of three vectors that are:a) Collinearb) Coplanarc) Not coplanar
- Q Explain them:Wireline perforation?Tubing conveyed perforating?
- Q The equation of parabola is x2 = 4ay . Find the length of thelatus rectum of the parabola and length of the parabolic arcintercepted by the latus rectum. (a) Length...
- Q z2 = xy-3x+9 Find the point closest to the origin onthe surface.
- Q Consider the following LOP P.Max. z = 212x1 ?320x2 +273x3 ?347x4 +295x5s.t. ?4x1 ?2x3 +8x5 ? ?222x1 +3x2 ?x4 = 31?5x2 +3x3 ?2x5 ? 27?7x1 ?8x3 +6x4 = ?38?9x3 ?2x4...
- Q 1. In 2003, gross sales at McDonald’s and Burger King totaled$60.9 billion. McDonald’s sales exceeded Burger King’s sales by$22.1 billion.(a) Write a system of equations whose solution gives theindividual sales...
- Q Sketch the graph of the given function. (x^2+x-2) / x^2Givea) x interceptb) y interceptc) Vertical asymtoped)Horizontal asymtopee) first derivativef)second derivativeg)critical numbersh)extrema max/mini) y coordinate of extermaj) possible point of infletionh)y...
- Q How do I solve this equation? (1/3(5)-1/4(-3))(-3/4(3))
- Q A small business owner contributes $3000 at the end of eachquarter to a retirement account that earns 8% compoundedquarterly.(a) How long will it be until the account is worth $150,000?(Round...
- Q Benoit believes that he didn’t invent the Mandelbrot set. Arecomplex numbers invented or discovered? Whichever position youtake, please research from reputable sources how complex numberscame about and make sure to...
- Q A utility-maximizing consumer who consumes quantity x and y oftwo goods has a quadratic utility function given byUx,y=x+y-0.05x2-0.05y2subject to2x+5y=128Where $128 is the consumer’s budget and the prices of the twogoods...
- Q Assuming that x>0, use the method of reduction of order tofind a second solution tox^2y''?3xy'+4y=0Given y1(x)=x^2
- Q Two circles intersect at A and B. P is any point on thecircumference of one of the circles. PA and PB are joined andproduced to meet the circumference of the...
- Q 4(a) Suppose a particle P is moving in the plane so that itscoordinates are given by P(x,y), where x = 4cos2t, y = 7sin2t.x2 y2(i) By finding a, b ?...
- Q Consider F and C below.F(x, y, z) =2xz + y2i + 2xy j +x2 + 15z2kC: x = t2, y = t +2, z = 4t ? 1, 0 ? t? 1(a) Find...
- Q Curvilinear integral of the function f (x, y) = x2 +y2 on a (3,0) centered and 3 radius circle.a)Calculate the curvilinear integral by expressing the curve inparametrically.b)Calculate the curvilinear integral...
- Q Find the point of intersection of the tangent lines to the curver(t) = 5 sin(?t), 2 sin(?t), 6 cos(?t) at the points where t = 0and t = 0.5. (x,...
- Q You are looking at a hot air balloon that sinks vertically at aspeed of 4.5 m / s.You stand a horizontal distance A from the point in the ground where...
- Q Let V be the set of all ordered triples of real numbers. For u =(u1, u2, u3) and v = (v1, v2, v3), we define the followingoperations of addition and...
- Q What level of output would generate a net income of $15,000 if aproduct sells for $24.99, has unit variable costs of $9.99, andtotal fixed costs of $55,005?
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