Basic Math question and answers for August 05, 2023
- Q Discuss the curve y = x^3/1+x^2 with respect to intervals ofincreasing and decreasing, local maximal and minimal points,intervals of concavity, and points of inflection. Use thisinformation to sketch the curve.
- Q 1. A resort is roping of a children's swimming area in the lakeat the resort. They have 150m of rope to use. What is the maximumarea they can rope off...
- Q - A cylindrical tank is being filled simultaneously with waterand sugar. The input of water and sugar is carefully adjusted sothat the concentration of sugar in the water is held...
- Q 1)Find the general solution of the given second-orderdifferential equation.y'' − 7y' + 6y = 02)Solve the given differential equation by undeterminedcoefficients.y'' + 4y = 6 sin(2x)
- Q Consider the integral01e-x2dxGive an explanation for why this integral cannot be solvedmanually using substitution or integration by partsEstimate this integral using the average of left and rightsums, n = 5...
- Q 1. Suppose the velocity of a moving object is given by thefunction f(t) = √ t for the time interval 0 ≤ t ≤ 2 sec.Approximate the total distance this...
- Q Evaluate the double integral explicitly by reversing the orderof integration:? Integral from 0 to 8 and integral from (sub3square root of y) to 2 Â Â ex dxdy
- Q A group of 100 students form 5 voting blocs, A, B, C, D, and E.They agree to use 57 votes as the number needed to pass a motion.This results in...
- Q graph the function A. Show steps how you find the domain, the xand y-intercepts, the horizontal and vertical asymptotes, theintervals of increasing and decreasing, the relative extrema, theintervals of concave...
- Q A price pp (in dollars) and demand xx for a product are relatedby2x2+8xp+50p2=7400If the price is increasing at a rate of 2 dollars per month whenthe price is 10 dollars,...
- Q Consider the function q(x)=x^11−3x^10+2. Find the x-coordinatesof all local maxima. If there are multiple values,give them separated by commas. If there are no local maxima, enter∅.
- Q Prove that the following statements are equivalent. A. TheEuclidean parallel postulate holds. B. Given any triangle â–³ABC andgiven any segment DE, there exists a triangle â–³DEF having DE as oneof...
- Q Find the mass and center of mass of the lamina with the givendensity.Lamina bounded by y = x2 − 7 andy = 29, (x, y) = square of the distancefrom...
- Q 1) x2y'' - 8xy' -8y =02) y''- 3y' - 2y =10sin(x)
- Q 1114) intg{ 2x ln(x^2) dx } = (Ax^B)*(ln(x^2)+F) + C. Determine A,B,F. ans:31130) Evaluate intg_9_17{ (x^2 - 4x + 7) dx }. ans:1 1132) Integrate from 3 to 7 the...
- Q Determine which of these sets spans R^3q) (1,0,1) , (3,1,0), (-1,0,0),(2,1,5)x) (2,1,2) , (1,1,1), (-3,0,-3)y) (-1,2,1),(4,1,-3),(-6,3,5)z) (1,0,0),(0,2,0),(1,2,0),(0,-1,1)a) only qb)q and xc) q and zd) only z
- Q (a)On a separate sheet of paper, sketch the parameterized curvex=tcost,y=tsint for 0≤t≤4π. Use your graph tocomplete the following statement:At t=6t=6, a particle moving along the curve in thedirection of increasing...
- Q Approximate the area under the graph of​ f(x) and above the​x-axis with​ rectangles, using the following methods withn=4.​f(x)=88x+55                              fromx=44tox=66a.Use left endpoints.  b.Use right endpoints.  c.Average the answers in parts a and b.d.Use midpoints.
- Q 1.) (1 point) Find the particular antiderivative that satisfiesthe following conditions:dy/dx=7−4x; y(0)=2y=2.) (1 point) Find the particular antiderivative that satisfiesthe following conditions:p′(x)=−50/x^2; p(3)=7p(x)=3.) (1 point) Find the particular antiderivative that...
- Q (1 point) Find yy as a function of xx ify‴+9y′=0,y‴+9y′=0,y(0)=−2,  y′(0)=24,  y″(0)=−18.y(0)=−2,  y′(0)=24,  y″(0)=−18.y(x)= ?
- Q Suppose a company's revenue function is given byR(q)=−q^3+360q^2 and its cost function is given by C(q)=300+19qwhere q is hundreds of units sold/produced, while R(q) and C(q) arein total dollars of...
- Q A rectangular swimming pool is to be built with an area of 1800square feet. The owner wants 5-foot-wide decks on either side and10-foot-wide decks at the two ends. Find the...
- Q Q2. Given the line integral C F (r) · dr whereF(x,y,z) = [mxy − z3,(m − 2)x2,(1 − m)xz2]∫(a) Find m such that the line integral is pathindependent;(b) Find a...
- Q A third-party Amazon seller who has acquired a supply of singlerolls of toilet paper has been watching prices and has determinedthat the demand function isD(p)=(p+1500)/(0.03p^3+12)Where p is the price of...
- Q Find the local maximum and minimum values and saddle point(s) ofthe function. If you have three-dimensional graphing software,graph the function with a domain and viewpoint that reveal all theimportant aspects...
- Q STM 2100 Quiz April 2 2020Consider the radioactive decay modeldy/dt = -0.1yy(0) = 10a. Use separation of variables to solve the ODEb. At what time does y(t) = 5?2. Consider...
- Q I have a question in that if v is s any nonzero vector, and v ispositioned with its initial point at the origin, then the terminalpoints of all scalar multiples...
- Q 5. For the function ?(?)=−3?^4−12?^3Find the domain and intercepts.Find the critical numbers, intervals where f (x) is increasingand decreasing, and any local maximum and local minimum points(find both coordinates).Find the...
- Q Some airlines have restrictions on the size of items of luggagethat passengers are allowed to take with them. Suppose that one hasa rule that the sum of the length, width...
- Q Find the solution of the given initial value problem:2y′′′+26y′−232y=0y(0)=7, y′(0)=38, y′′(0)=−233Enclose arguments of functions in parentheses. For example,sin(2x).
- Q Find equations of the tangent plane and the normal line for thelevel surface 2xy2 − 3yz2 + xyz = −40 at the point (1, 2, 3).
- Q Differentiate: do the Derivative for all(a) f(x) = x ^3 − 5e + x ^5/3(b) g(x) = x ^2+e^ x / √ x+1(c) h(x) = 2^sec(x)(d) j(x) = cos(sin(xe^x ))(e)...
- Q Assume the demand function is D(p) = 150 – 5p (p is price).a. What is the slope? 5(30-p) Oe=150-5p p=30b. What is the y-intercept = 180c. Using the definition of...
- Q A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of V mm3, has a 2 mm thick solid...
- Q Find the mass and center of mass of the solid E with the givendensity function ?. E is the tetrahedron bounded by the planes x =0, y = 0, z...
- Q A) Find the equation of the curve with slope 4x^2/x^2+1 andpasses through the point (1,0)B)Find the equation of the curve with slope 4x/ x-5 and passesthrough the point (6,0)C) Find...
- Q y=x2/(7x+4) determine the intervals on which thefunction is increasing, decreasing, concave up, concave down,relative maxima and minima, inflection points symmetry vertical andnon vertical asymptotes and those intercepts that can be...
- Q using method of undetermined coefficients obtain real solutiony''''+y''=12x^2+4sinx
- Q 1.The amount of goods and services that costs $400 on January 1,1997 costs $â¢432.86 on January 1, 2003. Estimate the cost of thesame goods and services on January 1, 2019....
- Q consider the following function.A piece of wire 14 m long is cut into two pieces. One piece isbent into a square and one bent into an equilateral triangle. Howshould the...
- Q Given f(x)=2x3-7x2+9x-3, use the remainder theorem to findf(-1)
- Q Part A: Compute the derivative of ?(?)=(4?^4 + 2?)(?+9)(?−6)Part B: Compute the derivative of ?(?)= (9x^2 + 8x +8)(4x^4 +(6/x^2))/x^3 + 8Part C: Compute the derivative of?(?)=(15?+3)(17?+13)/(6?+8)(3?+11).
- Q Consider the parabola y=1-x^2. Find the point on the parabolafor which the tangent line through that point creates a triangle inthe 1st quadrant and that triangle has minimum area.
- Q 6- Find the latitude and longitude of the location on Earthprecisely opposite the geographic center of the contiguous UnitedStates (Lebanon, Kansas at 39° 50′ N, 98° 35′ W).
- Q Suppose that Polonium decays at a rate propotional to the amountpresent. If a sample ofPolonium -210 decays so that there is 50 gr left after 140 daysand 25 gr after...
- Q compute the unit tangent vector T and the principal normal unitvector N of the space curve R(t)=<2t, t^2, 1/3t^3> at thepoint when t=1. Then find its length over the domain...
- Q Given f(x) = x^4 - 4x^31) find the intervals on which f is increasing ordecreasing.2) find the local maximum and minimum values of f.3) find the intervals of concavity and...
- Q How are disjoint events related to complementary events? Explainyour reasoning, and give examples to justify your ideas. Your postmust have a minimum of 5 sentences.
- Q Convert x=cos(3t)+sin(3t) & y=cos(t)-sin(t) into an equationof x-y form (cartesian equation). Thank you
- Q Estimate the numeric value of 51/7 accurately to 6decimal places, using Newton’s Method. Note: You may use Excel tosolve this problem.
- Q Solve the following linear programming problem.Maximize: z=10x ＋12ysubject to: 7x＋4y<=2810x＋y<=28x>=0y>=01. The Maximun value is ____at the point____.
- Q Problem #3:A particle travels across a at surface, moving due east for 4m, then due north for 9 m, and then returns to the origin. A forcefield acts on the...
- Q Consider the following vector function. r(t) =<3t, 1/2 t2,t2> (a) Find the unit tangent and unit normal vectors T(t) andN(t).(b). Find the curvature k(t).
- Q Find the tangent plane to Z= xsin(x+y) at (1,1,0)
- Q Find an equation for the tangent plane of the surface xy^2 +yz^2 − 2xz = −3 at the point (2, −1, 1)
- Q Asporting good store sells 100 pool tables per year. It costs $62 tostore one pool table for a year. To re-order, there is a fixed costof $31 per shipment plus...
- Q Find the point on the line −4x+4y+4=0 which is closest to thepoint (−3,−5)
- Q A chain lying on the ground is 10 meters long and it has adensity of Ï(x) = x(10 − x) kg/m. How much work is required toraise one end of...
- Q Summarize the pertinent information obtained by applying thegraphing strategy (Explain the increasing/decreasing intervals,Local maximum/minimum values, concave up/down intervals Inflectionpoint(s), intercepts) and sketch the graph ? = ?(? + 2) 3.
- 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 Ihave a project about how is calculas related to mechanicalengineer. I must have a total of 500 word can someone help meplease?
- Q Find the radius of convergence, R, of the series. Findthe interval, I, of convergence of the series. (Enter youranswer using interval notation∞(−1)n (x −4)n3n +1n = 0∞(x −4)nn7 + 1n =...
- Q Sodium 24 has a half-life of approximately 15 hours. Consider asample of 100 milligrams.a. Write an equation to determine the number of milligramsremaining after t days. Show all work.b. How...
- Q A 500 cm 2 of paper will be used to make a rectangular poster.The poster has 4 cm margins onthe sides and bottom. The top margin is 6 cm. The...
- Q Suppose P(t) t(3cubed)– 4t + 4 represents the position of amoving particle after t seconds.a. At what time(s) does the particle change directions?b. When is the speed of the particle...
- Q Consider the equation below. (If an answer does not exist, enterDNE.) f(x) = x3 − 6x2 − 15x + 9 (a) Find the interval on which f isincreasing. (Enter your...
- Q  part 1)Use implicit differentiation to find an equation of the tangent line to the curvesin(x+y)=6x−6y at the point (π,π)Tangent Line Equation: y=part 2)Find an equation of the tangent line to...
- Q Two spacecraft are following paths in space given byr1=〈sin(t),t,t2〉r1=〈sinâ¡(t),t,t2〉 andr2=〈cos(t),1−t,t3〉.r2=〈cosâ¡(t),1−t,t3〉. If the temperature for thepoints is given by T(x,y,z)=x2y(6−z),T(x,y,z)=x2y(6−z), use theChain Rule to determine the rate of change of the...
- Q - Populations of birds and insects are modelled by thedifferential equationsdx/dt = 4x − 0.2xy and dy/dt = −2y + 0.08xy(a) Which of the variables, x or y, represents the...
- Q Find the center mass of the solid bounded by planesx+y+z=1x+y+z=1, x=0x=0, y=0y=0, and z=0z=0, assuming a mass densityof Ï(x,y,z)=5√z.
- Q Pythagoras is at it again. He is pumping into my backyard pool 3gal/min of water in one hose that contains a concentration of 2g/gal of liquid catnip and 4 gal/min...
- Q I need a box and it must adhere to the following:L+2W+2H<130, L<70, W<40, H<18. I'd like to know thedimensions required to maximize my box volume. Any help isappreciated, and please...
- Q Two angles of a quadrilateral measure 140° and 80°. The othertwo angles are in a ratio of 3:4. What is the value of x? What arethe measures of those two...
- Q Find a polynomial f(x) of degree 3 that hasthe indicated zeros and satisfies the given condition.−5, 1, 2;    f(3) = 48Find a polynomial f(x) of degree 3 that hasthe indicated zeros...
- Q A 20 foot piece of wire is to be cut into two pieces. One pieceis used to form a circle and the other is used to form a square(imagine fence...
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