Basic Math question and answers for July 14, 2023
- Q 14. If the cylinder of largest possible volume isinscribed in a given sphere, determine the ratio ofthe volume of the sphere to that of thecylinder.15. Determine the first quadrant point on thecurve y2x =...
- Q Use induction to solve the problem. Can you show me the stepstoo? I don't understand how to solve this.3+4+5+...+(n+2)=1/2n(n+5)1+5+52+...+5(n-1)=1/4(5n-1)
- Q You are flying from Joint Base Lewis-McChord JBLM toan undisclosed location 24km south and 212km east. Mt. Rainier islocated approximately 56km east and 40km south of JBLM. If you areflying...
- Q Solve the given non-homogeneous recurrence relations:an = an-1 + 6an-2 + f(n)a)an = an-1 + 6an-2 -2n+1 with a0 = -4, a1= 5b)an = an-1 + 6an-2 + 5 x3n...
- Q The volume created by revolving the area created from 5x-5,x^.5-1 and x=5 around x=5. Please show both shell and washermethod. Answer for shell and washer should be the same.
- Q A tug of war has teachers and the principal challenging thestudents! In the first round 3 teachers and 5 students came to adraw. In the second round the principal joined...
- Q Theofficers of a high school senior class are planning to rent busesand vans for a class trip. Each bus can transport 80 students,requires five chaperones, and cost $1000 to rent....
- Q In an effort to replace the destruction of trees, five regionsof the US have been tracking the annual rate of trees being planted(per thousand) in each region and the annual...
- Q (a) Show that the linesr 1 (t) = (2,1,?4) + t(?1,1,?1) and r 2 (s) = (1,0,0) +s(0,1,?2)are skew.(b) The two lines in (a) lie in parallel planes. Find equations...
- Q Let?:?2(R)??1(R)bedefinedby?(?+?x+?x2)=(?+?)+(???)x,where?, ?, ? are arbitrary constants.a. DeterminethetransformationmatrixforT.(6pts)b. Find the basis and the dimension of the Kernel of T. (10pts)c. Find the basis and the dimension of the Range of T....
- Q Determine if the following series converge or diverge. If itconverges, find the sum.a. ?n=(3^n+1)/(2n) (upper limit of sigma?, lower limit isn=0)b.?n=(cosn?)/(2) (upper limit of sigma? , lower limit is n=1c.?n=(40n)/(2n?1)^2(2n+1)^2...
- Q Find Cartesian equation of a plane through the point a andparallel to the given vectors p and q.a = (1, - 1, 3) , p= ‹2, -1, 0›, q= ‹2,...
- Q Illustrate with a picture showing that the following aresimply not true in Hyperbolic Geometrya). The area of a triangle can be made arbitrarilylargeb). The angle sum of all triangles is...
- Q Howmuch would be in your account after 10 years if you invested $1000in an account paying1) 3.6% simple interest?2) 3.6% interest compounded monthly?3) 3.6% interest compounded continuously?
- Q Find the general solution to the nonhomogeneous differentialequation: y"-y=tsint
- Q ty'''+4y''=t^2cost
- Q (1 point) Let F=?3yi+4xjF=?3yi+4xj. Use the tangential vectorform of Green's Theorem to compute the circulation integral?CF?dr?CF?dr where C is the positively oriented circlex2+y2=25x2+y2=25.
- Q Write up a formal proof that the angle bisectors of a triangleare concurrent, and that the point of concurrency (the incenter) isequidistant from all three sides.
- Q Can somebody explain to me Derivative of HyperbolicFunctions? May I know its importance and applications in real life?I need it for my essay. Thank you.PS. I can't find it on...
- Q Use the Intermediate Value Theorem and the Mean Value Theorem toprove that the equation cos (x) = -10x has exactly one realroot.Not permitted to use words like "Nope", "Why?", or"aerkewmwrt".Will...
- Q A rectangular area adjacent to a river is to be fenced in, butno fencing is required on the side by the river. The total area tobe enclosed is 114,996 square...
- Q Laplace Question : y''-3y'+2y=4cos2t,y(0)=-2,y'(0)=0
- Q Problem: A bottle is shaped with a right cone placed ontop of a right cylinder. The radius of the cone and thecylinderis 1.5 inches. The height of the cone is...
- Q Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Ruleto approximate the given integral with the specified value ofn. (Round your answers to six decimal places.)?/2031 + cos(x)dx, n = 4
- Q Find an equation of the tangent plane to the surfacex5+5z2ey?x=848 at point P=(3, 4, 11e?).(Use symbolic notation and fractions where needed. Your answershould be in the form ax+by+cz=1.)
- Q y''(t)+(x+y)^2*y(t)=sin(x*t+y*t)-sin(x*t-y*t), y(0)=0, y'(0)=0,x and y are real numbers
- Q 1) Find the Taylor series (to second order terms) of thefunction f(x,y) = x^2 ?4x + y + 9 around the point x = 3, y =?1.2)Explain why the corresponding...
- Q The value of the cumulative standardized normal distribution atZ is 0.8925. Calculate the value of Z.
- Q The base of a solid is the segment of the parabola y2= 12x cut off by the latus rectum. A section of the solidperpendicular to the axis of the parabola...
- Q A typical thickness for a sheet of paper is 0.004 inches. If youfold a sheet of paper once, the thickness ofthe folded paper will double to a value of 0.008...
- Q give a) Domain b) VA c) HA* d) OA* e) y-int f) x-int foreach2) f(x) = 4 /3x - 93) g(x) = (x -1)(x + 4) /(x + 1)(x -...
- Q Find the first 3 nonzero terms of the Maclaurin series for thefunction and the values for which the series convergesabsolutely.f(x)= x^4 * e^x^2
- Q Use the given conditions to write an equation for the line in?point-slope form and? slope-intercept form.Passing through ?( ?3?,?4?) and (2,6?)What is the equation of the line in? point-slope form???__?(Simplify...
- Q complete the following activities with these cricket chirpdata.Temperature (F degree) 69.7, 93.3, 84.3, 76.3, 88.6, 82.6, 71.6,79.6Chirp in 1 minute 882, 1188, 1104, 864, 1200, 1032, 960, 9001. Find the...
- Q Consider the curve given by the equation y^2 - 2x^2y = 3a) Find dy/dx.b) Write an equation for the line tangent to the curve at thepoint (1, -1).c) Find the...
- Q Vectors in the plan.Define scalar product and explain the relationship betweenscalar product defined by coordinates respectively at lengths andangles between vectors.Significance of the scalar product sign.The determinant of a vector...
- Q Maximization by the simplex methodSolve the following linear programming problems using thesimplex method.1>.Maximize z = x1 + 2x2 +3x3subject to x1 + x2 +x3 ? 122x1 + x2 + 3x3...
- Q can a polar graph exhibit symmetry, even if it fails algebraicsymmetry test? If so, give an example.
- Q Letf?(t) ?={70 ??? t ??? 2?cos(5t)2? ?<? t ??? 4?e3(t?4?)t ?>? 4?(a)?f?(t) can be written in the formg1(t) ?+?g2(t)U(t ?2?) ?+?g3(t)U(t ?4?)where U(t) is the Heaviside function. Enter thefunctions g1(t),g2(t),...
- Q A conical container of radius 10ft and height 40ft is filled toa height of 38 ft of a liquid weighing 62.4 lb/ft^3. How much workwill it take to pump the...
- Q Find a, b, c, and d such that the cubic functionf(x) = ax3 + bx2 + cx + dsatisfies the given conditions.Relative maximum: (3, 9)Relative minimum: (5, 7)Inflection point: (4,...
- Q How can you determine if two lines are parallel, perpendicular,or neither ?
- Q diameter: 1.90, 3.30, 4.23, 6.04 and 6.60 and theircorrosponding circumferences are 5.93, 10.45, 13.30, 18.45 and21.20 respectively (Note: both are measured in centimeters). Now,use these data to obtain the following:1....
- Q [2 marks] Suppose that the characteristic polynomial of thefollowing Cauchy-Euler equationx2?y?? +?x?y? + ??y?=? 0has roots m1 ?=? 2 ? 3i, andm2 ?=? 2 + 3i. Find ? and?.Enter the...
- Q a.) Using disks or washers, find the volume of the solidobtained by rotating the region bounded by the curves y=1/x, y=1/x,y=0, y=0, x=1, x=1, and x=3x=3 about the xx-axis.b.) Using...
- Q Test ReviewPart IIn two or more complete sentences, describe thetransformation(s) that take place on the parent function,f(x) = log(x), to achieve the graph of g(x) =log(-3x-9) + 1.In two or...
- Q Geometric NetsSuppose you could split open and flatten an ice cream cone.Before doing so, you measure the circumference around the top ofthe cone and find it is 9.4 inches.What is...
- Q Question 1a. cos ? =-24/25, ? in quadrant 3, find sin ?b. sin ?=12/13, ? in quadrant 2, find cos ?c.cos ? =12/13,270 degrees<? <360 degrees, find sin ?d.find the...
- Q Two linearly independent solutions of the followingequation(1 ? x)?y? ?+?x?y? ??? y ?=? 0are ?y1(x) ?=?4ex and?y2(x) ?=? 8x.(a)Find the WronskianW(y1,?y2) ofy1 and y2.(b)Using the method of variation of parameters,...
- Q Question : y'''+4y' =0 , y'''-2y''+4y'-8y=0 , y'''-3y''+3y'-y=0, y^4 -4y'''+6y''-4y+y=0 , y^4+6y''+9y=0 , y^6+y'''=0
- Q A farmer is going to divide her 60 acre farm between two crops.Seed for crop A costs $20 per acre. Seed for crop B costs $40 peracre. The farmer can...
- Q A tank contains 220 L of pure water. Solution that contains 0.08kg of sugar per liter enters the tank at the rate 8 L/min, and isthoroughly mixed into it. The...
- Q A thermometer is taken from a room where the temperature is 23oCto the outdoors, where the temperature is ?1oC. After one minutethe thermometer reads 15oC.(a) What will the reading on...
- Q 1. triple integral... first form 0 to pi, second from 0 to pi/3,third to sec(phi) to 2 of p^2*sin(phi) dp d(phi) d(theta)2. triple integral... first form 0 to pi, second...
- Q Determine los extremos relativos de las siguientes funciones.Determine the relative extremes of the following functionsf(x,y)=9-(x2+y2-2x+1)1/2 f(x,y)=y4-4y3+2x2+8xy
- Q Which of the following sets of functions are linearlyindependent on the interval (??,??)?(i) ?f1(x) ?=?x, f2(x)?=?6x, f3(x)?=? x2 + 3(ii) ?f1(x) ?=?2e2x, f2(x)?=?4e4x, f3(x)?=? 8e8x(iii) ?f1(x) ?=?4sin2x, f2(x)?=?10cos?2x, f3(x)?=? x(A) (ii) only (B) (iii) only (C)...
- Q A pilot on a heading of 320o with an air speed of 240km/h. Her actual ground velocity is 250 km/h at a bearing of318o. Calculate the speed and direction of...
- Q A. In the following parts, consider the function f(x)=1/3x^3+3/2x^2?4x+ 7(a)Find the intervals on which f is increasing/decreasing andidentify any local extrema.(b) Find the intervals on which f is concave up/down...
- Q Prove the transitivity of similarity: If ? ???~ ? ??? and ? ???~? ??? then ? ???~ ? ???. Write this proof in the numberedstatements and reasons style.and also a...
- Q An airplane is flying at an air speed of 420 km/h on a headingof 210o. A 45 km/h wind is blowing from a bearing of50o. Determine the bearing and ground...
- Q Find the Fourier cosine and sine series of f(t) = t^2 ,0 < t< ?
- Q Findthe general solution of the differential equations.A:cos(x)y?(x) +y(x) sin(x) = 0B:2xy +(x2 + y2)y? = 0C:(4x3+2xy2 +1)dx+(2x2y?1)dy=0.D:x(4x3+2xy2 +1)dx+x(2x2y?1)dy=0withsteps please.
- Q Let Vector_1=[Column (1&-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&...Let Vector_1=[Column (1&-2&1)],Vector_2=[Column(2&-1&1)],Vector_3=[Column(-2&-2&0)],Vector_4=[Column(1&-2&-2)].Show that S={Vector_1,Vector_2,Vector_3,Vector_4} is linearlydependent.Show that Vector_3 can be written as a linear combination ofVector_1,Vector_2 and Vector_4.Show that T={Vector_1,Vector_2,Vector_4} is linearlyindependent.Show that the set of all...
- Q Jeannie makes flower arrangements. she has 13different cut flowers and plans to use 5 of them. how manydifferent selections of the 5 flowers are possible?
- Q Find point PP that belongs to the line and direction vector vvof the line. Express vv in component form. Find the distance fromthe origin to line L. 251. x=1+t,y=3+t,z=5+4t,x=1+t,y=3+t,z=5+4t,t?R answers...
- Q The demand function for a particular product is given byD(x)=3x2?7x+110????????????????D(x)=3x2?7x+110 dollars, where x isthe number of units sold. What is the marginal revenue when 44items are sold? Round your answer...
- Q 1. Find p and graph the parabola y+12x?2x^2=162. Find e, d and determine which conic that has the equation r=4 / 5 - 4sin(theta)Please show steps. Thanks a lot.
- Q 3. a) Consider the vector field F(x, y, z) = (2xy2 z, 2x 2 yz,x2 y 2 ) and the curve r(t) = (sin t,sin t cost, cost) on theinterval...
- Q A company manufactures x units of Product Aand y units of Product B, on two machines, I andII. It has been determined that the company will realize a profitof $2/unit...
- Q Find all zeros of the polynomial function. Use the RationalZero? Theorem, Descartes's Rule of? Signs, and possibly the graphof the polynomial function shown by a graphing utility as an aid...
- Q Find a polynomial function P of the lowest possible? degree,having real? coefficients, a leading coefficient of? 1, and withthe given zeros. 1+3i?, -1?, and 2?
- Q I am stuck on these:Find or Calculate the derivative of the function.y = (x0.3 ?3x ? 6)(x?1 +x?2)f(x) =(6.4x ? 6)?2 + (4.3x? 1)?2f(x) =5x + x2h(x) =4x2 ?xr(x) =ln(x...
- Q Solve the following IVP specifically using the Laplace transformmethod(d^3)x/d(t^3)+x=e^(-t)u(t) f(0)=0 f'(0)=0 f''(0)=0where u(t) is the Heaviside step function
- Q Find the constants a, b, c, d, e, r0, r1 for the ellipse r=15/(3?2cos?) and sketch the graph.
- Q Describe the level surfaces of G(x,y, z) = 1 – y^2 – z. Makesure to provide all the following: their equations, types, plots,and a short word description of their geometric...
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