Basic Math question and answers for August 16, 2023
- Q Using the methods of Lagrange multipliers, find out the point onthe plane 2x+y-2z=5 closest to the origin. Please show allwork.
- Q 6) Evaluate using U-Substitutiona) x2x3+5dx          ;      Let U = x3 + 5b) e5xdx           ;       Let U = 5xc) dx25-x2           ;        Let x = 5 sinU  d) (sec2(1 - 4x) dx01(3t-1)50 dt
- Q Solve linear equations by Gaussian Elimination2x-3y+z-w+u=04x-6y+2z-3w-u=-5-2x+3y-2z+2w-u=3
- Q Solve for​ Y(s), the Laplace transform of the solution​ y(t) tothe initial value problem below. y'''+7y''+4y'-12y= -24, y(0) = 11,y'(0)= 5, y''(0) = -43
- Q Let f(t) be the weight (in grams) of a solidsitting in a beaker of water after t minutes have elapsed.Suppose that the solid dissolves in such a way that the...
- Q (1 point) If C is the curve given byr(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radialvector field F(x,y,z)=xi+yj+zk, compute the work done by F on aparticle moving along C.
- Q 688^79 mod 3337 (i think it is about RSA and I want the detailstep)Thanks
- Q UseEuler's Method to make a table of values for the approximatesolution of the differential equation with the specified initialvalue. Use n steps ofsize h. (Round youranswers to six decimal places.)y'...
- Q Consider the following vectors:→a =5−133→b =5010→c =−103−3−7For each of the following vectors, determine whether it is inspan{→a, →b, →c}. If so, express it as a linear combination usinga, b, and...
- Q Prove that the angle bisectors of a triangle are concurrentusing the Pointwise Characterization of an Angle Bisector.
- Q Suppose a system of linear equations has 2 equations and 3variables.(a) True or False: The system could have no solutions.(b) Produce an example of a system with 2 equations and...
- Q Because of the relatively high interest rates, most consumersattempt to pay off their credit card bills promptly. However, thisis not always possible. An analysis of the amount of interest paidmonthly...
- Q Use the definition of Taylor series to find the first threenonzero terms of the Taylor series (centered at c) for thefunction f.f(x) = 7 tan x,  c = 9π
- Q T::R2->R2, T(x1,x2) =(x-2y,2y-x). a) verify that thisfunction is linear transformation. b)find the standard matrix forthis linear transformation. Determine the ker(T) and the range(T).D) is this linear combo one to one?...
- Q A pair of fair dice are rolled once. Suppose that you lose $7 ifthe dice sum to 3 and win $12 if the dice sum to 4 or 12. How...
- Q Using either logarithms or a graphing​ calculator, find the timerequired for ​$5000 to be at least equal to ​$9000 when depositedat 5 ​% compounded monthly.
- Q Describe the method of establishing and evaluating for a tripleintegral. Provide an example using one of the following options:(a) iterated triple integral, (b) use of spherical coordinates, (c)use of cylindrical...
- Q Consider f(x) = 2 + 3x2 − x3a) Find local max and min valuesb) Find intervals of concavity and infection points
- Q Find all the vectors in R4 that are perpendicular to the threevectors <1,1,1,1>, <1,2,3,4>, and <1,9,9,7>
- Q (a) Find symmetric equations for the line that passes throughthe point(5, −5, 6)and is parallel to the vector−1, 3, −2.−(x − 5) = 3(y + 5) = −2(z − 6).x...
- Q Let g(x) = 1/(x + 1)(a) Does g satisfy the conditions of the Mean Value Theorem overthe interval [1, 3]? Explain.(b) Find a number c that satisfies the conclusion of...
- Q Draw a convex quadrilateral ABCD, where the diagonals intersectat point M. Prove: If ABCD is a parallelogram, then M is themidpoint of each diagonal.
- Q The Alaskan oil fields, in operation since 1977, had anestimated reserve of 4.9 billion barrels in 1999. In 2009, thefields had an estimated reserve of 3.5 billion barrels. Assume therate...
- Q A box has a bottom with one edge 7 times as long as the other. If the box has no top and the volume is fixed at ?V, what dimensions...
- Q f(t) = 1- t 0<t<1a function f(t) defined on an interval 0 < t < L is given.Find the Fourier cosine and sine series of f and sketch the graphsof...
- Q A road perpendicular to a highway leads to a farmhouse located22 mile away. An automobile traveling on the highway passes throughthis intersection at a speed of 55mph.55mph.How fast is the...
- Q a) How many ways can the letters of the word COMPUTER bearranged in a row?b) How many ways can the letters of the word COMPUTER bearranged in a row if...
- Q a dead body was found within a closed room of a housewhere the temperature was at 21°C. at the time of discovery thecore temperature of the body was determined to...
- Q Belirli bir radyoaktif maddenin, miktarıyla orantılı bir hızlayok olduğu bilinmektedir. Eğer başlangıçta 50 mg madde varsa ve 2saat sonra maddenin başlangıçtaki kütlesinin %10 unun yok olduğugözlenmiş isea) Herhangi bir t...
- Q Consider the boundary value problem X ′′ +λX=0 , X ′ (0)=0 ,X′(π)=0 . Find all real values of λ for which there is anon-trivial solution of the problem and...
- Q Consider the function f(x) = 3/(3x+ 4), c= 0 a)Find the powerseries for the function centered at c b)Determine the interval ofconvergence
- Q A​ sparkling-water distributor wants to make up 200 gal ofsparkling water to sell for $5.00 per gallon. She wishes to mixthree grades of water selling for$99​.00, ​$22​.00, and​ $4.50 per​...
- Q The number of bacteria after ? hours in a controlled laboratoryexperiment is ? = ?(?).a. Describe the meaning of ?′(4) and include right units.b. If the supply of nutrients is...
- Q A water trough is 8 m long and has a cross-section in the shapeof an isosceles trapezoid that is 30 cm wide at the bottom, 80 cmwide at the top,...
- Q A quadratic function f is given.f(x) = x2 + 6x + 8(a) Express f in standard form.f(x)=(b) Find the vertex and x- and y-intercepts off. (If an answer does not...
- Q A bakery makes Jumbo biscuits and Regular biscuits. The bakeryis limited to: a. The oven can bake at most 150 biscuits per day.b. Each jumbo biscuit requires 2oz of flour...
- Q An air traffic controller spots two airplanes at the samealtitude converging to a point as they fly at right angles to eachother. One airplane is 120 miles from the point...
- Q The cleaning process of a certain industrial tankconsists of 2 phases:• Phase 1: It begins by placing 2,000 L of water in the tanktogether with 100 kg of a certain...
- Q 1.Explain the difference between the difference quotient and averagerate of change . create a problem for your classmates a problem tosolve using the avergae rate of change .2. A classmate...
- Q {sinx, 2cosx, 3sinx+cosx} find the wronskian solution.
- Q Â Create a function f(x) of at least degree 3 that has at least three terms. For that function, use derivatives to find the following information:1. The function needs to have...
- Q Consider the polynomial f (x) = 125x5 − 275x4 − 2265x3 −3213x2 − 1728x − 324 and c = −3/5 is a zero of multiplicity 3. findthe rest of the...
- Q a) Let D be the disk of radius 4 in the xy-plane centered at theorigin. Find the biggest and the smallest values of the functionf(x, y) = x 2 +...
- Q Suppose that a cup of soup cooled from 90C to 60C after 15minutes in a room whose temperatures was 20C. Use Newton's law ofcooling to answer the following questions.a. How...
- Q Find the work done by the force field F(x,y,z)=8x^2yzi+5zj-4xykr(t)=ti+t^2j+t^3k (0
- Q Find volume of D enclosed by surfacesz = x² + 3y² and z = 8 - x² - y²
- Q Use symmetry and the region area formula under the parametriccurve to calculate the area of the region enclosed by theastroid.x= a cos^3(t)y= a sin^3(t)0 < t < 2pia= 3
- Q The Digital Star Company makes two different models of computertablets, which are assembled on two different assembly lines. Line1 can assemble 30 units of the Star model and 40 units...
- Q 5. Equations of the form y’ = P(x)*y^2 + Q(x)*y + R(x) arecalled Riccati equations.i) If we know a solution y = φ(x) of this equation, then anyother solutioncan be...
- Q For each graph below, state whether it represents a function.
- Q In each case, check that { v1,...vn} is a basis for R^n, andexpress the given vector b as a linear combination of the basisvectors.(a). v1=(2,3), v2=(3,5). b=(3,4)(b) v1=(1,0,3), v2=(1,2,2), v3=(1,3,2)....
- Q 1. The time rate of change of a rabbit population P isproportional to the square root of P. At time t = 0 (months) thepopulation numbers 100 and after 8...
- Q For each graph below, state whether it represents a function.
- Q For each graph below, state whether it represents a function.
- Q For each graph below, state whether it represents a function.
- Q For each graph below, state whether it represents afunction.
- Q An xy trail M is greedy if every edge incident to y is containedin M. Let H be an Eulerian graph, and let x be a vertex in H. Provethat...
- Q A mass weighing 16 pounds stretches a spring 8/3feet. The mass is initially released from rest from a point 3 feetbelow the equilibrium position, and the subsequent motion takesplace in...
- Q Evaluate the iterated integral.π07x0xz13x2 sin y dy dz dx0
- Q use the four step process to find f'(x) and the find f'(4) f'(6)and f '(8)f(x)= 10 square root x+2a. f'(x)b. f'(4)c. f'(6)d. f'(8)
- Q A company produces a special new type of TV. The compant hasfixed costs of $471,000 and it costs $1200 to produce each Tv. Thecompany projects that if it charged $2300...
- Q 1. For the function ?(?)=−3(?−1)^2+5, choose a domainrestriction to make ?(?) a one-to-one function, and then find theinverseof ?(?).2. For the following function, find the horizontal and verticalasymptote(s):?(?)=3?^2+3?−18 /?^2+5?+63. Find...
- Q 1- Find the solution of the following equations. For eachequation, 2- determine the type of the category that the equationbelongs to. Separable equation, Homogenous equation, Linearequation, or Bernolli equation?1. ydx...
- Q The volume of a large cube is 64 cubic inches. A new shape isformed by removing a smaller cube from one corner of the largercube. What is the surface area...
- Q For examples 1, you will consider a standard 4-year car loan of$10,000, with 6% APR compounded monthly. Payments are $234.85 permonth, assuming $0 down payment. All of our expected values...
- Q A young couple buying their first home borrow $65,000 for 30years at 7.4%, compounded monthly, and make payments of $450.05.After 5 years, they are able to make a one-time payment...
- Q Fertilizer with weed control costing $38 per pound bag is to bemixed with less expensive fertilizer costing $6 per 50 pound bag tomake 16 bags of fertilizer that can be...
- Q Suppose that y′=0.162sin2(ty)+1. Plot y(t) from t=0to t=4 with y(0)=1.286 using Euler's method with a step size of0.4.
- Q Â A rock is thrown upward from a bridge that is 83 feet above a road. The rock reaches its maximum height above the road 0.61 seconds after it is thrown...
- Q 2. Find all eigenvalues and corresponding linearly independenteigenvectors of A = [2 0 3 4] (Its a 2x2 matrix)4. Find all eigenvalues and corresponding linearly independenteigenvectors of A = [1...
- Q Apply the Gram-Schmidt orthonormalization process to transformthe given basis for Rn into an orthonormal basis. Use the vectorsin the order in which they are given. B = {(1, 3, 0),...
- Q find Fourier series of periodic function ?(?) = { −?, −1 ≤ ? ≤ 0with the period 2{ ?, 0 ≤ ? ≤ 1
- Q let G = D2n ={e,r,r^2,...,rn-1,s,sr,sr2,..,srn-1}a diedergroup of order 2n, where n >=3(a) prove that [G,G] = <r2>(b) prove that G/[G,G] consists of two elements if n is uneven and4 elements...
- Q Homework #3a) Find the point of intersection of the line x = 2-3t, y = 3 +t, z = 5t and the plane 3x-2y + z = 5b)Find the equation...
- Q company manufactures a series of 20-in. flat-tube LCDtelevisions. The quantity x of these sets demanded each week isrelated to the wholesale unit price p by the followingequation.p = −0.007x +...
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