Basic Math question and answers for July 11, 2023
- Q Find a particular solution to the following differentialequation using the method of variation of parameters.x2y?? ? 11xy? + 20y?=? x2?ln?x
- Q LetS ? R3 be the sphere of radius 1 centered on the origin. a) Provethat there is at least one point of S at which the value of the x...
- Q Factor the following:a) f(x)=x^5+5x^4-21x^3-137x^2-88x+240, knowing that f(5)=0 andf(-3)=0.b) f(x)=x^3+8x^2+5x-50c)f(x)=-x^4-4x^3+19x^2+46x-120, knowing that (x+5) and (x-2) arefactors.
- Q Details of main methods (up to 3) that currently exist forinterfacing HIS and RIS with PACS
- Q Letthe following ODE be given. Let x be a real number.xy"+(1-x)y' = (k-1/2)yGive an explict solution for k=-2.5
- Q Consider the function and the value of a.f(x) =?2x ? 1, a = 9. (a) Use mtan = lim h?0f(a + h) ? f(a)hto find the slope of the tangent...
- Q Evaluate the integral. (Use C for the constant ofintegration.)(x^2-1)/(sqrt(25+x^2)*dxEvaluate the integral. (Use C for the constant ofintegration.)dx/sqrt(9x^2-16)^3Evaluate the integral. (Use C for the constant ofintegration.)3/(x(x+2)(3x-1))*dx
- Q 63=1/2(2x+10)(x+3)
- Q 1) Evaluate the integral from 0 to 1 (e^(2x) (x^2 + 4) dx)(a) What is the first step of your ‘new’ integral?(b) What is the final antiderivative step before evaluating?(c)...
- Q Instructions: For each solid described, set up, BUT DONOT EVALUATE, a single definite integral that represents the exactvolume of the solid. You must give explicit functions as yourintegrands, and specify...
- Q A bicycle shop sells two styles of a road bike, 10-speed and14-speed. During the month of September, the management expects tosell exactly 45 road bikes. The monthly profit is given...
- Q ?" + 3?? + 2? = ????, ?(0) = 0, ??(0) = 21) Please solve using an annihilator2) Please solve using the Method of Variation of ParametersThank you.
- Q Find the directional derivative of f at the given pointin the direction indicated by the angle ?.f(x, y) =ycos(xy), (0,1), ? = ?/4Duf(0,1) =
- Q A mass of 1.5 kg stretches a spring 0.05 mm. The mass is in amedium that exerts a viscous resistance of 240 NNwhen the mass hasa velocity of 6 msms....
- Q Questions Determine whether or not the vector field isconservative. If it is conservative, find a vector f f such that .F?=?f. ? F ( x , y , z )...
- Q Given the curve C in parametric form :C : x = 2cos t , y = 2sin t , z = 2t ; 0? t ? 2pia) the velocity v(t)b)...
- Q Given that v? 1=[?3,1] and v? 2=[2,?1] are eigenvectors of thematrix-22-48818determine the corresponding eigenvalues. ?1= . ?2= .
- Q Find all distinct roots (real or complex) ofz2+(?6+i)z+(25+15i). Enter the roots as a comma-separated list ofvalues of the form a+bi. Use the square root symbol '?' whereneeded to give an...
- Q Solve the following initial-value problem:(ye2xy + x)dx ? (y2 ? xe2xy)dy= 0, y(2) = 0
- Q Explain in your own words how you approach solvingany quadratic equation by factoring. What are thekey things you keep in mind as you’re working towards finding theanswer(s)? Your explanation must...
- Q Find all distinct (real or complex) eigenvalues of A.Then find the basic eigenvectors of A corresponding toeach eigenvalue.For each eigenvalue, specify the number of basic eigenvectorscorresponding to that eigenvalue, then...
- Q Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Ruleto approximate the given integral with the specified value ofn. (Round your answers to six decimal places.)?/2032 +cos(x)dx, n= 4(a) the Trapezoidal...
- Q Consider the function f(x)= tan 1/xUse the following table to guess the limit f(x) as x goes to0+xf(x) = tan 1/x1/?1/2?1/3?1/4?1/5?4/?4/5?4/9?4/13?4/17?
- Q Revenue, cost, and profit. The price–demandequation and the cost function for the production of table saws aregiven, respectively, byx=6,000?30pandC(x)=72,000+60xx=6,000?30pandC(x)=72,000+60xwhere x is the number of saws that can be sold at...
- Q Find the equation of the osculating circle at the local minimumof3x^3 -7x^2 +(11/3)x+4
- Q if you a square that is 3' 5" in width, length and height. Howmany five point stars (2" in size) filled with air will fit intothe square? Please show all...
- Q Question 5Find all solutions of this system.4x + 2y + 3z = 0 3x y + 2z = 0 x + 2y ? z = 0Compare the value of the...
- Q Find the velocity, acceleration, and speed of a particle withthe given position function. r(t) = 2 cos(t), 2t, 2 sin(t)
- Q For each statement, determine whether the statement is true or false. Give a sentence justifying your answer.a. If tan(t)=0, then cos(t)=1 .b. The function f(x)=sin(x)cos(x) has period 2?.c. The graph...
- Q Find the Laplace transform of the followingfunctions.(a)?f?(t) ?=?{60 ?<? t ??? 48t ??? 4(b)?f?(t) ?=?{t20 ??? t ?<? 30t ??? 3(c)?f?(t) ?=?{00 ??? t ?<? ?/4cos[7(t ? ?/4)]t ??? ?/4
- Q A linear system of equations Ax=b is known, where A is a matrixof m by n size, and the column vectors of A are linearlyindependent of each other. Please answer...
- Q 1) Find the maximum and minimum values of the functiony = 13x3 +13x2 ? 13x on theinterval [?2, 2].2) Find the minimum and maximum values of the function f(x) =4?sin(x)?cos(x)...
- Q For each of the following integrals find an appropriatetrigonometric substitution of the form x=f(t)x=f(t) to simplify theintegral.the inteagrala) ?x(3x^2+30x+73)^(1/2)dxb)?x/(?25?3x^2+18x)^(1/2)dx
- Q What other application's can we think of related to this topicleasing.
- Q 1 = Derivative of a Constant; 2 = Power Rule; 3 = Product Rule;4 = Quotient Rule; 5 = Derivative of Exponential Function; 6 =Derivative of Logarithmic Function; 7 =...
- Q Consider the 2nd order NHDE belowd2xdt2+k2x=F0e?t With the following initial conditionsx0=0 andx'0=0. (Assumek??)Find the complimentary solutionyc(t)Find the particular solutionyp(t)Find the general solution for the IVP.
- Q Joanne sells? silk-screened T-shirts at community festivals andcraft fairs. Her marginal cost to produce one? T-shirt is $ 2.50 .Her total cost to produce 60 ?T-shirts is??$ 220 comma and...
- Q Q-1)1 to 5 in bag A; 1 to 11 in bag B there are numbered cards.A random from the randomly selected bag card is selected. Sincethere is an odd number...
- Q (1 point) The count in a bacteria culture was 600 after 10minutes and 11613 after 20 minutes. Assume the growth can bemodelled exponentially by a function of the formQ(t)=AertQ(t)=Aert, where...
- Q Aluminum, iron and magnesium are used to manufacture certainmetal parts.The quantity of parts produced from x tons of aluminumy tons of iron and z tons of magnesium is Q (x,...
- Q Consider the helixr(t)=(cos(2t),sin(2t),?3t)r(t)=(cos(2t),sin(2t),?3t).Compute, at t=?/6A. The unit tangent vector T=T= ( , , )B. The unit normal vector N=N= ( , , )C. The unit binormal vector B=B= ( ,...
- Q Find the point on the plane curve xy = 1, x > 0 where thecurvature takes its maximal value.
- Q How do we interpret a confidence interval?
- Q Prove that if a diagonal of a parallelogram bisects the angleswhose vertices it joins, the parallelogram is a rhombus
- Q 1. FERTILIZER NUTRIENTS (Please Use Excel and show screenshots:) )A produce farmer is purchasing fertilizer containing threenutrients: nitrogen, phosphorus, and potassium. The farmer’sminimum weekly requirements are 240 units of nitrogen,...
- Q The production costs, in $, per week of producing x widgets isgiven by C(x)=65000+4x+?0.2x?^2-?0.00002x?^3 and the demandfunction for the widgets is given by p=500-0.5x . Find the MarginalRevenue equation. Find...
- Q Find the distance between the skew lines given by thefollowing parametric equations:L1: x=2t y=4t z=6tL2: x=1-s y=4+s z=-1+s
- Q Let f (x, y) = -x3 - y3 + 9xy - 26. Checkthat (0,0) and (3,3) are stationary points of f and classify thesepoints as maximum, minimum or saddle point....
- Q A farmer wants to fence in a rectangular plot of land adjacentto the north wall of his barn. No fencing is needed along the barn,and the fencing along the west...
- Q Find the equation (in terms of x and y) of the tangent line tothe curve r=2sin5? at ?=?/3.
- Q The temperature in Gavin's oven is a sinusoidal function oftime. Gavin sets his oven so that it has a maximum temperature of320°F and a minimum temperature of 260°. Once the...
- Q Given f(x) = 1 x 2 ? 1 , f 0 (x) = ?2x (x 2 ? 1)2 and f 00(x) =2(3x 2 + 1) (x 2 ? 1)3 ....
- Q 1. Find the equation of the line with slope of m = ?" # and through the point (8,?1).Write your final answer in slope -intercept form. ______________________________2. Find the equation...
- Q Find a basis for the subspace of Pn defined by V={p an elementof Pn, such that p(1)=0}. What is the dimension of V?
- Q in the triangle PQR, the point S divides the line PQ in theratio 1:3, and T divides the line RQ in the ratio 3:2.PR =a and PQ =bexpress the following...
- Q For each of the following mathematical functions (orequations):(i) Take the first derivative dy/dx,(ii) Set dy/dx = 0, then solve for x .(iii) Take the second derivative d(dy/dx)/dx. Is the secondderivative...
- Q Find the equation (in terms of x and y) of the tangent line tothe curve r=5sin5? at ?=?/3
- Q Show that ? = {1 ? ?, 2 + ?2, 1 + ? ? ?2} forms a basis for?2(?)
- Q We consider a rectangular parallelepiped-shaped box based on arectangle and open from above. The height of the box is 4 dm. Thebase of the box has a fixed perimeter 20...
- Q Find the Taylor series or polynomial generated by the followingfunctionsa. )f(x) ? x centred at x=4 , of order 3b.) f(x) cosh x= e^x+e^-x/(2), centred at x=0c.) f(x) = x...
- Q Find the local maximum and minimum values and saddle point(s) ofthe function.f(x,y)=5-10x+12y-5x^2-4y^3
- Q The National Bank, like most other large banks, found that usingautomatic teller machines (ATMs) reduces the cost of routine banktransactions. National installed an ATM in the corporate offices ofthe Fun...
- Q 9) R is the region bounded by the curves ? = x^3 , y=2x+4 , Andthe y-axis.a) Find the area of the region.b) Set up the integral you would use...
- Q Find the Taylor series for f (x) = 2/(1+3x) at x = a where a =0
- Q A roofer requires 10 h to shingle a roof. After the roofer andan apprentice work on a roof for 5 h, the roofer moves on toanother job. The apprentice requires...
- Q A cereal box, in the shape of a rectangular prism and with aclosed top, is to beconstructed so that the base is twice as long as it is wide. Itsvolume...
- Q find all local and global minimus and maximusf(x)=x/sqrt(x^(2+2) +1)
- Q Consider the linear transformation T : P2 ? P2 given by T(p(x))= p(0) + p(1) + p 0 (x) + 3x 2p 00(x). Let B be the basis {1, x,x2}...
- Q Solve each inequality and graph the solution. Thank you!1. -3/8(x) - 20 +2x > 62. 2/3(x) + 14 - 3x > -73. 0.5x - 4 - 2x ? 24. 4x...
- Q The motion of a particle in space is described by the vectorequation?r(t) = ?sin t, cos t, t?Identify the velocity and acceleration of the particle at(0,1,0) How far does the...
- Q Calculate the arc length of the indicated portion of the curver(t).r(t) = i + (9t sint)j + (9t cos t)k ; -3 ? t ?7
- Q Suppose products A and B are made fromplastic, steel, and glass, with the number of units of each rawmaterial required for each product given by the table below.?PlasticSteelGlassProduct A310.50Product B50.502?Because...
- Q 12a Find an equation of the tangent plane to the surface ? = 2?2 + ? 2 ? 5?, ?? (1, 2, ?4).12b If ? = ? 2 ? ??...
- Q Determine the amplitude, the period and the phase shift of thefunction1. y = -3 cos ( 4 x - PIE ) + 22. y = 2 + 3 cos (...
- Q Westside Energy charges its electric customers a base rate of$4.00 per month, plus 12¢ per kilowatt-hour (kWh) for the first 300kWh used and 3¢ per kWh for all usage over...
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