Basic Math question and answers for August 09, 2023
- Q 1. Find the partial derivatives of f(x,y) = xe^(4xy)fx=? fy=?2. Find the partial derivative of f(x,y) = sqrt(x^3 + 4y^5)fx=? fy=?
- Q Â General question: how do you find constraints in an optimization problem?For example, in this question:\"Find two natural numbers whose sum is 16 and whose product is a maximum.\" the solution...
- Q Making buried food is an ancient technique used today. Arestaurant makes pure buried food to please its diners. Foodusually comes out at a temperature of 145 ° C. In the...
- Q Give an example of a relation that ï¬ts the given requirements.If you think that there is no such relation, you must explain why.In each case, you may not use any...
- Q Let f(x, y, z) = 3x^(2)y + 4e^(2x+y) − 6 cos(xyz)(a) Find fx(b) Find fy(c) Find fz(d) Find fxy(e) Find fyx(f) Find fxzx(g) Find fzzz
- Q A company manufactures and sells x cellphones per week. Theweekly​ price-demand and cost equations are given below.p=400-.05x and C(x)=20,000 + 135xA) What price should the company charge for the​ phones,...
- Q The number of new businesses established in the US since1990 can be modeled by the functionNx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990and the domain is [0, 25].6. Use the Second...
- Q Solve the following given differential equations by using thefollowing method: method of variations of parameters.1. ?′′′ −?′′ −?′ +? = ??2. ?′′ − 2?′ + ? = ?? sin−1 ?
- Q An open rectangular box is made from a 9 inch by 12 inch pieceof cardboard by cutting squares of side length ? from the corners.Determine the length of the sides...
- Q Retailers will buy 40 items from a wholesaler if the price is$175 and 60 items if the price is $150. The wholesaler is willingto supply 30 items if the price...
- Q Find the absolute maximum and absolute minimum values of f(x) =cos(2x)+2 sin(x) in the interval [0; pi]
- Q f(x) = 7xex(a) Find the intervals on which f is increasing ordecreasing. (Enter your answers using interval notation.)(b) Find the local maximum and minimum values of f. (If ananswer does...
- Q prove that f(x)=x^2019 +x-1 has only one realroot
- Q Use a double integral to find the area of the region. The regioninside the cardioid r = 1 + cos(θ) and outside the circle r = 3cos(θ). Can someone explain...
- Q For the series , go through the entire list of series tests, andsayWhy the test cannot be applied orWhy the test can be appliedList of TestsGeometric SeriesTest for DivergenceIntegral Testp-series...
- Q Find the work it would take to build a limestone pyramid with asquare base with sides 560 ft and a height of 400 feet. (thedensity of limestone is 150 lb/ft^3)
- Q Explain, in your own words, what a derivative representsgeometrically.
- Q Let r(t) = (cos(Ï€t), sin(Ï€t), 3t). Calculate r'(t), T(t) andevaluate T(1).
- Q Find the solution ofy'' + y' = cos(2x) + 9x
- Q A boat leaves a dock at 2:00 PM and travels due south at a speedof 15 km/hr.Another boat has been heading due east at 20 km/hr and reaches thesame dock...
- Q Find all values of x on the interval -4< x< 3 for whichthe graph of g has a point of inflection. Give a reason for youranswer.
- Q --------------------------------------------------------------------------------A vat holds 20 cubic feet of liquid and is initially full. Watercontaining 6 grams of salt per cubic foot is being poured into thevat at the rate of 4...
- Q The quantity of a drug,Q, mg, present in the body t hours afteran injection of the drug is given isQ=f(t)=100te1-.5tfind f(1),f'(1),f(10) and f'(10). give units and interpret theanswers
- Q A company plans to design an open top rectangular box withsquare base having volume 4 cubic inches. Find the dimension of thebox so that the amount of materiel required for...
- Q How do you define the area of the region between the graphs oftwo continuous functions? When calculating the area between twocurves, explain, in your own words, the significance of a...
- Q (2)Please determine : FIRST: (A) W’(X) ; THEN: (B) W’(0); W(X)IS DEFINED BELOW:W(X) = [ (10* (X^4) ) – 8 ] * { [ (30*X ) + 25 ] ^...
- Q Find the Fourier series of the function.c. f(t) = sin(3pit), -1</ t </ 1
- Q Find the total area between y=25-x2 and the x-axis for0≤x≤7.5.Round your answer to three decimal places.The total area between y=25-x2 and the x-axis is what?
- Q Determine whether the following statements are true or false,and give an explanation or a counterexample.(a) log3y< log2y for y> 1(b) The domain of f(x) = ln(x^2) is x > 0
- Q As dry air moves upwards, it expands and then cools at a rate of1°C for each 100 m rise, up to about 12 km.a. If the ground temperature is 20°C,...
- Q An oil company wants to build a pipeline to take oil from an oilwell to a refinery. Unfortunately, the well and the refinery are oneither side of a straight river...
- Q Two objects are traveling in elliptical paths given by thefollowing parametric equations.x1 = 4cost and y1 = 2sintx2 = 2sin2t and y2 = 3cos2tAt what rate is the distance between...
- Q Use Euler's method with step size 0.2 to estimatey(0.4),where  y(x) is thesolution of the initial-value problem y' =3x − 4xy,y(0) = 0. (Round your answer to four decimalplaces.)y(0.4) =(b) Repeat part...
- Q Mackenzie manages a store that sells cell phones. Each Boomertakes 2 hours to create the plastic pieces, 2 hours to create theelectronics, and 16 hours of labor to assemble the...
- Q The project will be graded both for mathematical quality and for expository quality. Look at the six examples in section 4.7 of our text for good ideas about expository style....
- Q (a) Estimate the area under the graph of f(x) = 4 cos(x) from x= 0 to x = π/2 using four approximating rectangles and rightendpoints. (Round your answers to four...
- Q Consider the function f(x,y) = e^xy and closed triangular regionD with vertices (2,0), (0,2) an (0,-2). Find the absolute maximumand minimum values of f on this region.Need an explanation pls
- Q Find the volume of the solid enclosed by the two paraboloidsy=x2+z2y=x2+z2 and y=2−x2−z2y=2−x2−z2.
- Q You have been asked to design a can with a volume of 500cm3 thatis shaped like a right circular cylinder. The can will have aclosed top. What radius r and...
- Q A man gets a job with a salary of 35700 dollars a year. He ispromised a 2830 dollars raise each subsequent year.His total earning for a 9-year period is dollars.Suppose...
- Q A) Find the equation of the plane that passes through (2, -1,3) and is perpendicular to the line x = 2-3t, y = 3 + t, z = 5tB) Find...
- Q Use the Alternating Series Estimation Theorem to estimate therange of values of x for which the given approximation isaccurate to within the stated error. Check your answergraphicallyX^2
- Q theconcentration of hydronium ions C in a solution with a pH of x is C= 10^-x, with C measured in moles per liter. How quickly is the pHchanging when the...
- Q Let z=e^(x) tan y.a. Compute the first-order partial derivatives of z.b. Compute the second-order partial derivatives of z.c.∗ Convert z = f(x,y) into polar coordinates and then computethe first- order...
- Q A) Find a Vector Perpendicular to Vectors 2i + 3j-k and 3i +kB) Find the area of ​​the triangle whose vertices are (2, -1,1),(3,2,1) and (0, -1,3)C) Find the volume...
- Q a.maximize and minimize −2xy on the ellipse x^2+4y^2=4b.Determine whether or not the vector function is the gradient∇f (x, y) of a function everywhere defined. If so, find all thefunctions with...
- Q A rock is thrown upward from a bridge into a river below. Thefunction f(t)=−16t^2+36t+136 determines the height of the rockabove the surface of the water (in feet) in terms of...
- Q Use the Rational Zero Test to list all possible rational zerosof f. Test each possible rational zero to determinewhether it is an actual zero of f. (Enter your answers asa...
- Q Solve the IVP by applying the Laplacetransform:y''+y=sqrt(2)*sin[sqrt(2)t]; y(0)=10, y'(0)=0
- Q 1. If an open box is made from a tin sheet 10 in. square bycutting out identical squares from each corner and bending up theresulting flaps, determine the dimensions of...
- Q Compute the flux of the vector field F = <xy, 5yz, 6zx>through the portion of the plane 3x + 2y + z = 6 in the firstoctant with the downward...
- Q Two chemicals A and B are combined to form achemical C. The rate, or velocity, of the reaction isproportional to the product of the instantaneous amounts ofA and B not...
- Q Explain how to find zeros of rational functions.
- Q Find the half-range cosine series for the functionf(x) = x(n - r) in o<r<n. Deduce that1/14 +1/24 +1/34+…. =Ï€4 /90.Â
- Q Explain how limit has change moving from 1-variable functionsto 2 or more variables. Why is showing lim(x,y)→(a,b ) f (x, y)exists more difficult in so many cases than showing limx→a...
- Q Coastal Soda Sales has been granted exclusive market rights tothe upcoming Beaufort Seafood Festival. This means that during thefestival Coastal will have a monopoly, and it is anxious to takeadvantage...
- Q Suppose that ?(?)=?^4−5?^3(A) List all the critical values of ?(?). Note: If there are nocritical values, enter 'NONE'.(B) Use interval notation to indicate where f(x) isincreasing.Note: Use 'INF' for ∞,...
- Q Find ∫C((x^2+5y)i⃗ +y^3j⃗ )⋅dr⃗ where C consists of the threeline segments from (3,0,0) to (3,2,0) to (0,2,0) to (0,2,2).
- Q Lynbrook West, an apartment complex, has 100 two-bedroom units.The monthly profit (in dollars) realized from renting outx apartments is given by the following function.1.) To maximize the monthly rental profit,...
- Q 1.) The cost of producing x units of a product is modeled byC(x) = 180+90x-260lnx where x is greater than and equal to 1a. Find the average cost functionb. Find...
- Q 1) Find all of the second partial derivatives off(x,y)=3(x^4)y-2xy+5x(y^3).2) Find an equation of the tangent plane to z=32-3(x^2)-4(y^2)at the point (2,1,16).
- Q Ant on a metal plate. The temperature at a point ( x, y) on ametal plate is T(x, y) = 4x2 - 4xy + y2 . Anant on the plate...
- Q Find the curvature of the parametrized curve ~r(t) =< 2t 2 ,4 + t, −t 2 >.
- Q Graph the polynomial function​f(x)=8x5+52x4+80x3 and determine the end behavior ofthe graph of the function.
- Q Explain the concept of optimization. Explain the generalprocedure used to do an optimization problem. Use an example andinclude steps
- Q For the function f(x,y) = 4xy - x^3 - 2y^2 find and label anyrelative extrema or saddle points. Use the D test to classify. Giveyour answers in (x,y,z) form. Use...
- Q Use spherical coordinates to evaluate the triple integralâˆe^−(x^2+y^2+z^2)/(x^2 + y^2 + z^2) dV , Where E is the regionbounded by the spheres x^2 + y^2 + z^2 = 4 and...
- Q A mass weighing 8 pounds stretches a spring 4 feet. The mediumthrough the mass moves offers a damping force numerically equal tosqrt(2) times the instantaneous velocity. Find the equation ofmotion...
- Q The planey + z = 7intersects the cylinderx2 + y2 = 41in an ellipse. Find parametric equations for the tangent line tothis ellipse at the point(4, 5, 2).(Enter your answer...
- Q (x+5y)^21 expand using Pascal's triangle
- Q Refer to f(x)=1/x^21)Give an upper bound for the error you get when using thefourth degree Taylor polynomial centered at c = 2 toapproximate f(2.1)2)What is the actual error of your...
- Q The length â„“, width w, and height h of a box change with time.At a certain instant the dimensions are â„“ = 4 m and w = h = 1...
- Q (b)For the following IVP, find thesolution for x>0,.                             y'''=1+3x2-4x3+9√x.                                                   y1=8                       y'1=9              y''1=10                                                                                                                                       (c) Test for exactness and solve theIVP,                    (x+5exy)dx=-exdy                             y0=-2                                                                                                           Â
- Q Use the formulas for arc length and surface area and theequation x^2+y^2=R^2(a)... to derive the formula for the surface area of a spherewith radius R(b)... to derive the formula for...
- Q A company manufactures and sells x television sets per month.The monthly cost equation is?(?)=??,???+???and the monthlydemand−price equation is ?=???−???Use thisinformation toanswerquestions below.1.a.What is the maximum monthly revenue?b.What price should the...
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