Basic Math question and answers for July 13, 2023
- Q Find the local maximum and minimum values of the function.Tell the intervals where the graph of the function is increasingand decreasingf(x)= 2x^3 +3x^2 - 12x
- Q Use the given conditions to write an equation for the line in?point-slope form and in? slope-intercept form.Passing through (-5,-6) and parallel to the line whose equationis y= -5x+1______________________________________________________________________________________________________________________________________________Write an equation...
- Q Formulate a system of equations for the situation below andsolve.A manufacturer of women's blouses makes three types of blouses:sleeveless, short-sleeve, and long-sleeve. The time (in minutes)required by each department to...
- Q A cheetah can run at 105 ft/s, but only for 7 seconds. Thecheetah is at (0,0) when it sees an antelope which is movingaccoording to the parametric equation (x,y)= (-39+40t...
- Q evaluate the indefinite integralsqrt(4-x^2)
- Q Use an appropriate comparison test to determine theconvergence/divergence of the following series:a.)? n= (1)/(?n?1) (Upper limit of the sigma is ? and the lowerlimit of the sigma is n=2)b.) ?...
- Q integration of ((8(x+a))/(x^2+a^2))dx. using trig. sub.
- Q Find the Taylor series for f ( x ) centered at the given valueof a . (Assume that f has a power series expansion. Do not showthat R n (...
- Q Find the absolute maximum value and absolute minimum value, ifany, of the function g(x) = x ?(4 ? x2) on the interval [?2,2].
- Q Which of the following is the volume of the regionbounded by x * 2 + y * 2 = 4 cylinders, z = 0 and z = 4 - xplanes?
- Q A ferris wheel is 50 meters in diameter and boarded from aplatform that is 5 meters above the ground. The six o'clockposition on the ferris wheel is level with the...
- Q i) A bowl collects 1.67 cm height of water in its firstweek in a dewdrop. Each week the height of the water increases by4% more than it did the week...
- Q Use Lagrange multipliers to find the absolute extrema of f(x,y)= x2 + y2 - 2x - 4y + 5 on the regionx2 + y2 <= 9.
- Q Let L1 be the line passing through the pointP1=(?1, ?2, ?4) with direction vector?d=[1, 1, 1]T, and let L2be the line passing through the point P2=(?2,4, ?1) with the same...
- Q Write down Green’s Circulation Theorem. Explain when Green’sCirculation Theorem applies and when it does not. Give an exampleof Green’s Circulation Theorem showing the function, the integraland drawing the region.
- Q Round your answers to the three decimal places.A dock is 1 meter above water. Suppose you stand on the edge of thedock and pull a rope attached to a boat...
- Q Let f(x, y) =x^2+ 3y^2?2x?12y+ 13 on the domain A given by thetriangular region with vertices (0,0),(0,6), and (2,0).Find the maximum of f on the boundary of A.
- Q Question 1. Let V and W be finite dimensional vector spaces overa field F with dimF(V ) = dimF(W) and let T : V ? W be a linearmap. Prove...
- Q Find a possible formula for the trigonometric function whosevalues are in the following table.x04812162024y8404840
- Q Determine the solution to the initial value differentialequation;y?=0.0015y(1100?y), y(0)=321. y(x) = ?2. What is the maximum value of this function. In other words,evaluate: lim x-> inf y(x)3. Determine x for...
- Q Let PQ be a focal chord of the parabola y2 = 4px. LetM be the midpoint of PQ. A perpendicular is drawn from M to thex-axis, meeting the x-axis at...
- Q While shopping for a car loan, you get the following offers:Solid Savings & Loan is willing to loan you $10,000 at 5%interest for 4 years. Fifth Federal Bank & Trust...
- Q A gift shop expects to sell 400wind chimes during the next year.It costs $1.20 to store one wind chime for one year. There is afixed cost of $?15 for each...
- Q Show that if P;Q are projections such that R(P) = R(Q) and N(P)= N(Q), then P = Q.
- Q The COV-19 virus has virtually changed the way we work, studyand shop. People are scared and frightened of contracting thedeadly virus. Traditional grocery stores such as Loblaws, Longo’s,etc. have seen...
- Q a. consider the plane with equation -x+y-z=2, and let p be thepoint (3,2,1)in R^3. find the distance from P to the plane.b. let P be the plane with normal vector...
- Q The function f(x)=3x+2 is one-to-onea) find the inverse of fb) State the domain and range of fc) State the domain and range of f-1d) Graph f,f-1, and y=x on the...
- Q Find a cubic function y = ax3 + bx2 + cx + d whose graph hashorizontal tangents at the points (?2, 8) and (2, 2).Find an equation of the normal...
- Q 1. Test the series below for convergence using the RootTest.??n=1 (2n/7n+5)^nThe limit of the root test simplifies to lim n?? |f(n)| wheref(n)= The limit is: Based on this, the seriesDivergesConverges2. Multiple...
- Q Find the general solution of the given system using thecharacteristic equationdxdt=6x-ydydt=5x+2yFind the general solution of the given system using thecharacteristic equationdxdt=6x-ydydt=5x+2y
- Q T?w?o? ?l?i?n?e?a?r?l?y? ?i?n?d?e?p?e?n?d?e?n?t??s?o?l?u?t?i?o?n?s? ?o?f? ?t?h?e? ?f?o?l?l?o?w?i?n?g??e?q?u?a?t?i?o?n? ?(?1? ??? ?x?)???y??? ???+??? ?x???y??? ????????y? ???=??? ?0? ?a?r?e? ???y?1?(?x?)? ???=??? ?3?e?^?x? ?a?n?d? ???y?2?(?x?)????=??? ?6?x?.? ?a?)? ?F?i?n?d? ?t?h?e? ?W?r?o?n?s?k?i?a?n? ?W?(?y?1?,???y?2?)??o?f? ?y?1? ?a?n?d? ?y?2?.? ?(?b?)?...
- Q Use two functions below for parts a and b.? ?(?)=????? ?(?)=ln(?)+ln(1??)+3a) Find the stationary points, if any, of the following functionsand label them accordingly (local or global minima/maxima orinflection point).b)...
- Q Find the equation of a circle that passes through (1,7). (6,2)and (4,5) using a matrix.
- Q Solve the initial value problem y’cosx = a + y where y(?/3)=aand 0please explain how you do everything
- Q Part 1. Describe the boundaries of the triangle with vertices(0, 0), (2, 0), and (2, 6). (a) Describe the boundary with the topfunction, bottom function, left point, and right point....
- Q True/FalseIf SS is a sphere and FF is a constant vector field, then?SF?dS=0.
- Q Determine the eigenvalues and the corresponding normalizedeigenfunctions of the following Sturm–Liouville problem: y''(x) +?y(x) = 0, x ? [0;L], y(0) = 0, y(L) = 0,
- Q Find the integral that represents the volume of the followingsolids:1. below the surface z=1+xy and over the triangle with vertices(1,1), (4,1) and (3,2).2. enclosed by the planes y=0, z=0, y=x...
- Q Find dy/dx for a & ba) sin x+cos y=1b) cos x^2 = xe^yc)Let f(x) = 5 /2 x^2 ? e^x . Find the value of x for which thesecond derivative...
- Q Find the area of the surface correct to four decimal places byexpressing the area in terms of a single integral and using yourcalculator to estimate the integral.The part of the...
- Q Multivariable Calculus[A] Consider the region R in the first quadrant that is outsidethe circle r = 1 and inside the four-leaved rose r = 2 sin 2?).(A.1) Draw a sketch...
- Q Solve this differential equation:9x - 7i > 3(3x - 7u)Please provide detailed solution
- Q Show that the equation has exactly one real root.3x + cos(x) = 0
- Q Set up the triple integral of an arbitrary continuous functionf(x, y, z) in spherical coordinates over the solid shown. (Assume a= 4 and b = 8. ) f(x, y, z)...
- Q 3: Find the volume of the torus shown using:a. The Shell Method.b. The Washer Method.
- Q If three resistors with resistance of R1, R2, R3 are wired inparralle, their combined combined resitance R is given by thefollowing formula:1/R= 1/R1 + 1/R2 +1/R3The design of a voltmeter...
- Q A student asks if the precision with which manufacturers mustcalibrate their tools is at all related to statistics. How do yourespond?
- Q 1. horizontal versus oblique asymptotea. under what circumstances does a rational function have ahorizontal asymptote of y=0b. under what circumstances does a rational function have ahorizontal asymptote that is not...
- Q Find the cubic equation.F(x)=ax^3+bx^2+cx+dF(-1)=3F(1)=1F(2)=6F(3)=7What is the value of a,b,c,d
- Q A tank contains 400 gallons of brine (salt in solution) in which125 pounds of salt has been dissolved. Freshwater (with no saltadded) runs into the tank at a rate of...
- Q Show that if the opposite angles of a quadrilateral add up totwo right angles, then the vertices are concyclic
- Q Differential Calculus - [Related Rates]—At Noon, ship A is 200 km east of ship B and ship A issailing north at 30 km/h. ten mins later, ship B starts to...
- Q In this problem, p is in dollars and x is thenumber of units.Find the producer's surplus for a product if its demand functionisp = 144 ? x2 and its supply...
- Q A tank contains 90 kg of salt and 2000 L of water: Pure waterenters a tank at the rate 8 L/min. The solution is mixed and drainsfrom the tank at...
- Q Find all pairs of x and y for both of the following twoequalities hold:x + y = 10xy - 4
- Q A manufacturing firm has a monthly production of units modeledby?(?, ?) = 50?0.7?0.3 where x is the number of units of labor andy is the number of units of capital.The...
- Q Calculate k(t) when r(t) = <4t^-1,-6,6t>Thank you!
- Q Use Newton's method to find all real roots of the equationcorrect to six decimal places. (Enter your answers as acomma-separated list.)8/x = 1 + x^3
- Q Solve the second-order linear differential equationy?? ? 2y? ? 3y = ?32e?x using the method of variation ofparameters.
- Q A rectangular garden of area 50 square feet is to be surroundedon three sides by a fence costing $2 per running foot and on oneside by a brick wall costing...
- Q Find the limit, if it exists. (If an answer does not exist,enter DNE.) lim x ? ? 3x ? 1 / 2x + 5
- Q Integration question: Fluid flows into a tank for 10 minutes.The tank is initially empty. After t minutes, fluid flows in at arate of 1 + t/2 litres per minute. How...
- Q The U.S. census questionnaire defines kitchens with completefacilities as those having a sink with piped water, a range, and arefrigerator. Homes that lack complete kitchen facilities have beenrare in the...
- Q Solve the following boundary value problem by Laplace Transform.(If you solve with anothermethod you will NOT get credit. There is nothing wrong about theconditions.)d2ydt2 + y = cos(2t); y0(0) =...
- Q (a) Find the limit of the following functions:-lim as x approaches 0 (1-cos3(x)/x)-lim as x approaches 0 (sin(x)/2x)-lim as theta approaches 0 (tan (5theta)/theta)(b) Find the derivative of the following...
- Q Find the mass of the solid bounded by the ??-plane, ??-plane,??-plane, and the plane (?/2)+(?/4)+(?/8)=1, if the density of thesolid is given by ?(?,?,?)=?+3?.
- Q Prove that:a) |sinx|<= |x|b) x = sin x has only one solution in real number using meanvalue theorem
- Q Let f(x,y) = x^2 + y^2 + 8xy + 75y + 10. Find all the critical points and determine if each is a maxima, minima, or saddle points.
- Q How are art and science similar?How are art and science different?
- Q 6. (a) let f : R ? R be a function defined byf(x) =x + 4 if x ? 1ax + b if 1 < x ? 33x x 8...
- Q Suppose f(x) is a rational function in which the degree of thenumerator is greater than the degree of the denominator. Tointegrate f(x), the first step isa) Factor the denominator into...
- Q Compute the Maclaurin series for the following functions: (a)f(x) = (2 + x)^5 (b) f(x) = (x^3) * sin(x^2)
- Q Let f(x) = ln(x^2 + 9) Find the first two derivatives of f .Find the critical numbers of f . Find the intervals where f isincreasing and decreasing. Determine if...
- Q Given : the plane region R is bounded by the curves ? = 0 , ? =2 , ? = 3??2-Compute the volume of the solid that has the region...
- Q A company manufactures and sells x television sets per month.The monthly cost and? price-demand equations are ?C(x)=75,000+40xand p(x)= 300-x/30 ?, 0 less than or equal to x less than or...
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