Basic Math question and answers for August 06, 2023
- Q (2x−y3−yex)dx=(2+ex+3xy2)dy, y(0)=2.Solve the initial value problem and verify exact.
- Q Find the Maclaurin series using the definition of a Maclaurinseries as well as the interval of convergence.a) f(x) = 1/((1-x/3)^2)b) f(x) = sin(2x)
- Q A primal maximization problem is given.Maximizef = 60x1 + 30x2subject to3x1+2x2≤150x1+x2≤70.(a) Form the dual minimization problem. (Usey1 and y2 as the variablesand g as the function.)Minimize g =    subject to  ≥60  ≥30y1, y2≥0.(b)...
- Q Check that each of the following functions solves thecorresponding differential equation, by computing both theleft-hand side and right-hand side of the differential equationA) y=tan(x) solves dy/dx =y^2 / sin^2 (x)B)...
- Q Find the extreme values of the function and where theyoccur.y= (x+1)/(x^2+3x+3)
- Q I have a logistic growth equation for a population where K = 820carrying capacity, and P(0) =550 initial population with a growthrate r of 0.25. Using the equation P= K/(1+A.e^-rt)...
- Q integrate e3tsint
- Q 3. State thoroughly and precisely Euclids fifthpostulate.According to Playfair, \"Given a line l and a point P not on l,there is exactly one line through P that is parallel to...
- Q Find the second-degree Taylor polynomial off(x)=ln(1+sinx) centered atx=0.
- Q Find all second order derivatives for r(x,y)=(xy)/2x+5y.(I need most detail at the rx/ry to rxx/ryy part, I can't getthe top correct)
- Q Find the volume ofD= {(x,y,z): x^2+y^2+z^2<_ 4, x _>0, y_>0
- Q Letf(x,y) = 3x^2 + 6xya) find the rate of change of f at the point P(3,2) in thedirection of u = [3,4]b) In what direction does f have the maximum...
- Q Determine whether the lines and are parallel, skew, orintersecting.L1:X=1+2t, Y=2+3t , z=3+4tL2: X=-1+6s, Y=3-s ,z=-5+2s
- Q An object is thrown vertically upward with an initial velocityof 10 m/sec from a height of 3 meters. In meters, find the highestpoint it reaches. (Round your answer to three...
- Q laplace y\"-y=x
- Q A company's total sales (in millions of $) t monthsfrom now is given by the function S(t)=2√t+101. Find the average rate of change in sales in four to sixmonths from...
- Q Use Newton’s Method to approximate the value of x wheref(x) = x3 +10x2 + 15x – 2 has a local maximum.Give the value accurate to 3 decimal places.
- Q An oil refinery is located 1 km north of the north bank of astraight river that is 2 km wide. A pipeline is to be constructedfrom the refinery to storage...
- Q Solve the given LDE using the method of undeterminedcoefficients. y'''-y'=4e^-x+3e^2x; y(0)=0, y'(0)=-1,y''(0)=2
- Q Find the four second partial derivatives. Observe that thesecond mixed partials are equal.z =25xey −8ye−x
- Q . [4 pts] The temperature of a 4 foot metal rod at a point xfeet from its left endpoint is given by T(x) = 1 + 3x 2 , 0...
- Q UniformitarianismChoose one:A. can be illustrated by scientists' seeing pillow lavaforming only underwater, then theorizing that pillow lava foundhigh in the mountains today did nevertheless form underwater.B. means that neither the...
- Q Find the equation of the osculating circle at the local minimumof f ( x ) = 3 x^3 + 8 x^2 -17/9 x − 6 Equation:
- Q A farmer, well versed in traditional optimization problems, hasdecided to buy a rectangular plot of 200 square meters of land onthe bank of a river, and surround it on three...
- Q Question 3. Determine if the following vector fields areconservative. If they are,find their potential functions.a.F=〈y,x+z,−y〉.b.F=〈y+z,x+z,x+y〉.
- Q (a) Write a general expression for yp(x) a particularsolution to the nonhomogeneousdifferential equation [Do not evaluate the coefficients]y′′ + 2y′ + 2y = e-x (4x + sin x) + 2...
- Q A long jumper leaves the ground with initial vertical velocityof 4.0 m.s-1 and an initial horizontal velocity of 3.0 m.s-1.How do you find the total flight time and horizontal distancetraveled?
- Q Â part 1)A farmer is constructing a rectangular pen with two additional fences across it, separating it in three equal parts as shown below. Find the maximum area that can be...
- Q  part 1)For the function f(x)=ln(x)/x^2 on the interval [1,4] find the absolute extrema, as well as all values of x where they occur.Absolute maximum of  at x=(If an extremum occurs at...
- Q 2. Use the Taylor series for ?(?) = 1 / ?2 centeredat x0 = 1 to find the seventh-degree polynomial of?(?)
- Q Which option?Find the area of the specified region.Shared by the cardioids r = 6(1 + sin θ) and r = 6(1 - sin θ)?18(3π - 8)9(5π + 8)18(3π + 8)1636Find...
- Q Evaluate the surface integralSF · dSfor the given vector field F and the orientedsurface S. In other words, find the flux ofF across S. For closed surfaces, use thepositive (outward)...
- Q Find the Fourier series expansion of f(x)=sin(x) on [-pi,pi].Show all work and reasoning.
- Q Verify that the differential equation:(3y cos(xy) - 2xy2 - e-x) dx + (3x cos(xy) -2x2y - e-y) dy = 0;is exact and then solve it.
- Q For the amusement of the guests, some hotels have elevators onthe outside of the building. One such hotel is 300 feet high. Youare standing by a window 100 feet above...
- Q In a class of 65 students, 25 speak Spanish, 32 are excellentcooks, and 50 love dogs. Each student is in at least one of thesecategories. There are 18 Spanish speakers...
- Q Suppose a bacterial population at any given point in time isgiven by N(t). Suppose that it grows at 1.8 percent per hour.Construct differential equation to capture the population growthdynamics and...
- Q Consider the following macroeconomic model: C(t) + I(t) = Y (t)I(t) = 0.8 dC(t) dt C(t) = 0.4Y (t) + 1 where C(t), I(t), Y (t)denote respectively the consumption, investment...
- Q Use the method of Undetermined Coefficients to find the solutionof the boundary value problem x^2 y '' + y' + 2y = 6x +2 y(1) = 0y(2) = 1
- Q Let f(x) = ln x for 1 ≤ x ≤ 3. Write down the formula forSimpson's Rule with n = 4 that approximates the integral of ln x on[1, 3].Without...
- Q A winter recreational rental company is fencing in a new storagearea. They have two options. They can set it up at the back cornerof the property and fence it in...
- Q For a normal random variable, with  μ = 19, and σ = 6, find the following probabilities.(a)Pr(X  ≤  32.2)(b)Pr(X  >  4.00)
- Q Use logarithmic differentiation to find the derivative of thefunction:y= sqrt(x)e^(x^3) (x^4 +1)^9 sin x
- Q Use the method of cylindrical shells to find the volumegenerated by rotating the region bounded bythe curves about the given axis.y = cos(πx/2), y = 0, 0 ≤ x ≤...
- Q Find dy/dx by implicit differentiation:cos(x+y)=y^3 sin x
- Q For the functiony = -x2/3-xa) Find the slope of tangent at x=4b) find y''
- Q Consider the following function.g(x, y)  = e− 4x2 + 5y2+ 24 x(a)Find the critical point of g.If the critical point is (a, b) then enter'a,b' (without the quotes) into the answerbox.(b)Using your critical point in...
- Q Consider the function below. (If an answer does not exist, enterDNE.)f(x) =12x4 − 4x2 + 2(a) Find the interval of increase. (Enter your answer usinginterval notation.)(−2,0)∪(2,∞)  Find the interval of decrease....
- Q For the given cost function ,C(x)=3136+787x+x^2a) The average cost at the production level 49 isb) The marginal cost at the production level 49 isc) The production level that will minimize...
- Q A 500-liter tank initially contains 200 liters of a liquid in which 150 g of salt have been dissolved. Brine that has 5 g of salt per liter enters the...
- Q Find the equations of the tangent lines to the circle x^2 + y^2= 9 which pass through the point (−7, 2).(Ans.: Using decimal approximations, the lines are approximatelyy = −0.847493x...
- Q (a) Does the series X∞ k=1 (−1)^k+1 /k + √ k converge? (b) Essaypart. Which tests can be applied to determine the convergence ordivergence of the above series. For each...
- Q Consider the series X∞ k=3 √ k/ (k − 1)^3/2 . (a) Determinewhether or not the series converges or diverges. Show all yourwork! (b) Essay part. Which tests can be...
- Q 1) Convert the point (x,y,z)=(−2,−3,−1) to cylindricalcoordinates. Give answers as positive values, either asexpressions, or decimals to one decimal place.(r,θ,z) =2) Convert the point (x,y,z)= (3,−2,−3) to sphericalcoordinates. Give answers...
- Q Let F(x, y, z)=2xy^2 +2yz^2 +2x^2z.(a) Find the directional derivative of F at the point (−2, 1,−1) in the direction parallel to the line x = 3 + 4t, y...
- Q Which of the following are true?(1) The sum of two invertible matrices is invertible(2) The determinant of the sum is the sum of thedeterminants(3) The determinant of the inverse is...
- Q Consider the function: f(x) = (x-1)4(x+1)a) Differentiate and simplify completelyb) Find all the Critical Numbers (if any). If there are no CNs,write “none.†Explain why.c) Construct the correct sign diagram...
- Q Find the absolute maximum and absolute minimum values off on the given interval.f(x) = x3 − 6x2 + 9x +4,    [−1, 8]
- Q We are tasked with constructing a rectangular box with a volumeof 1313 cubic feet. The material for the top costs 1010 dollars persquare foot, the material for the 4 sides...
- Q A tank contains 365 gallons of water and 50 oz ofsalt. Water containing a salt concentration of1/6(1 + 1/4 sin t)oz/gal flows into the tank at a rate of 8...
- Q If the infinite curve y = e−3x, x ≥ 0, is rotated about thex-axis, find the area of the resulting surface. (answer needs to bein fraction form if possible)
- Q Find the absolute max/min values of f(x) = x/x2+1 onthe interval [-2,2].
- Q Your company has developed a new videoconference gaming platformthat allows players to see and hear their friends while they playtogether remotely. The sales can be modeled by q(p)=350000-2430p^2where p is...
- Q Use the method of eigenvalues and eigenvectors to find thegeneral solution to the following system of differentialequations.x′(t) = 2x(t) + 2y(t) − z(t)y′(t) = 0 + 3y(t) + z(t)z′(t) =...
- Q Find the derivativeY=ln(3-2x)
- Q Consider a rectangle in the first quadrant with two sides alongthe axes (so that one corner is at (0, 0)). Find the dimensions ofthe largest such rectangle that is inscribed...
- Q Consider the series X∞ k=2 2k/ (k − 1)! . (a) Determine whetheror not the series converges or diverges. Show all your work! (b)Essay part. Which tests can be applied...
- Q Find the maximum and minimum of the function f(x, y, z) =(x^2)(y^2)z in the region D = {(x, y, z)|x^2 + 2y^2 + 3z^2 ≤1}.
- Q Determine whether the geometric series converges or diverges. Ifit converges, find its sum.-1/9 + 1/27 - 1/81 + 1/243 - ...
- Q Uselaplace transform to solve IVP2yâ€+3y’+y=8e^(-2t) , y(0)=-4 , y’(0)=2
- Q 1) Find f(x) by solving the initial value problem. f'(x) = e x − 2x; f (0) = 22) A rectangular box is to have a square base and avolume...
- Q a) A cylindrical length of wire has a radius of 4 mm and alength of 10 cm. If the length is growing at a rate of 2 cm/sec andthe radius...
- Q Use a graph or level curves or both to find the local maximumand minimum values and saddle points of the function. Then usecalculus to find these values precisely. (Enter your...
- Q Calc 1Use the 11-step process to graph the function f(x)=(6x^2)/(2x^2-8)?
- Q Find the approximate area under the curve by dividing theintervals into (n) subintervals and then adding up the areas of theinscribed rectangles. The height of each rectangle may be found...
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