Basic Math question and answers for August 04, 2023
- Q If the total revenue function for a computer isR(x) =1200x − 32x2 −x3,find the level of sales, x, that maximizes revenue andfind the maximum revenue in dollars.x=computersR(x)=$B.) The profit per...
- Q Two cars start driving from the same point. One travels north at30 miles per hour, and the other travels east at 45 miles per hour.At what rate is the distance...
- Q Find the absolute maxima and minima forf(x)on the interval[a, b].f(x) =x3 − 2x2− 4x + 4,    [−1, 3]absolute maximum    (x, y) =  absolute minimum    (x, y) =  2.f(x)on the interval[a, b].f(x) =x3 − 3x2− 24x...
- Q You wish to create a cylindrical can that can hold a volume of475 mL. The cost of the material to make the top and bottom the cancost twice as much...
- Q Find the cost function if the marginal cost function is given byC' (x) = x^1/3 +9 and 27 units cost ​$415.C(x) =
- Q A pizza pan is removed at2 : 00 PM2:00 PMfrom an oven whose temperature is fixed at425 degrees  into a room that is a constant71 degrees   After 5​ minutes, the pizza...
- Q 5. Explain (concisely) along with a labelled diagram thefollowing terms: a) local or relative extrema b) absolute extremac) turning points d) inflection point e) critical points
- Q Find the critical numbers of the function.1. g(y) = (y-1)/(y^2-y+1)2. h(t) = t^3/4 - 2t^1/43. F(x) = (x^4/5)*(x-4)^24. f(x) = 2cos(x)+sin^2(x)
- Q Find a, b, c, and d suchthat the cubic functionf(x) =ax3 + bx2+ cx + dsatisfies the given conditions.Relative maximum: (3, 21)Relative minimum: (5, 19)Inflection point: (4, 20)
- Q in2002, the population of a colony is 50,000 and is increase at 2.5%per year.a) what will the population be after 6 years?b) in what year will the population double?
- Q Follow the graphing strategy and analyze the function f(x) =x4 + 4x3 . State all the pertinentinformation and sketch the graph of f.
- Q A laptop computer that costs $1200 new has a book value of $425after 2 years. (a) Find a linear model V = mt + b. V(t) =Incorrect: Your answer is...
- Q A rectangular storage container with an open top is to have avolume of 14 cubic meters. The length of its base is twice thewidth. Material for the base costs 14...
- Q Consider8 the homogenous linear second order differentialequationy′′ −10y′ +25y = 0 (⋆)Follow the presentation of Example 2 in the handwritten notesfor class 15 on March 24 closely to eventually find...
- Q Time(weeks): 0 |   2 |   6 | 10Level: 210| 200 | 190| 1801. The table above gives the level of a person’s cholesterol atdifferent times during a 10-week treatment period....
- Q Given function f(x,y,z)=x^(2)+2*y^(2)+z^(2), subject to twoconstraints x+y+z=6 and x-2*y+z=0. find the extreme value off(x,y,z) and determine whether it is maximum of minimum.
- Q How many times would integration by parts needs to be performedto evaluate ∫75xn ln(x)dx  (where n is a positiveinteger)? Multi Choice.  A- Integration by parts need to be performed 1 time in...
- Q Suppose that a particle has the following acceleration vectorand initial velocity and position vectors.a(t)  =  7 i  + 9t k,   v(0)  =  4 i − j,    r(0) =  j  +  5 k(a)Find the velocity of the particle at time t.(b)Find...
- Q Find the indicated coefficients of the power series solutionabout ?=0 of the differential equation(?2−?+1)?″−?′+5?=0,?(0)=0,?′(0)=7Answer: ?=7?+....
- Q Consider the function f(θ) = θ + sinθ on (0,2π).1) Draw diagrams showing the intervals where f^i and f^ii arepositive or negative.2) Find the critical points.3) Find the local maxima...
- Q A bicycle manufacturer buys 5000 tires a year from a distributor. It cost 6 to store one bicycle tire for a year. To re-order, there is a fixed cost of...
- Q 6)a). Find the equation of the plane through the origin andperpendicular to x+y+z = 5 and 2x+y−2z = 7b). Let A = (−1,3,0), B = (3,2,4) and C = (1,−1,5).(...
- Q 2.)Use any method to find the volume of the solid rotated about theline x=2, whose area is bounded by y=x^(1/3) and y=x^2
- Q lim[(tanx-1)/x] as x->0.lim[ (1+sin(4x))^cot(x)] as x -> 0 from the positiveside.lim[ [(a^(1/x) + b^(1/x))/2]^x] as x -> infinity
- Q the amount of caffeine in a persons body follows an exponentialfunction, as do many drugs. the half life of caffeine is typicallyabout 5.5 hours. if you drink a can of...
- Q f(x)=(x-3)^4/(x^2+2x) Find the values of x at which the curve y= f(x) has a horizontal tangent line
- Q A surveyor standing some distance from a hill, measures theangle of elevation from the ground to the top of the hill to be40°29′5\" The surveyor then walks forward 902 feet...
- Q What would be steps and reason toanswering the following question? Also thank you ahead for helpingme understand the question. :)approximate the value ofsin(0.8).Find the Maclaurin series forsin(x).Do we have enough...
- Q 1189) The following values of y (cm) were measured for some unknown function. y = 5 3 3 5 9 15 23 every 1 cm. Find the area bounded...
- Q A market named Econland expects to sell 2,000 boxes of shoes inthe upcoming week at a steady rate. The cost of placing an orderwith the manufacturer is $50. Carrying costs,...
- Q Consider the graph defined by f(x) = (x-3)2a) state the coordinates of the vertex and the direction ofopening of f(x)b) Find the maximum and minimum values of f(x) on the...
- Q The radius of a melting snowball is decreasing at a rate of 1centimeter per minute, then(a) How fast is the volume of the snowball changing when itsradius is 3 centimeters?(b)...
- Q Find the general solution of the given second-order differentialequation.1. 4?'' + 9? = 152. (1/4) ?'' + ?' + ? = ?2 − 3xSolve the differential equation by variation of...
- Q What are the steps of finding the absolute maximum and absoluteminimum?
- Q Problem A) Convert the equation x^2 + y^2 = 4z^2 intocylindrical coordinates.Problem C) Use cylindrical coordinates to find the volume of theregion above the paraboloid z = x^2 + y^2...
- Q Find integral from (-1)^4 t^3 dtplease show all steps :)
- Q 1a.)Find the exact value of tan(1/2 * arccos(2/3))1b.)verify the following identity (1 - cos(4x))(2 + tan^2 (x)+ cot^2 (x)) = 8
- Q Give an example where the concept of \"rate of change\" is used inreal life.
- Q The World Cereal Organization (WCO) has asked you to redesigncereal boxes to more efficiently use paper. Assume the box must berectangular with a square base, and that the top and...
- Q A tree trunk is approximated by a circular cylinder of height100100 meters and diameter 33 meters. The tree is growing taller ata rate of 11 meters per year and the...
- Q  (a) How do you find the second derivative of a function?(b) If both  are positive numbers, what does that tell you about the function itself?(c) If we know that a function...
- Q Let F (x, y) = y sin x i – cos x j, where C is the line segmentfrom (π/2,0) to (π, 1). Then C F•dr isA 1B 2C 5/2D...
- Q A baseball team plays in a stadium that holds 66000 spectators.With the ticket price at $11 the average attendance has been 27000.When the price dropped to $10, the average attendance...
- Q Business: cost from marginal cost. A gourmet popcorn companydetermines that the marginal cost, in dollars, of the xth bag ofgourmet popcorn is given by C' (x) = -0.0004 x +...
- Q Find the maxium number of units that must be produced and soldin order to yield the maximum profit. Assume that revenue R(x) andthe cost, C(x) of producing x units are...
- Q Consider the vector function given below.r(t) =2t, 3 cos(t), 3 sin(t)(a) Find the unit tangent and unit normal vectors T(t) andN(t).T(t)Â Â = Â Â N(t)Â Â = Â Â (b) Use this formula to find...
- Q Say S is the unit sphere at the origin. There are two planes: R: x + y + z = 2 and T : 2x + y + z =...
- Q LetF(x, y,z) = ztan−1(y2)i+ z3ln(x2 + 8)j +zk.Find the flux of F across S, the partof the paraboloidx2 +y2 + z = 28that lies above the planez = 3and is...
- Q point) The count in a bacteria culture was 500 after 10 minutesand 32518 after 30 minutes. Assume the growth can be modelledexponentially by a function of the form Q(t)=A e...
- Q Find maximum, minimum and saddle point by using the secondderivative test: Show all the workf(x, y) =8xy-x^4-y^4
- Q 1) Evaluate the double integral ∬Dx^2 y dA, where D is the tophalf of the disc with center the origin and radius 2 by changing topolar coordinates.2) Use a double...
- Q Find the average value of f(x,y)= 4x+2y over region bounded bycoordinate axis and lines x+y=4 and x+y=8
- Q A plane is flying horizontally at an altitude of 2 mi and aspeed of 500 mph passes directly over a radar station. Find therate at which the distance from the...
- Q The sum of three nonnegative numbers is 36. One of the numbersis twice one of the other numbers. None of the numbers are greaterthan 12. What is the maximum value...
- Q Verify that the function satisfies the three hypotheses ofRolle's Theorem on the given interval. Then find all numbersc that satisfy the conclusion of Rolle's Theorem. (Enteryour answers as a comma-separated...
- Q 1. Dinosaur fossils are too old to be reliably dated usingcarbon-14, which has a half-life of about 5730 years. Suppose wehad a 68 million year old dinosaur fossil. How much...
- Q Overview: For the final project, you will illustrate yourprocess for solving selected precalculus problems. In this way, youwill defend the validity of your solutions and demonstrate yourability to effectively communicate...
- Q transform the given initial value problem into an algebraicequation for Y=L{y}Y=L{y} in the ss-domain. Then find the Laplacetransform of the solution of the initial value problem.y′′−2y′+2y=t^2e^t+7y(0)=1, y′(0)=1
- Q Evaluate the integral. (Use C for the constant ofintegration.)9x3 + 7x2 + 27x +7(x2 + 1)(x2 + 3)dx
- Q Set up an integral to find the volume of the solid generatedwhen the region bounded by y = x^3 and y = x^2 is (a) Rotated aboutthe x-axis using washers...
- Q We must build a box that has no top and whose base length is ï¬vetimes the base width. We have $1000.00 to buy materials to buildthis box. If the material...
- Q y''+2y'+2y=0,y(45)=2,y'(45)=-2
- Q Write two different integrals (one with respect to x, and onewith respect to y) that express the surface area obtained byrevolving the curve y = 2√ x between the points...
- Q At time t=0 a tank holds 550 gallons of water with 100 pounds ofdissolved salt. An input pipe brings in solution at 8 gallons perminute at a concentration of 2...
- Q By cutting away an x-by-x square from each corner of arectangular piece of cardboard and folding up the resulting flaps,a box with no top can be constructed. If the cardboard...
- Q Find the Elasticity of Demand and Explain your answer, for thefollowing function:P+5(p^2)q=1010 Â Â Given p=10
- Q A bus company charges $30 per person for a sightseeing trip if28 people are in the group. For each additional 2 people, they dropthe price $1. How many people will...
- Q 1. Until recently hamburgers at the Erwin Center cost $2 each.The food concessionaire sold an average of 10,000 hamburgers on agame night. When the price was raised to $2.40, hamburgers...
- Q III.) (20)Use polar coordinates to evaluateDx2+y2dAwhere D is the part of the diskx2+y2=9 thatlies above the x -axis. Sketch the region ofintegration.IV.) (20) Set up a triple integral in cylindricalcoordinates...
- Q Calculate the producers' surplus for the supply equation at theindicated unit pricep.HINT [See Example 2.] (Round your answer to the nearestcent.)p = 7 +2q1/3;Â Â p = 10
- Q For which values of x (if any) is f(x) =2x3 +3x2 – 12x –7Increasing at an increasing rate?
- Q Find the point(s) of intersection of the curves r=2 and r=4cosθ
- Q f(x)=2x2/(x2-x-2)Find:y'=y''=domain=x-intercept=y-intercept=VA=HA/SA=Increase=Decrease=local max=local min=concave up=concave down=IP=
- Q The height (h) of the water in metres at a certainpoint at the wave pool over a period of seconds is modelled by theequation h(s) = sin^2s + 1/2 sin...
- Q The domain of the function h(x) = ln(x + 3) + x2 − 4 is(A) {x∈R| −3<x<−2or−2<x<0}(B) {x∈R| −3<x<−2or−2<x≤0}(C) {x∈R| −3≤x<−2or−2<x≤0}(D) {x∈R| −3<x<−2or0≤x<2}(E) {x∈R| −3<x<−2or(x≥0andx̸=2)} (F) None of (A) -...
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