Basic Math question and answers for August 08, 2023
- Q Evaluate the surface integral  SF · 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 Create a mathematical proof to prove the following:Given an integer n, and a list of integers such that thenumbers in the list sum up to n. Prove that the product...
- Q Nutt’s Nut Company has 500 pounds of peanuts, 100 pounds ofpecans, and 50 pounds of cashews on hand. they package three typesof 5-pound cans of nuts: Can I contains 3...
- Q Using method of variation of parameters, solve the differentialequation: y''+y'=e^(2x)Find the general solution, and particular solution using thismethod.
- Q Curve sketching: Choose two of the functions to sketch a graph.you should include the following parts for each.a). domain b). x and y intercepts c). any asymptotes d).intervals of increase/decrease...
- Q Two large containers A and B of the same size are filled withdifferent fluids. The fluids in containers A and B are maintainedat 0° C and 100° C, respectively. A...
- Q A person starts walking from home and walks:3 miles East5 miles Southeast6 miles South2 miles Southwest3 miles EastA. Find the total displacement vector for this walk: _ i+_ jB. If...
- Q We have a parametric curve x = - 6t + t^3 + 1, y = -2t − t^2a) Sketch a graph of the curve (use technology to help)b) Find the...
- Q Find the maximum profit given by the revenue and cost functions​below, where x is in thousands of units and​ R(x) and​ C(x) are inthousands of dollars.R(x)= 115x-x^2c(x)=1/3x^3-6x^2+91x+38A. 682 thousand dollarsB....
- Q Suppose gg is a function which has continuous derivatives, andthat g(1)=1,g′(1)=5, g″(1)=4, g‴(1)=2(a) What is the Taylor polynomial of degree 2for g near 1?P2(x)=(b) What is the Taylor polynomial of...
- Q Let r(t) = 2t ,4t2 ,2t be a position function for someobject.(a) (2 pts) Find the position of the object at t = 1. (b) (6pts) Find the velocity of...
- Q A firm has monthly average costs, in dollars, given byC =42,000x+ 200 + xwhere x is the number of units produced per month. Thefirm can sell its product in a...
- Q Please answer all 3 questions and explain . thank you.(1) Determine the length of the curve y= 3 + 2x^(3/2) for 0 ≤ x≤ 2. You can use your calculator...
- Q F(x)=g(x)*h(x) = 4x3-2x2+3x-1 solution
- Q for each of the following equations, state all adjectives that holdfor each equation from the list ( first order, second order, linearetc)1. y' +2xy= x^32. y'' + y= y'x +...
- Q Use a triple integral to find the volume of the solid enclosedby the paraboloids y= x2+z2 and y=x2+z2
- Q If all proper nontrivial subgroups of a nontrivial group areisomorphic to each other, must G be cyclic?
- Q The demand for nurses in the US between 2000 and 2015 isestimated to be D(t) = 0.7t 2 + 0.265t + 2000 thousand, where 0 ≤ t≤ 15, and t...
- Q 1. Find absolute max and min of    f(x,y)=x^2- xy + y^2 +1 on the closed triangular plate in the firstquadrant x=0, y=4, y=x2. Given position of a particle by π...
- Q 1. a) Based on recent statistics, Green Way Airlinesexpects 4.2% of its customers will be “no showsâ€. If the airlinesold 260 seats for a flight, how many people would the...
- Q A patient's pulse measures 150 bpm, 80 bpm, then 100 bpm. Todetermine an accurate measurement of pulse, the doctor wants toknow what value minimizes the expression(x − 150)2 + (x...
- Q (i) Find the cylinder inscribed in a sphere with radius one withthe largest surface area.
- Q The total weekly revenue earned at Royal Ruby Retailers is givenbyR(p) =−7/3p2 + 98pwhere p is the price (in dollars) RRR charges per ruby.Use this function to determine the following.(a)...
- Q Using calculus and the SDT (then FDT if necessary), find allglobal and local maximumand minimums given the function ?(?) = ?^3 + ?^2 − ? + 1 where ?∈ [−2,...
- Q A rectangle storage container with an open top should have avolume of 33 meters^3. The length of its base is 2 timesthe width. Material costs for the base are $10/meter^2...
- Q For x = Ïsinφcosθ; y = Ïsinφsinθ; z = Ïcosφ:a/ Express ∂^2/∂y^2 with Ï, φ, θ, and their partials.b/ Express ∂^2/∂z^2 with Ï, φ, θ, and their partials.c/ Express the...
- Q The indicated function y1(x) is a solution of the givendifferential equation. Use reduction of order or formula (5) inSection 4.2, y2 = y1(x) e−∫P(x) dx y 2 1 (x) dx...
- Q Let  f(x) = x^4 -4x^3 - 18 x^2  + 77  a)   a) Find all critical values of thefunction.       [10]  b)   b) Find all intervals of increase anddecrease.      [10]      c) Find all relative extrema.Use the second derivative test.         Label each as...
- Q what is the absolute maximum of the function f(x)=(e^x)/x,x>0?
- Q Solve the following Differential Equationa. ?′ = sec ? cot ?b. ?′ = ??-y(cos(?2)) ; ?(0) = 0c. ?′ = ?(2 − ?)d. ?2 + dy/dx = (y2 )/(1+x2) ;?(0)...
- Q equation for part A ?(?) = −0.48?^2 + 7.2? + 63equation for part B ?(?) = −?^2 + 8? + 84the Georgia marching band discovers that the amount of time...
- Q Let Q1, Q2, Q3, Q4 be constants so that R (2x + 3) sin 4x dx =(Q1x + Q2) sin 4x + (Q3x+Q4) cos 4x+C, where C is a constant...
- Q A vat of volume 1100 gallons initially contains 4 lbs of salt.For t > 0 a salt brine of concentration 0.15 lbs per gallon ispumped into the vat at the...
- Q (Minimizing Costs) For its beef stew, Betty Moore Company usesaluminum containers that have the form of right circular cylinders(a cylinder whose base is a circle and whose elements areperpendicular to...
- Q A record turntable is rotating at 33 rev/min. A watermelon seedis on the turntable 6.4 cm from the axis of rotation.(a) Calculate the acceleration of the seed,assuming that it does...
- Q Find a function y = y(x) that has a y-intercept at (0, 4), ahorizontal tangent line at the y-intercept, and satisfies thedifferential equation y''-10y'+25y=0.
- Q to calculate the integral from (-infinty) to (+ infinity) of[x^2 / (x^4 + 4)[ dx . Â Â poles, residues.
- Q Ifln(8x) = y2,finddy/dx.
- Q find the absolute minimum and absolutely maximum value offunction f(x,y)= e^xy subject to the constraint x^2+y^2= 18
- Q Aclosed rectangular container with a square base is to have volumeof 36,000 cubic centimeters. The material for the top and bottom ofthe container will cost $0.10 per square centimeter, and...
- Q Let f(x) = -2x3 - 9x2 - 12x + 3. Find thefollowing:a) The domain of f Answer can be an interval or inwordsb) The y-intercept Answer must be a pointc)...
- Q Given the following vector force field, F, isconservative:F(x,y)=(2x2y4+x)i+(2x4y3+y)j,determine the work done subject to the force while traveling alongany piecewise smooth curve from (-2,1) to (-1,0)
- Q A toy manufacturer's cost for producing q units of a game isgiven by C(q) = 1460 + 3.5q + 0.0006q2. If the demandfor the game is given by p =...
- Q part 1)Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of fand determine its inflection point(s).part 2)Find the absolute extrema of f(x) = x^4 + 4x^3...
- Q 1. . Find the limit: lim ?→ ∞ (? + √?2 + 2?)2. If 1200 ??2 of material is available to make a box with a squarebase and an open...
- Q Consider the region R between the x-axis and the curve y = x^3 /3 , between x = 0 and x = 1.(a) Calculate the surface area of the solid...
- Q Solve the problem43) Find equations for the horizontal and vertical tangent linesto the curve r = 1 - sinθ, 0 ≤ θ < 2π.Please check if your answer is correct...
- Q Given the equation:sin(x+y)=x+cos(y)a) Differentiate y with respect to xb) Give the equation of the line tangent to the curve of at thepoint (0,Ï€/4)
- Q A closed rectangular box of volume 324 cubic inches is to bemade with a square base. If the material for the bottom costs twiceper square inch as much as the...
- Q Consider the following planes. 5x − 3y + z = 2, 3x + y − 5z = 4(a) Find parametric equations for the line of intersection of theplanes. (Use the...
- Q You go to Verizon to buy a new Iphone. You expect to pay $800for a new phone and $70 a month. But this is not the onlyoption.Option 1: Pay $800...
- Q 1. a.) determine vector and parametric equations for the linethrough the point A(2, 5) with direction vector = (1,−3).   b.)Determine a vector equation for the line through the points(-1, 4)...
- Q Determine where the given function is concave up and where it isconcave down.​f(x)= 2x^3-6x^2-90xFind the maximum profit and the number of units that must beproduced and sold in order to...
- Q let R be the region bounded by the line y=0, by the upper partof the circle x2+y2=4, and by the upper partof the circle x2+y2=9. Find the circulationof the force...
- Q Consider the function ?(?,?)=3?^2−4?+??^2 on the closed region?={(?,?):−1≤?≤1 and −1≤?≤1}R={(x,y):−1≤x≤1 and −1≤y≤1}.(a) Find all critical points of ?(?,?)f(x,y) inthe region ?R, if any, and classify them (local maximum, localminimum, or...
- Q The table below shows the number of hybrid carssold (in thousands) in the US in the followingyears.                                                         * Source: WikipediaYearHybrid cars sold in US (inthousands)20009.35200236.04200484.202007352.272010274.212014452.15Find an exponential regression equation for thedata....
- Q 8. [C] The surface of the Earth can be modeled by a unit sphere.The Arctic Circle is the circle on the unit sphere at an angle of φ= 23.5 ◦...
- Q Problem PageQuestionA scientist has two solutions, which she has labeled Solution Aand Solution B. Each contains salt. She knows that Solution Ais60%salt and Solution B is85%salt. She wants to obtain80ounces...
- Q 1. In League of Legends, a player’s Effective Health whendefending against physical damage is given by E = H(100 + A)/100where H is health and A is armor. Health costs...
- Q cosxdx + [7+(2/y)]sinxdy = 0Find if the equation is exact. If it is exact, solve.If it is not exact, find an integrating factor to make it exact,verify that it is...
- Q a. Find the two first partials ?? and ?? of the followingfunction. ?(?, ?) = ?3?5 + ?4xsin(?)b. Find and classify all critical points of ?(?, ?) =?3 − 3?...
- Q A bicyclist is riding on a path modeled by the functionf(x) = 0.07x,where x and f(x) are measured inmiles (see figure). Find the rate of change of elevation atx =...
- Q Solve boundary value problem, use the method of undeterminedcoefficients when you solve for the particular solutiony'' + 2y' + y = e-x(cosx-7sinx)y(0)=0y(pi) = epi
- Q The boundary of a lamina consists of the semicirclesy =sqrt(1 − x2)and y =sqrt(9 − x2)together with the portions of the x-axis that jointhem. Find the center of mass of...
- Q Solve by power series around x=0: y\"-2xy'-2y=0 (Find the firstthree nonzero terms of each of the LI solutions)
- Q In this multi-part exercise, we'll prove another result alludedto in class, namely that if the Pythagorean theorem holds in aneutral geometry, then the geometry is Euclidean. So, assume thePythagorean theorem...
- Q A Production Model predicts that the total output T is given interms of the amounts of labor x and capital investment y accordingto the formula:T = x p y qfor...
- Q 5. Consider the function f(x) = -x^3 + 2x^2 + 2.(a) Find the domain of the function and all its x and yintercepts.(b) Is the function even or odd or...
- Q A manufacturer of tennis rackets finds that the total costC(x) (in dollars) of manufacturing xrackets/day is given byC(x) = 900 + 3x + 0.0003x2.Each racket can be sold at a...
- Q The volume of a sphere increases at 2.5 cubic cm/s. Calculatethe rate atwhich the area of the sphere changes when the diameter is 12cm.
- Q (a) On the 24th day, the number of active cases are 53,697 andon the 26th day, the active cases increase to 82,272. Find thevalue of the constants in the above...
- Q (1 point) Bacteria grow at a rate of 27% per hour in a petridish. If there are initially 100 bacteria and a carrying capacityof 500000 cells, how long does it...
- Q Solve the following initial value problems(1) dy/dt = t + y y(0) = 1 so y(t) =(2)Â Â dy/dt = ty y(0) = 1 so y(t) =
- Q Find the absolute maximum and minimum values for thefunctionf(x, y) = xy on the rectangle R defined by −8 ≤ x ≤ 8,−8 ≤ y ≤ 8.
- Q (A) Use logarithms to solve the problems.How long will it take $15,000 to grow to $18,000 if theinvestment earns interest at the rate of 5%/year compoundedmonthly? (Round your answer to...
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