Basic Math question and answers for August 07, 2023
- Q Suppose that we have a rectangle ABCD with AB = 4 inches and BC= 16 inches.Find the perimeter of a square that has the same area isABCD.Find the length and...
- Q Two ships leave the same port at noon. Ship A sails north at 14mph, and ship B sails east at 17 mph. How fast is the distancebetween them changing at...
- Q Determine which of the following vector fieldsF in the plane is the gradient of a scalarfunction f. If such an f exists, find it. (If ananswer does not exist, enter...
- Q Evaluate the integral using partial fractions. ∫▒( x+3)/((x-9)^2(x+2))
- Q find a particular solution toy'' + 5y' + 6y = 18te3tYp=?
- Q 1. A tank starts with 100 litres of water and 1,000 bacteria init. For now we assume the bacteria do not reproduce. Let B(t) bethe number of bacteria in the...
- Q Find the equation of the osculating circle at the local minimumoff(x)=4x^3−9x^2+(15/4)x−7.
- Q  (a) Determine the point of intersection of the line given by (x, y, z) = (4+t, −1+8t, 3+2t), t ∈ R with the plane given by 2x − y +...
- Q Two boats are leaving port at the same time. Ship A is sailingdue east at 40 km/h, and Ship B due south at 30 km/h. How fast arethey moving away...
- Q ind the intervals of increase or decrease, the local maximum andminimum values, the intervals of concavity, and the inflectionpoints for each of the following:?(?)=2?^3―3?^2―12??(?)= ? (Square root) ?+3?(?)=ln(?^4+27)
- Q [x^4e^-x] from 0 to infinity
- Q Let f(x,y) = 3x3 + 3x2 y − y3 −15x.a) Find and classify the critical points of f. Use any methodtaught during the course (the second-derivative test or completingthe square).b)...
- Q 1. Consider the spiral S in the xy-plane given in polar form byr = e ^θ . (a) (5 points) Find an arc length parametrization for Sfor which the reference...
- Q The consumer demand equation for tissues is given byq = (100 −p)2,where p is the price per case of tissues and qis the demand in weekly sales.(a) Determine the price...
- Q Find the coordinates of all local extrema and inflections of y =x − 4√x. Give the intervals where the function is increasing,decreasing, concave up, and concave down.
- Q Find two positive integers such that the sum of the first numberand four times the second number is 100 and the product of thenumbers is as large as possible.please double...
- Q Consider the equation below. (If an answer does not exist, enterDNE.)f(x) = e^(3x) + e^(−x)(a)Find the interval on which f is increasing. (Enter your answerusing interval notation.)Find the interval on...
- Q use laplace transform to solve the initial valueproblem x'' +3x'-10x=5e^-4t; x(0)=3, x'(0)=-10
- Q consider the following planes.-3x+y+z=318x-6y+3z=9a.) find the angle between the two planes. (round your answer totwo decimal places.)b.) find a set of parametric equation for the line of intersectionof the planes....
- Q 1) Solve the given quadratic equation by usingCompleting the Square procedure and byQuadratic formula ( you must do it both ways).Show all steps for each method and put your answer...
- Q Find the eigenvalues and eigenfunctions of the given boundaryvalue problem. Assume that all eigenvalues are real. (Letn represent an arbitrary positive number.)y''+λy=0，y（0）= 0，y'（π）= 0
- Q company makes two types of biscuits: Jumbo and Regular. Theoven can cook at most400 biscuits per day. Each jumbo biscuit requires 2 oz offlour, each regular biscuit requires 1 oz...
- Q Find the Taylor series for f(x)= ln(2+x) centered at x=0 andcompute its interval of convergence. Show all work and use propernotation.
- Q Abdul is making a map of his neighborhood. He knows thefollowing information:His home, the middle school, and high school are all on thesame street.His home, the elementary school, and his...
- Q Use the simplex method to solve the linear programmingproblem.Maximize objective function: Z= 6x1 + 2x2Subject to constraints:3x1 + 2x2 <=9x1 + 3x2 <= 5when x1, x2 >=0
- Q Use the trapezoid rule, midpoint rule, and Simpson’s rule toapproximate the given integrals with the given values of n.?) ∫ ? ? / 1+? 2 ?? (from 0 to 2)   ?...
- Q area between curves1. Find the area between x=1 and x=3 for: f(x) = x+4 andg(x)=12. Find the area between x =-1 and x=1 for: f(x) = 2-x^2 andg(x) =33. find...
- Q 2. a. A particle moves in a straight line along with the ? −???? its displacement is given by the equation ?(?) = 5? 3 − 8? 2 +12? +...
- Q b) a matrix is skew symmetric if AT=-A.If A is askew-symmetric matrix of odd order,show that A is notinvertiblec)Let A and B be n*n matrixes with detA=detB not equal to...
- 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.)40ln(3 + ex) dx,    n =...
- Q Solve the following system of equations using matrices(rowoperations). If the system has no solution, say that it isinconsistent.x - 3y + 4z = 232x + y + z = 4-3...
- Q Find the length and width of a rectangle whose perimeter is 21meters and whose area is 20 square meters.Assign variables to the unknown(s)...Form a system of equations...Solve the system and...
- Q At a price of ​$2.25 per​ bushel, the supply of a certain grainis 7400 million bushels and the demand is 7700 million bushels. Ata price of ​$2.3 per​ bushel, the...
- Q Suppose that a cell culture that exhibits exponential growth hasa growth constant of λ = 0.05 per day. Find the amount of time ittakes for the initial amount of bacteria...
- Q Determine whether the integrals are divergent or convergent.Calculate the convergent ones.?)∫ 1 / ?^2+? ?x (from 1 to positive infinity)?) ∫ ? −√? / √? ?? ( from 1 to...
- Q Differentiate the following:1) f(x) = √2x-4. (all under square root)2) f(x) = x/5-x3) y=cos(4x^3)4) f(x)=tan(x^2)5) f(x)= 3e^2x cos(2x)6) y= sin2x/cosx7) y= √sin(cosx) (all under the square root)
- Q Find the solutions ofy'' + 4y' + 3y = sen(x) + 3 cos(2x) + e˄(−x)+ 2 x˄2
- Q 1. Solve the initial value problemsa.) y\"-10y'+25y=e^5x, y(0)= 1 and y'(0)= 6b.) y\"+y'-2y=2sin(x), y(0)= 1 and y'(0)= 2c.) y\"+14y'+49y=0, y(0)= -1 and y'(0)= 92. Find a two-parameter family of solutions...
- Q By cutting away identical squares from each corner of arectangular piece of cardboard and folding up the resulting flaps,an open box may be made. If the cardboard is 15 in....
- Q determine which is the integrating factor and the solution ofthe DE: y (6 + 12x + 4y ^ 2) dx + x (12 + 16x + 12y ^ 2) dy...
- Q Show the complete solution.Determine the unit tangent vector (T), the unit normal vector(N), and the curvature of ?(?) = 2? ? + ?^2 ? – 1/3 ?^3 k at t...
- Q Suppose that a triangle has sides of length a = 15 cm, b = 37cm, and c = 29 cm, then α = _______, β = ______., and γ =______...
- Q Solve the system below having the initial valuesx(0) = 1 = y(0)x’ = x + 2yy’ = -5x + 3yPlease use solving systems of linear des by elimination. ThankYou
- Q Show the complete and neat solution.1. A plane through the origin is perpendicular to the plane 2? −? − ? = 5 and parallel to the line joining the points...
- Q A farmer decides to enclose a rectangular​ garden, using theside of a barn as one side of the rectangle. What is the maximumarea that the farmer can enclose with 60...
- Q Use the method of this section to solve the linear programmingproblem.Minimize  C = 2x −3y + 6zsubject to  −x+2y−z≤9x−2y+2z≤102x+4y−3z≤12x ≥ 0, y ≥ 0,z ≥ 0  The minimum is C =  at (x,...
- Q why is the reflection of y=-(x+2)2 +3 the same as thereflection of -y=(x+2)2-3I know they're the same algebraically but which vertical shiftto do -3 or +3 ?? and how do...
- Q Show complete solution1. Show that the lines ?/1 = y+3/ 2 = z+1/3 and x-3/2 = y/1 =z-1/-1 intersect by finding their point of intersection. Find theequation of the plane...
- Q A farmer wants to fence in a rectangular pasture of1.5 million square feet and then divide the pasture in half with afence parallel to the sides of the rectangle. How...
- Q Analyze and sketch the curve y = x3 − 6x2 +9x. A full analysis includes the following:critical points, intervals of increase/decrease,concavity, points of inflection, domain and range, intercepts.Organize your...
- Q A hotel has 210 units. All rooms are occupied when the hotelcharges ​$90 per day for a room. For every increase of x dollars inthe daily room​ rate, there are...
- Q Â How much of each a 10% gold alloy and a 24% gold alloy should be mixed together to make 40 grams of a 22% gold alloy?A cold water faucet can...
- Q A milk truck carries milk with density 64.6 lb/ft3 in ahorizontal cylindrical tank with diameter 4 ft. (a) Find the forceexerted by the milk on one end of the tank...
- Q Prove that the four triangles of an orthocentric system have thesame orthic triangle and the same nine point circle.
- Q The distance between the parallel planesax + by +cz + d1 = 0 andax + by + cz+ d2 = 0isD =|d1 − d2|a2 + b2 +c2.Find equations of the...
- Q Consumers' Surplus The demand function for a certain model ofBlu-ray player is given by p = 600 0.5x + 1 where p is the unitprice in dollars and x (in...
- Q What are the dimensions of a rectangle whose perimeteris 5600 units and whose area is as large as possible?
- Q A) Find the equation of the tangent line to the curve y= 5e-8x at the point (0, 5).B) Solve for t.e0.09t = 9C) Rancher Johann wants to build a three-sided...
- Q By cutting away identical squares from each corner of arectangular piece of cardboard and folding up the resulting flaps,an open box may be made. If the cardboard is 15 in....
- Q Is there a fourth degree polynomial that takes these values?x1-203-17y-2-56-24-16376
- Q Let C be the curve of intersection of the parabolic cylinder x2= 2y, and the surface 3z = xy. Find the exact length of C from theorigin to the point(5,...
- Q An application of modeling with differential equations from aparticular field, such as Physics,Biology, Business, Chemistry,etc.
- Q 1) Find the critical numbers of the function. f(θ) = 16 cos θ + 8 sin^2 θθ=?2) Find the absolute maximum and absolute minimum values of f on the given interval.f(x)...
- Q Suppose f is defined by f(x)=3x/(4+x^2), −1≤x<3.What is the domain of f?Find the intervals where f is positive and where f isnegative.Does f have any horizontal or vertical asymptotes. If...
- Q Solve the differential equation by variation of parameters.2y'' + y' = 6x
- Q Consider a single source procurement situation: You have ademand rate of 151 units per period, replenishment rate of 2,550units per period, lead time of 8 periods, item cost of 21.18,...
- Q Find the area of the following region. The region inside theinner loop of the​ limaçon r = 7 - 14 cos theta
- Q Solve : y''+2y'+y=e^-x + sinx by Undetermined Coefficientsmethod and Variation of Parameters
- Q Consider the equation below. (If an answer does not exist, enterDNE.) f(x) = x3 − 9x2 − 21x + 9(a) Find the interval on which f is increasing. (Enter youranswer...
- Q Consider the function f(x, y) = 4xy − 2x 4 − y2 .(a) Find the critical points of f.(b) Use the second partials test to classify the criticalpoints.(c) Show that...
- Q Theproduct of two positive real numbers x and y is 10. Find theminimum value of the expression 2x+y
- Q Let the cardinal number of N, the set of all natural numbers, be×0. Prove that the product set N × N = {(m,n);m ∈ N,n ∈ N} has thesame cardinal...
- Q A 39-inch by 104-inch piece of cardboard is used to make anopen-top container by removing a square from each corner of thecardboard and folding up the flaps on each side....
- Q Â In your own words, describe why the graph of a rational function can cross its horizontal asymptote but it can never cross a vertical asymptote.
- Q Using the formulas given in class for continuous and compoundinterest, show your calculated values for each investmentbelow.A) Placing $875 in an account giving 13.5% APR compounded dailyfor 2 years:B) Placing...
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