Basic Math question and answers for August 01, 2023
- Q Find the solution of the following simple harmonic motion: . A24-lb weight stretches a spring 8 ft. Initially the weight releasedfrom 2ft above equilibrium position with upward velocity 2 ft/sec.Find...
- Q Find the surface area of the part of the paraboloid x = y^2 +z^2 that lies inside the cylinder y^2 + z^2 = 25
- Q Explain or use evidence why each is true orfalseIf C is any smooth, closed curve then Z C ex^2 dx =0Let F(x, y) = <P(x, y), Q(x, y)> be a...
- Q 1. A particle is moving with the given data. Find the positionof the particle.a(t)=2t+7, s(0)=8, v(0)=-32.Find ff'(x)=1 sqrt(1-x2) , f(1/2)=8
- Q 1. a. Evaluate the following limit: lim ?→4 ( 2? 3−128 √?−2 ) b. Find the number ? ???ℎ ?ℎ?? lim ?→−2 ( 3? 2+??+?+3 ?2+?−2 ) exists, then find...
- Q Given a general cubic function y = ax^3 + bx^2 + cx + d provethe following,a) That a cubic must change at a quadratic rate.        I believe thisto be the...
- Q Consider the following function. (If an answer does not exist,enter DNE.)f(x) = 1 + (5/ x) - (2/ x^2)(a) Find the vertical asymptote(s). (Enter your answers as acomma-separated list.)Find the...
- Q Use Stokes' theorem to compute the circulationF · drwhere F =8xyz,2y2z,5yzand C is the boundary of the portion of the plane2x + 3y +z = 6in the first octant. Here...
- 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 Practice Integrals to describe Motion A cart’s acceleration isdescribed by the function a = (10 - t) (m/s/)/s. The initialconditions are xi = -2 m and vi = -2 m/s...
- Q A tumor has the same shape as the solid formed by rotating thecurve y = 4x – x 2around the x axis. Given that x and y are measured in...
- Q Suppose that vectors x and y are such thatIxI=3 and IyI=4, and the angle between xand y is 71°. Solve the triangle determined bythe vectors 3x , y, and I3x...
- Q Find a power series for the function, centered atc.f(x) =32x − 1,   c = 2f(x) =∞n = 0Determine the interval of convergence. (Enter your answer usinginterval notation.)
- Q #3. Given the conic section written in general form:x^2 - y^2 - 4x - 4y + 9 = 0FIND:Part a) Identify which type of graph the conic section has.Part b)...
- Q Solve the following linear programming problem. Restrict x ≥ 0and y ≥ 0. Maximize f = 3x + 5y subject to x + y ≤ 5 2x + y ≤...
- Q Write the basic feasible solution from the tableau given.x1x2x3s1s2z86−1100160524010148−6−10−5001146
- Q A mug of beer chilled to 36 degrees, if left in a 72-degreeroom, will warm to a temperature ofT(t) = 72 −36e−3.5tdegrees in t hours.(a) Find T(0.35) andT'(0.35).(Round your answers...
- Q In this exercise, we examine one of the conditions of theAlternating Series Test. Consider the alternating series1−1+1/2−1/4+1/3−1/9+1/4−1/16+⋯,where the terms are selected alternately from the sequences{1/n} and {−1/n^2}.Explain why the nth...
- Q A rectangular storage container with an open top is to have avolume of 16 cubic meters. The length of its base is twice thewidth. Material for the base costs 15...
- Q Sketch the region enclosed by the given curves.y = 8 cos8x,  y = 8 − 8 cos8x,  0 ≤ x ≤π/6I already have the sketch however I need its AreaA) Find its...
- Q Chapter 6, Section 6.1, Go Tutorial Problem 012 Find the area ofthe region that is enclosed between the curves x = y and x = y – 12integrating with respect...
- Q Solve differential equation:y'+y=sin(x)
- Q There are at most two squares (not necessarily with the samesize) such that the sum of the area(s) is 8 in^2 . Maximize andminimize the sum of the perimeter(s)?
- Q Consider the following differential equation:(t^2)y'-y=(y^2), where y'=dy/dt.(a) find y(t) if y(1)=1/2(b)find limt->infinityy(t)
- Q Letf(x) = 5x^(1/3) - x^(5/3)Find the intervals of concavity and the inflectionspoint(s).Graph the function.
- Q A large-scale corporate bakery needs to determine how many oftheir three bestselling products they can make each day. Theirbagels require 9 minutes to prepare, 22 minutes to bake, and 6minutes...
- Q Explain, in your own words. how differentiability and continuityare related?Need well Described answer
- Q a5.5m ladder is leaning against a house when its base starts toslide away. By the time the base is4.44.4mfrom the​ house, the base ismoving away at the rate of9.99.9​m/s.a. Whatis...
- Q find fx, fy and fz for the following function:f(x,y,z) = (xz/1-x2-y2)-3/4if you can show working for the partial derivatives would begreat thanks,Ben.
- Q How there are 3 possibilities for the intersection of 2planes?
- Q A particlemoves according to a law of motion s = f(t), t is greater than orequal to 0, where t is measured in seconds and ? infeet.f(t)=t^2 •e^(-t)a) finevelocity at...
- Q Research the topic of hyperbolic functions and present how theyand their derivatives are defined.
- Q Find the power series expansion for(fx)=x2ex^2 centered at a=0 and at a=-3
- Q let f(x)=(x^2 + 2x) / (x - 1)^2a) Find the domain and if any interceptsb)find the horizontal asymptotesc) find the vertical asymptotesd)find the intervals on which the function is increasing...
- Q On a math test there are 10 multiple-choice questions with 4possible answers and 15 truefalse questions. In how many possibleways can the 25 questions be answered?
- Q Let f(x, y) = 2x^3 − 6xy + 3y^2 be a function defined onxy-plane(a) Find first and second partial derivatives of.(b) Determine the local extreme points of f (max., min.,...
- Q given the curve x(t)=t^2+3 and y(t)=2t^3-3t^2 find the following:a.) find the derivative of the curve at t=1b.) dind the concavity of the curvec.) graph the curve from t=0 to t=2d.)...
- Q A record club has found that the marginal​ profit, Upper P primeleft parenthesis x right parenthesis​, in​ cents, is given by UpperP prime left parenthesis x right parenthesis equals negative...
- Q Let c be a positive number. A differential equation ofthe form below where k is a positive constant, is called adoomsday equation because the exponent in the expressionky1+c is larger...
- Q Analyze the function given by f(x) = (2x − x^2 )e^x . That is:find all x- and y-intercepts; find and classify all criticalpoints; find all inflection points; determine the concavity;...
- Q find the surface area of the paraboloid z = 4−x^2 −y^2 in thefirst octant.
- Q setup an integral to find the volume of the solid generated when theregion bounded byy=x^2 and y=3xi) rotate about x-axis using washer methodii) Rotate about y-axis using washer methodiii) rotate...
- Q Find the total value TV of the given income stream andalso find its future value FV (at the end of the giveninterval) using the given interest rate. HINT [See Examples...
- Q A hot, wet summer is causing a mosquito population explosion ina lake resort area. The number of mosquitos is increasing at anestimated rate of n(t) = 1900 +10e0.5t per week...
- Q Explain Oil and gas reservoir?
- Q Find the mass and center of mass of the solid E withthe given density function Ï.E is bounded by the parabolic cylinderz = 1 − y2and the planesx + 4z...
- Q Approximate the sum of the series correct to four decimalplaces.∞(−1)n − 1n212n
- Q On the graph of f(x)=sinx and the interval [−2π,0), for whatvalue of x does f(x) achieve a minimum?
- Q Consider the given function.Evaluate the Riemann sum for 0 ≤ x ≤ 3, with n= 6, taking the sample points to be right endpoints.
- Q Define the Machine Cycle
- Q Company D showed a profit of $1.5 million last year. The CEO ofthe company expects the profit to increase by 0.04 million dollarseach year over the next 5 years and...
- Q Find the general solution of this ODE:d^2y/dt^2+7 dy/dt+10y=5t^2−3t+6The solution will be of the form:y(t)=Cy1(t)+Dy2(t)+yp(t)so use C and D as the arbitrary constants.y(t)=y(t)=  Â
- Q Evaluate the following expressions.a. Summation from k equals 1 to 18 kb. Summation from k equals 1 to 7 left parenthesis 4 k plus 1right parenthesisc. Summation from k equals...
- Q suppose that 270 grams of a radioactive material was put in acontainer 8 years ago. If you found that 80 grams of the materialremain today, how long does it take...
- Q Give a proof by contradiction to show that if two lines l andm are cut by a transversal in such a way that the alternateinterior angles, x and y, have...
- Q Evaluate the integral Integral from 1 divided by 2 to 1 leftparenthesis x Superscript negative 3 Baseline minus 15 rightparenthesis dx using the Fundamental Theorem of Calculus.
- Q Find the length of the cardioid r = 3+3cosθ
- Q After a patient consumes a medication, the amount of drug thatremains in the body decays exponentially. Suppose a patient takesan 800 mg tablet of a given drug, and after 4.5...
- Q Find the angle θ between the vectors in radians and indegrees.u = cosπ3i + sinπ3j, v = cos3π4i + sin3π4j(a) radians(b) degrees
- Q Find the minimum distance from the point (1,1,14) to theparaboloid given by the equation?=?2+?2.
- Q A university is trying to determine what price to charge fortickets to football games. At a price of ​$27 per​ ticket,attendance averages 40,000 people per game. Every decrease of ​$33adds...
- Q You roll TWO six-sided die. Find the probability of each of thefollowing scenarios in fractions.1. P(sum=2)2. P(sum is less than or equal to 4)3. P(sum=13)4. P(product)= 20 (Product means multiply)5....
- Q Calculate the iterated integral.
- Q Compute the derivative of each functiona.) f(x)= x5/2 - 3x2/3b.) f(x) = 3x- log7x+7c.) f(x)= 8x6-5x3+3x2-11x+7
- Q a) Suppose that 650 bacteria are present initially in a culture.If the number of bacteria triple every 5 hours, how long is ituntil there are 50,000 bacteria in the culture?b)...
- Q let f(x)= 1/(7x^2+8). Find the open intervals on which f isconcave up (down). Then determine the x-coordinates of allinflection points of f.
- Q write parametric equations in 2D for a particle moving in aclockwise motion along a circle radius 2 such that at t=0 , theparticle is at point (-2,0)Please I need the...
- Q A stone is thrown upward on the moon with its height (in feet)after t seconds given by h(t) = 20 −5t2. Include units with your answer.a) What is the acceleration...
- Q Consider a fruit fly flying a room with velocity v(t) =< -sin(t), cos(t), 1 >a. if the z = 1 + 2(pi) is the room's ceiling, wherewill the fly hit...
- Q Find the net change of ?(?) = (? − 2)(? + 3) on the interval[-1, 1].Find the net change of ?(?) = 6 cos ? on the interval[−? /2, ?/2].Find...
- Q Use the First Derivative Test to find the exact location of allthe relative extrema of the given function.1. f(t) = t^3-3t^2, Domain [-1, +infinity)2. f(x) = 3x^4-2x^3, Domain [1, +infinity)3....
- Q L1di2dt+ Ri2 + Ri3 = E(t)L2di3dt+ Ri2 + Ri3 = E(t).Solve the system in part (a) ifR = 10 Ω, L1 =0.01 h, L2 = 0.05 h,E = 200 V,...
- Q 2. Find the following derivative y=4x?3. Find any maximum or minimum values of the function y(x)=1+x/e4x. Use a sign chart or a second derivative test to verify the answer(s) you...
- Q Define the basic concept of channel coding,and enumerate two types of channel coding?
- Q Evaluate the integral.∫4−2. (1/(x+5)((x^2)+16)) dx
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