Basic Math question and answers for August 18, 2023
- Q The effect of applying x milligrams of drug A and y milligrams of drug B is measured by f(x, y) = xy - 2x2 - y2 + 120x + 40y +...
- Q The pressure exerted by a certain liquid at a given point variesdirectly as the depth of the point beneath the surface of theliquid. The pressure at 80 feet is 320...
- Q Maximizing Profits The quantity demanded each month of theWalter Serkin recording of Beethoven's Moonlight Sonata, producedby Phonola Media, is related to the price per compact disc. Theequation p = −0.00044x...
- Q √xy+2x=√y . Use implicit differentiation to find y’.
- Q A rectangular storage container with an open top is to have avolume of 22 cubic meters. The length of its base is twice thewidth. Material for the base costs 11...
- Q Solve the c, d, e, f from the given equations.e+2f=-12d+e=-0.22c+d+3e+4f=-0.5-e-2f=1
- Q A heavy rope, 60 ft long, weighs 0.8 lb/ft and hangs over theedge of a building 110 ft high. How much work is done in pullingthe rope to the top...
- Q For the equation x^2+xy+y^2=0, find the equation of the normalto the tangent line at the point (−3,−1)(-3,-1).
- Q Let s(t)= ?? ? − ??? ? − ???? be the equation for a motionparticle.Find: a. the function for velocity v(t). Explain. [10]b. where does the velocity equal zero? Explain....
- Q Question1:x=2-t, y=3-2t, z=4-3ta) Explain why the work done by a force field ?(?, ?, ?) is theline integral ∫c ? ∙ ?? where C is a curve defined by ?(?)...
- Q Determine the next number in the sequence: a) 1/4. 4/9. 3/5.8/11. 5/6. 1/32.b) How is the relation of the sequence in \"a)\" different from:1. 4. 11. 29. 76. 199.
- Q At what point does the normal to y=1−3x−x2y=1−3x−x2 at(1,−3)(1,−3) intersect the parabola a second time?Hint: The normal line is perpendicular to thetangent line. If two lines are perpendicular their slopes...
- Q The temperature T in a metal ball is inverselyproportional to the distance from the center of the ball, which wetake to be the origin. The temperature at the point (1,...
- Q A)17= 0.03x^2+0.56x+8.63B) 4= 0.03x^2+0.56x+8.63Solve for x
- Q Consider the functionT:R3→R3defined byT(x,y,z) =(3x,x−y,2x+y+z).(i) Prove thatTis a linear transformation. (T’ninbir lineer d ̈on ̈u ̧s ̈um oldu ̆gunu g ̈osteriniz)(ii) Find therepresenting matrix ofTrelative to the basisβ={α1= (1,0,0),α2=(1,1,0),α3=(1,1,1)}ofR3.(R3 ̈unβ={α1=...
- Q The function​f(x,y,z)=4x−9y+7zhas an absolute maximum value and absolute minimum value subjectto the constraintx^2+y^2+z^2=146.Use Lagrange multipliers to find these values.
- Q A.) Find the partial derivative indicated. Assume the variablesare restricted to a domain on which the function is defined.z=sin(7x^3 y−3xy^4)B.)Compute the partial derivative: f(x,y)=sin(x^3−4y)fy(0,π)=C.) The equation r=5sinθ represents a circle....
- Q A box with an open top is to being created with a square pieceof cardboard 8 inches wide, by cutting four identical squares ineach corner. The sides are being folded...
- Q Consider the following function.g(x, y)  = e2x2 + 3y2 +12 y(a)Find the critical point of g.If the critical point is (a, b) then enter'a,b' (without the quotes) into the answerbox.(b)Using your critical point in...
- Q 1.2A large circle on a sphere is a circle that forms theintersection of the sphere with a plane through the center of thesphere. Consider the large circle C that arises...
- Q A piece of wire of length 50 is​ cut, and the resulting twopieces are formed to make a circle and a square. Where should thewire be cut to​ (a) minimize...
- Q A manufacture has been selling 1800 television sets a week at$390 each. A market survey indicates that for each $10 rebateoffered to a buyer, the number of sets sold will...
- Q For the first week of January 2020, Toronto Organic Coffee atEaton Centre sold a total of 8500 cups of organic coffee. The totalsales revenue for the coffee was $64,600. There...
- Q A square plot of land has a building 70 ft long and 60 ft wideat one corner. The rest of the land outside the building forms aparking lot. If the...
- 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 On this problem, you may use a computer to calculate thederivative. Consider the function f(t) = (2t^2) / (3t^2 + 1) :(a) On what intervals is the function concave up,...
- Q non-homogeneous ODE. solve this equation analytically.-2y''+5y'+3y=exp(-0.2x) b.c y'(0)=1, y'(10)=-y(10)
- Q Use the method of cylindrical shells to find the volumeV generated by rotating the region bounded by the givencurves about the specified axis.y = ex, x = 0, y =...
- Q Consider the function f(x)=arctan [(x+6)/(x+5)]Express the domain of the function in interval notation: Findthe y-intercept: y= . Find all the x-intercepts (enter your answeras a comma-separated list): x= . Does...
- Q Assume that when adults with smartphones are randomly​ selected,49​% use them in meetings or classes. If 15 adult smartphone usersare randomly​ selected, find the probability that exactly 11 ofthem use...
- Q Let A0.A1,A2,A3,A4 devide a unit circle (circle of radius one)into five equal parts. Prove that the chords A0 A1, A0 A2satisfy:(A0 A1 * A0 A2)^2 = 5.
- Q A swimming pool is 20 ft wide, 40 ft long, 3 ft deep at theshallow end, and 9 ft deep at is deepest point. A cross-section isshown in the figure....
- Q The flat circular plate has the shape of the region ? 2 + ? 2 ≤4. The plate, including the boundary ? 2 + ? 2 = 4, is heated...
- Q Maricopa's Success scholarship fund receives a gift of $165,000.The money is invested in stocks, bonds, and CDs. CDs pay 3.5 %interest, bonds pay 3.1 % interest, and stocks pay 9...
- Q Determine the interval of convergence for the power seriesrepresentation of the following function.f(x)=(69x)/(4096x^6+1)
- Q Determine the centroid of the area bounded by x^2 − y = 0 and x− y = 0.
- Q 1) Inside the graph of r = 1 + cos 3Ό2) Inside the circle r = -6 cos Ό and outside the circle r =3
- Q Determine whether or not W is a subspace of R3 whereW consists of all vectors (a,b,c) in R3 such that1. a =3b2. a <= b <= c3. ab=04. a+b+c=05. b=a26....
- Q Estimate the area under the graph of f(x)=1/(x+4) over theinterval [-1,2] using five approximating rectangles andright endpoints.Rn=Repeat the approximation using left endpoints.Ln=
- Q Determine the first four terms of the Maclaurin series forsin(6)x and cos(7)x:b) By replacing x by (6)x and (7)x, respectively, in the powerseries for sin x and cos x
- Q 1) Aris uses a boat to cross from one side to the other side ofa river of width w = 32 m. The river flows at VC = 8 m/min....
- Q There are an infinite number of vector and parametric equationsfor a given plane. Why is the scalar equation of a given planeunique?
- Q Q(1): An object moving vertically is at the given heights at thespecified times. Find the position equations = 1/2at2 + v0t + s0for the object Att = 1 second, s...
- Q Find the family of curves orthogonal to: y4 =  k(x − 2)3.
- Q A certain element has a half life of2.52.5billion years.a. You find a rock containing a mixture of the element and lead.You determine that55?%of the original element? remains; the other9595?%decayed into...
- Q Solve y′′ + 4y′ + 3y = 15e^2t given y(0) = −7,y′(0) = 16 by themethod of Laplace transforms.
- Q If Dave is standing next to a silo of cross-sectional radiusr = 9feet at the indicated position, his vision will be partiallyobstructed. Find the portion of the y-axis that Davecannot...
- 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 Solve the given equation. 7 sin2(θ) − 36 sin(θ) + 5 = 0
- Q I planned on putting some math to work when I visited GoldenGate Park along with my new kite. I made sure my kite was always100ft above the ground and I...
- Q The number of customers in a local dive shop depends on theamount of money spent on advertising. If the shop spends nothing onadvertising, there will be 105 customers/day. If the...
- Q Part I: Constructing proofs.You must write down all proofs in acceptable mathematicallanguage: make sure you mark the beginning and end of the proof,define all variables, use complete, grammatically correctsentences, and...
- Q A farmer has 80 meters of fence to make an enclosure for his cows.The enclosure is divided into 2 sections by a fence parallel to one of the sides, as...
- Q A window has the shape of a rectangle surmounted by a semicirclesimilar to older buildings. The diameter of the semicircle is equalto the width of the rectangle. If the perimeter...
- Q A principal amount P0 is deposited in a bank account earning 3%interest compounded monthly. After 20 years there is $1000 in theaccount. What was the principal P0?Suppose you want to...
- Q What was the issue in the \"Blurred Lines\" Music case discussedin class?thesubject is business law
- Q There are four apples in a fruit basket which contains 10fruits. What fraction of the fruits are apples as it is (do notsimplify)?There are four apples in a fruit basket...
- Q Find a matrix representation of transformation T(x)=2x1w1+x2w2-3x3w3 from R3 to a vector space W, where w1,w2, and w3 ∈W. Clearly state how this matrix is representing thetransformation.
- Q The table below gives the net worth of the first 13 U.S.Presidents as measured in millions of 2010 dollars (that just meansthe numbers have been adjusted for inflation). President WashingtonAdams...
- Q Problem #2:Use separation of variables with λ = 36 to find aproduct solution to the following partial differentialequation,y∂2u∂x2 +  ∂u∂y =  0that also satisfies the conditions u(0, 0) = 9 andux(0, 0) = 4.
- Q Let R be the region bounded by the following graphs. Find thequantities below.y= (x−1)^2+ 1,y= 1,x= 0a. Volume of the solid formed by rotating R about the x-axis,using the shell...
- Q Solve the equation(? − 2)2 + 2?2 − 13? = 10by the method requested. Show the work in details. Do not skipany step. If steps are skipped you will receive...
- Q Consider the function on the interval (0, 2π).f(x) = sin(x) cos(x) + 2(a) Find the open interval(s) on which the function isincreasing or decreasing. (Enter your answers using intervalnotation.)increasing    ( )  decreasing    (...
- Q indicate which are the following options is the subsidiaryequation of the problem with initial conditions y(0) = 0 and y '(0)= 015 y + 8 y ′ + y ″...
- Q Suppose we know that the radius of a circle isincreasing at a rate of 10 feet each second, and we want to knowhow fast the area of the circle is...
- Q Find the reduced row echelon form of the following matrices.Interpret your result by giving the solutions of the systems whoseaugmented matrix is the one given.[ 0 0 3 -1 51...
- Q Let be the vector fieldAnswer by explaining as best you can.a. Can there be a flux curve in a horizontal plane?b. Can there be a flow curve in an ellipsoid?c....
- Q Verify that the indicated family of functions is a solution ofthe given differential equation. Assume an appropriate intervalI of definition for each solution.d^2y/ dx^2 − 6 dy/dx + 9y =...
- Q Find the extremum of​ f(x,y) subject to the given​ constraint,and state whether it is a maximum or a minimum.f(x,y)=(4x^2)+(3y^2)-4xy; x+y=22.Find the Lagrange function​F(x,y,lambda​).Find the partial derivatives.
- Q task one: Erika’s equations1. The point (1, 5) is on the curve: y = ax2 + bx + c. Thispoint gives the linear equation: 5 = a + b +...
- Q (a) Find the critical numbers of the functionf(x) = x8(x −1)7.(b) What does the Second Derivative Test tell you about thebehavior of f at these critical numbers?(c) What does the...
- Q Consider the following function:f (x , y , z ) = x 2 + y 2 + z 2 − x y − y z + x + z(a) This...
- Q 1. Find the absolute minimum and maximum value of f(x) = x4 −18x 2 + 7 (in coordinate form) on [-1,4]2. If f(x) = x3 − 6x 2 − 15x...
- Q Use Lagrange multipliers to find the maximum production levelwhen the total cost of labor (at $111 per unit) and capital (at $50per unit) is limited to $250,000, where P is...
- Q (a)Suppose that the tangent line to the curve y =f (x) at the point (−9, 53) has equationy = −1 − 6x. If Newton's method is used to locatea root of the...
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