Basic Math question and answers for August 03, 2023
- Q Ornithologists have determined that some species of birds tendto avoid flights over large bodies of water during daylight hours.It is believed that more energy is required to fly over water...
- Q I am desperate to know How to find or guess Particularsolution(Yp) of Non-Homogeneous higher order differentialequations,Please provide me with explanations.There is Key Identities method also to find Yp. But I...
- Q Set up the system of equations that are needed to be solvedusing Lagrange multipliers in order to find the dimensions of therectangular box with an open-top, having volume 4000 m^3...
- Q Find the mass M of the solid in the shape of the region4<=x^2+y^2+z^2<=49, sqrt[3(x^2+y^2)] <= z if the densityat (x,y,z) is sqrt(x^2+y^2+z^2).
- Q 1) Find the volume of the parallelopiped with adjacent edges PQ,PR, PS where P ( -2,-3,-3) , Q (0,0,0) , R (-3,-4,-4) and S (4,-5,-1)2) Find the area of the...
- Q The electrical resistance of a wire varies directly as itslength and inversely as the square of its diameter. A wire with alength of 200 inches and a diameter of one-half...
- Q The automobile assembly plant you manage has a Cobb-Douglasproduction function given byP =30x0.5y0.5where P is the number of automobiles it produces peryear, x is the number of employees, and y...
- Q Find the absolute maximum and minimum, if either exists, for thefunction on the indicated interval.f(x)=x^3-6x^2+9x+5(A) [-3,6] (B)[-3,3] (C)[2,6](A) Find the absolute maximum. Select the correct choice below​and, if​ necessary, fill...
- Q find the differential equation of dy/dx = y+y^3
- Q A manufacturing plant produces the cardboard cut outs that willbe used to wrap ice cream cones. Circles with a radius of 6 inchesare punched out of a sheet of cardboard....
- Q find f'(x)1. f(x)=3sinx-secx+5_______2. f(x)=e^xcot(3x)_______3. f(x)= cos^5(3x-1)_______
- Q The given curve is rotated about the y-axis. Find the area ofthe resulting surfacey=1/3x^3/2, 0 < x < 12
- Q The amount of skin covering a person's body (in square feet)depends on the person's height and weight. One model for estimatingthis skin surface area isA(w, h) =0.6416w0.425h0.725square feetfor a person...
- Q Find the derivative of the function.y = [x + (x + sin2(x))6]5
- Q Determine whether the following two lines are parallel,intersecting, or skew. If they are skew, find the distance betweenthem L1 : x = 3 + 2t, y = 4 − 3t,...
- Q Determine whether the following two lines are parallel,intersecting, or skew. If they are skew, find the distance betweenthemL1 : x = 3 + 2t, y = 4 − 3t, z...
- Q 1. Determine whether Rolle's Theorem can be applied tof on the closed interval[a, b].(Select all that apply.)f(x)=x2− 4x− 5x + 5,    [−1,5]Yes,Rolle's Theorem can be applied.No, because f isnot continuous on...
- Q Find the area between the curve and the x axis from [-1,5] .f(x)=5x2-3x+4 .Use the Fundamental Theorem ofCalculus.Find the Area using Right Hand Riemann Sums with n=10Explain the difference between...
- Q Ifsec(α) = −135whereπ2< α < πandtan(β) =247whereπ < β <3π2, find the exact values of the following.(a)    csc(α − β)(b)    sec(α + β)(c)    cot(α + β)
- Q a) Sketch the graph of the solution to the initial valueproblem.dy/dx = sin x , y(0) = 1over the interval 0 ≤ x ≤ 4πb) By finding a suitable antiderivative,...
- Q Use the First Derivative Test to find the relative extrema ofthe function, if they exist.16. f(x) = x^4 - 18x^2 + 8
- Q Find a power series that represents the function and find theinterval of convergence:a) g(x) = 1 / (3+x^2)^2b) h(x) = ln(5 + x^2)
- Q A university is trying to determine what price to charge fortickets to football games. At a price of ​$21 per​ ticket,attendance averages 40,000 people per game. Every decrease of $3adds...
- Q Find the equation of the hyperbola with:(a) Foci (1, −3) and (1, 5) and one vertex (1, −1).(b) Vertices (2, −1) and (2, 3), and asymptote x = 2y.Consider the...
- Q 1. Use the guidelines of this section to sketch the curve. y =x(x − 4)^3 . Provide answer to parts below–you may need anotherpiece of paper. (Note: Domain is all...
- Q 1)For the function f(x)=6x^2−2x, evaluate and simplify.f(x+h)−f(x)/h2)Evaluate the limit: limx→−6 if x^2+5x−6/x+63)A bacteria culture starts with 820820 bacteria and grows at arate proportional to its size. After 22 hours there...
- Q Find equations of both the tangent lines to the ellipse x2 + 9y2= 81 that pass through the point (27, 3)
- Q Given two planes 3x − 2y + z = 1 and 2x + y − 3z = 3. (a). Find the equation for the line that is the intersection of...
- Q Consider the following functions. f(x) = x − 3, g(x) = |x +3|Find (f ∘ g)(x).Find the domain of (f ∘ g)(x). (Enter your answer using intervalnotation.)Find (g ∘ f)(x).Find...
- Q Find a unit vector normal to the level curve f(x,y) = -4x^2-2y^2 + 5x + y  at the point (1,-2)
- Q f(x), find the derivative (f^-1)'(c) at the givenpoint c, first finding a=f^-1(c)1. f(x)=5x+9x^21. c=-14a=?(f^-1)'(c)= ?
- Q Let f(x)=−(3x^3+8)(a) List the critical point(s) of f=(b) f′(x)>0f′(x)>0 for x∈=(c) f′(x)<0f′(x)<0 for x∈=Note: the answers to the above questions can bea value, a list of values, an interval, a...
- Q Find the center of mass of the solid bounded by z = 4 - x^2 -y^2 and above the square with vertices (1, 1), (1, -1), (-1, -1),and (-1, 1)if...
- Q Gravel is being dumped from a conveyor belt at a rate of 40cubic feet per minute. It forms a pile in the shape of a rightcircular cone whose base diameter...
- Q 1.Consider the function: f(x, y) = 2020 + y3-3xy +x3.a) Find fx(x, y), and fye(x, y).b) Find all critical points of f(x, y).c) Classify the critical points of f(x, y)...
- Q Find the degree 4 Taylor polynomial of f (x) = sin(2x) centeredat π/6
- Q . If you had $5,000 to invest for 4 years with the goal ofgreatest return on your investment, would you rather invest in anaccount paying (a) 7.2% compounded quarterly, (b)...
- Q Solve the equation for the indicated variable.1/b +1/3 =1/sfor s
- Q Question threeDescribe the term simulationExplain the advantages and disadvantages of simulationtechniquesSolve the following transportation problem using any suitablemethod. The cell entries are unit costs                 D1      D2       D3      D4D5        available        O168354741518O25788913817O3916075456019O452532478213O551188213715                      Required                    16       18          20       14        14
- Q Use Lagrange Multipliers to determine maximum and minimum.f(x,y,z)=(3x^2)+(3y^2)+(3z^2) subject to xyz=2
- Q For each of the following statements, determine whether thestatement is true or false. If you say the statement is true,explain why and if you say it is false, give an...
- Q Find the global maximum and global minimum of the function f(x,y) = y^2 − 2xy + 4y on the square 1 ≤ x ≤ 3, 0 ≤ y ≤ 2.
- Q 1 Find the volume of the solid obtained by rotating the regionbounded by y=sin(5x^2), y=0, x=0, and x=√π/5 about the y-axis.2 Find the volume of the solid obtained by rotating...
- Q Let U be a subspace of V . Prove that dim U ⊥ = dim V −dimU.
- Q Marginal RevenueThe management of Ditton Industries has determined that thedaily marginal revenue function associated with selling xunits of their deluxe toaster ovens is given by the following,where R'(x) is measured...
- Q 2.Use Σ-notation to write down an example of a series for which theratio test is inconclusive but the integral test is conclusive. Youdon’t need to show how you got your...
- Q Solve the given initial-value problem.y'' + 4y =−1,    y(π/8)=3/4,y'(π/8) = 2,
- Q 2) A pond holding 1,230,000 gallons has been contaminated with150,000 pounds of salt. Pure water is pumped into the pond at arate of 120 thousand gallons per hour and contaminated...
- Q Find f.f ''(x) = 4 + 6x + 24x2,    f(0)= 4,    f (1) = 12
- Q All parts of this problem refer to the function below.y=(2+7x)^2/xa) Use logarithmic differentiation to finddy/dxdy/dx=b) Find the slope of the tangent line at x=1.Slope =c) Find the equation of the...
- Q y'=tan(x)^2(csc(y)^3)
- Q A particle moves along a line with velocity function ?(?) = ?^2− ?, where v is measured in meters per second. a. Find distancetraveled by the particle in time interval...
- Q A body weighing 9.25 grams force hangs from a spring stretching 1.4 centimeters. Initially the body part of rest 2.6 centimeters below its position balance. The medium where the body...
- Q Find the power series representation of the following functionsand find the corresponding radius of convergence.1. x2(ln(5+ x))2. 4x/(1 + x)3
- Q A particle is moving with the given data. Find the position ofthe particle. v(t) = sin(t) − cos(t), s(0) = 4
- Q Find the volume of the solid in R^3 above the plane z = 0 andbelow the surface z = 4 − x^2 − y^2.
- Q 18. A box is to be made out of a 10 cm by 16 cm piece ofcardboard. Squares of side length ? cm will be cut out of eachcorner, and...
- Q 1) Find the exact absolute max and exact min forf(x)=x^3-3x^2-6x+4 on the closed interval [0,3]2) Let f be continuously differentiable function on the Realswith the following characteristics:- f(x) is increasing...
- Q Find the Laplace transforms:F(s)=L{f(t)} of the functionf(t)=(8−t)(u(t−2)−u(t−5)),for s≠0.F(s)=L{f(t)}=
- Q Consider the initial value problemy′′−9y′+20y=0      y(0)=2, y′(0)=4.a. Take the Laplace transform of both sides of the givendifferential equation to create the corresponding algebraicequation. Denote the Laplace transform of y(t) byY(s). Do...
- Q Consider the following functions.g(x)=x3 − 10xh(x)=4x2+ 3xf(x)=(x3− 10x)(4x2 +3x)Find the derivative of each function.g '(x)=h '(x)=f '(x)=
- Q  The ends A and B of a rod I c.m. long have theirtemperatures kept at 30.C and 8CoC, until steady state conditionsprevail. The temperature of the end B is suddenly reduced...
- Q Find f by solving the initial-value problem. (Rememberto use absolute values where appropriate.)f '(x) = (x+9)/x   ; f(1) = 2f(x)=
- Q solve the given initial value problem using the method ofLaplace transforms.Y'' + Y = U(t-4pi) y(0) =1 y'(0) = 0
- Q The population of a country was 5.192 million in 1990. Theapproximate growth rate of the​ country's population is given by f(t) = 0.08083944 e ^ 0.01557t where t = 0corresponds...
- Q Given the ?(?) = 30? .001? and ?(?) = 80? −.001? find: d) Theequilibrium point. e) Determine the consumer’s surplus. Show theintegral used. f) Determine the producer’s surplus. Show theintegral...
- Q Set up the augmented matrix that describes the situation, andsolve for the desired solution.A bag of mixed nuts contains cashews, pistachios, and almonds.Originally there were 850 nuts in the bag....
- Q Use the Method of Variation of Parameters to determine thegeneral solution of the differential equation y'''-y'=3t
- Q Solve by using elimination. Find the center and the radius ofthe circle whose graph passes through points (2,5) (-4,-3) and(3,4). Use the given equation x^2 + y^2 + ax +...
- Q Determine the intervals on which the graph of?=?(?) is concave up or concave down,and find the points of inflection.?(?) = (?^(2) − 17)?^?Provide intervals in the form (∗,∗).Use the symbol...
- Q If the total cost function for a product is C(x) = 8(x + 5)^3dollars, where x represents the number of hundreds of unitsproduced, producing how many units will minimize average...
- Q Determine the intervals on which the graph of ? =?(?) is concave up or concave down, and find the?-values at which the points of inflection occur.?(?)=? (? − 9 √x),?...
- Q Find the velocity, acceleration, and speed of a particle withthe given position function.r(t) =9 cos(t), 8 sin(t)v(t)=a(t)=|v(t)|=Sketch the path of the particle and draw the velocity andacceleration vectors fort =Ï€3.
- Q A600 ft.^2 rectangular patch is to be enclosed by a fence anddivided into two equal parts by another fence parallel to one ofthe sides. what dimensions for the outer rectangle...
- Q Students in a seventh-grade class were given an exam. During thenext 2 years, the same students were retested several times. Theaverage score g can be approximated by the modelg(t) =...
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