Basic Math question and answers for August 13, 2023
- Q PROBLEM: Given f(x)=4x - x2 + k & (1,3+k) on thegraph of f.k = 2a) Write you equation after substituting in the value of k.b) Calculate the function values, showing...
- Q Find the particular solution to ?″+16?=−24sec(4?) Do not includethe complementary solution ??=?1?1+?2?2.
- Q A trough is filled with a liquid of density 850kg/m3. The ends of the trough are equilateral triangleswith sides 8 m long and vertex at the bottom. Find the hydrostaticforce...
- Q How many X intercept can the graph of a quadratic function have?How many Y intercepts? Explain your reasoning.
- Q Find the first five nonzero terms of the Maclaurin expansion off(x)=e^-xcos(x)(Use symbolic notation and fractions where needed.)
- Q Consider the following.y = −x3 + 6x2 +15x − 9Give the relative extrema and points of inflection. (If ananswer does not exist, enter DNE.)
- Q How many of the following characteristics can two differentlogarithmic functions share, while still remaining different?DomainRangey-interceptIntervals of increase or decreaseDecide how many key applicable characteristics there are andexplain with examples.
- Q Find equations of the following.2(x − 9)2 + (y − 6)2 + (z − 1)2= 10,    (10, 8, 3)(a) the tangent plane(b) the normal line(x(t), y(t), z(t))=
- Q Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 =x2 +y2. Show that these surfaces are tangent where they intersect,that is, for a point on the...
- Q What information about a graph can be found from the secondderivative? Explain
- Q Find the solution of the following nonhomogeneous linearsystemy1′ = y2 + 1 ,y2′ =−y1 + t.
- Q Poisoned water leaks from a crack in a storage tower at anincreasing rate of 6t L/day and flows into a pondcontaining 108 L of water. (Note: t is time in...
- Q maclaurin series
- Q 1.The graph of ​(x-1)^2+(y-1)^2=4 is shown on the right. Useimplicit differentiation to find the slopes of the tangent lines atthe points on the graph where x=2.2 .   Check your answers...
- Q Use implicit differentiation to find ∂z/∂x and ∂z/∂y if xz = cos(y + z).
- Q a. Squares with sides of length x are cut out of each cornerof a rectangular piece of cardboard measuring 5 ft by 4 ft. Theresulting piece of cardboard is then...
- Q Analysis of daily output by a factory employee shows that, onaverage, the number of units per hour produced after t hours on thejob can be modeled by y = 70t...
- Q Atank contains 100 gal of water. Brine enters the tank at the rateof 3 gal/min. The mixture, thoroughly stirred, leaves the tank atthe rate of 2 gal/min. If the salt...
- Q Casey’s theorem proof step by step
- Q Atank contains 100 gal of water. Brine enters the tank at the rateof 3 gal/min. The mixture, thoroughly stirred, leaves the tank atthe rate of 2 gal/min. If the salt...
- 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 474) Calculator exercise. Determine the principal diagonal ofthe inverse.A= [1 4 9 2 ] inverse(A) = A^(-1) = ai;|2 0 0 1 | Answers=ai11,ai22,ai33,ai44|2 0 1 2 | Â Â [1 9...
- Q 2.  PackagingBy 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 16 in....
- 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 In a typical optimization problem (max/min problem), we want tofind a relative maximum or relative minimum of a function. Ourprocess is to• find the derivative of the function,• set that...
- Q 1. Find the local maxima of the function:(1) f(x,y) = xy, subject to the constraint thatx+y-1=0. Result should be 1/4.2. Find the local minima of the functions:(1) f(x,y) = x^2+y^2,...
- Q 1) You drop a pebble into a well. 10 seconds later, you hear thesound of the pebble hitting the water. How deep is the well? Forwhat part of the 10...
- Q Thearea of a square is increasing at a rate of 2 square feet perminute. How fast is the perimeter changing in feet per minute whenthe area of the square is...
- Q A tank originally contains 100 gal of fresh water. Then watercontaining 1 2 lb of salt per gallon is poured into the tank at arate of 2 gal/min, and the...
- Q Derive expressions for the transverse modulus and thelongitudinal modulus of a 3-component composite
- Q (Optimization) A cylindrical container w/ circular base is tohold 64 in3. Find the dimension so that the amount of metalrequired is a minimum when the container is a) an open...
- Q Â Determine all the inflection points of g(x) = 3x2 - x3a) Only (1,2)b) Both (0,0) and (2,4)c) only (2,4)d) All of (0,0), (1,2), and (2,4)e) only (0,0)
- Q Determine the area of ​​the largest isosceles trianglethat can be written into the unit circle.It is advisable to let the corners in the triangle be given by(0.1), (x, y) and...
- Q 2. Sketch a function which satisfies both conditions OR statethat there is no such example.(a) Differentiable at x=0 AND not continuous at x=0(b) Not differentiable at x=0 AND continuous at...
- Q How to find the local extrema for y^3- 3yx^2 -3y^2-3x^2+1.Â
- Q Find the maximum area of a triangle formed in the firstquadrant by the x-axis, y-axis, and a tangent line to the graphf=(x+3)^-2. Area=?
- Q what are the impact test, and the types of impact testexplain in details with drawing
- Q Find the solutions to (-1+x^2)y''+4xy'+2y=0y_1=?y_2=?
- Q Consider the equation xln(x)= 1 for x≥1. In this problem, youare asked to show that this equation has a unique solution 1≤x<∞by completing both parts below. Note that you are...
- Q 1. List the possible rational zeros of the thepolynomial function. Do not find the zeros.f ( x ) = 3 x 5 − 5 x 2 + 6 x −...
- Q Sketch the graph of f by hand and use your sketch tofind the absolute and local maximum and minimum values off. (Enter your answers as a comma-separated list. If ananswer...
- Q Let {an} be a sequence defined recursively by a1 = 1 and an+1 =2√ 1 + an where n ∈ N(b) Does {an} converge or diverge? Justify your answer, makingsure...
- Q Find the absolute maximum and absolute minimum values off on the given interval.f(x) = x3 − 5x + 8,    [0, 3]absolute minimum value    absolute maximum value   Â
- Q 1. Find an equation of the tangent line to the graph of x^2 +4xy + y^2 =13 at point (2,1), by using implicitdifferentiation.
- Q 1.) Find the local maximum and minimum values and saddlepoint(s) (x,y,f) of the function. If you have three-dimensionalgraphing software, graph the function with a domain and viewpointthat reveal all the...
- Q Consider the following figure. A hexagon has six labeledvertices and a dashed line segment which divides the hexagon into atrapezoid and rectangle. The first side is horizontal, starts atvertex R,...
- Q Find the vertical asymptote (V.A.) and the horizontal asymptote(H.A.) of the function g(x) = 2x/ x- 5.Justify your answer using limits.a) The equation of the V.A. is ________ and the...
- Q Solve the given system of differential equations by systematicelimination.(D2 − 1)x−y=0(D − 1)x+Dy=0I had this as my answer and webassign rejected it:(x(t), y(t)) = c_1e^t+e^{-\left(\frac{t}{2}\right)}\left(c_2\cos\left(\frac{\sqrt{3}}{2}t\right)+c_3\sin\left(\frac{\sqrt{3}}{2}t\right)\right),e^{-\left(\frac{t}{2}\right)}\left(\left(-\frac{3}{2}c_2-\frac{3\sqrt{3}.}{4}c_3\right)\cos\left(\frac{\sqrt{3}}{2}t\right)+\left(\frac{-3}{2}c_3+\frac{3\sqrt{3}}{4}c_2\right)\sin\left(\frac{\sqrt{3}}{2}t\right)\right)
- Q The speed of a runner increased steadily during the first threeseconds of a race. Her speed at half-second intervals is given inthe table. Find lower and upper estimates for the...
- Q An isosceles right triangle, whose hypotenuse is 12 ft long, issubmerged vertically so that the hypotenuse is parallel to thesurface of the water. If its vertex is 3 ft above...
- Q 1. What is the difference between the Riemann integral and theDarboux Integral?2. Give the same characteristics between Riemann integrals andDarboux integrals !.
- Q Apply the eigenvalue method to find a general solution ofthegiven system.x'1 = 5x1-9x2, x'2=2x1 - x2
- Q The initial mass of a certain species of fish is 7 million tons.The mass of fish, if left alone, would increase at a rateproportional to the mass, with a proportionality...
- Q If you graph the function y = 3x  and y = 3–x  the graphs create a reflection about they-axis.  Explain why this occurs.Now, if you graph the function y = 3x  andy = -(3x)  the...
- Q Prove that the dual space of l^1 is l^infinity
- Q Queen Chloe is planning to build a castle inside of arectangular moat. A river runs horizontally along the bottom of herland, and that river will form the bottom of the...
- Q What is impulse response, why it is important? How else is itcalled?
- Q Find the absolute maximum of g(x,y)=x^2+y^2-2y+1 on the diskx^2+y^2 less than or equal to 4. Solve 2 ways, parametrization andlagrange multipliers. Please solve using both methods!
- Q Set up an integral for the following scenarios:Set up the integral in simplified form, do not integratea) Arc length of y = ln x , 2 ≤ x ≤ 4...
- Q Find (without using a calculator) the absolute extremevalues of the function on the given interval.f(x) = 3x2 − x3 on [0, 3]
- Q The absolute maximum values of f(x)=x^3-3x^2+12 on the closedinterval [−2, 4] occurs at x =
- Q 1A) Solve by substitution.2x − y + 3 = 0 x2 +y2 −4x=01B)Solving system by Gaussian Elimination and then by backsubstitution3x − 3y + 6z = 6x + 2y −...
- Q Find the mass and center of mass of the lamina that occupies theregion D and has the given density function Ï.D is bounded by y = 1 − x2 and...
- Q 13) For the given cost function C(x) = 48,400 +600x + x2,First, find the average cost function. Use it tofind:a) The production level that will minimize the average costx =Â Â Â Â Â b)...
- Q Find the general solution:dx/dt + x/(1+2t) = 5
- Q Determine if exact equation, then solve:x(y+2)y' = lnx+1 , y(1) = -1
- Q Use either the disk method or the washer method to calculate thevolume of the solid formed by revolving the given region about thegiven axis.Region bounded by ? = ? ?...
- Q The population of rats, R(t), in a small town's sewage systemt years after the beginning of the year 2000 is given byR(t)=5500e^0.049t. Find the AVERAGE population of rats in thesystem...
- Q Find the volume of the figure whose base is the region boundedby y = x^2 + 4, y = x^2, the y-axis, and the vertical line x =2,and whose cross...
- Q Find the volume of the figure created by rotating the regionenclosed by the graphs of y = x^2 and y = x^3a) around the x-axisb) around the y-axis
- Q Find the point on the liney = 3x + 4that is closest to the origin.(x, y) =Â Â
- Q Use the Divergence Theorem to evaluateSF · dS,whereF(x, y,z) =z2xi+y33+ cos zj +(x2z +y2)kand S is the top half of the spherex2 +y2 + z2 =4.(Hint: Note that S is...
- Q Jack is riding his bicycle from home to LeConte College with avelocity given by v(t)= -t^4 + 4-t^3 - 500t^2 +2000t in feet awayfrom his house per minute and where...
- Q A strawberry farmer will receive $37 per bushel of strawberriesduring the first week of harvesting. Each week after that, thevalue will drop $0.80 per bushel. The farmer estimates that thereare...
- Q How do you find the domain of:f(g)= 5x^2+4f(g)= 3x; -2<x<6f(g)= (1) / 3x-6f(g)= (x+2) / x^2-1f(g)= x^4 / x^2+x-6f(g)= sqrt (x+1)f(g)= sqrt (x^2+9)
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