Basic Math question and answers for July 12, 2023
- Q Consider a circle with AB as diameter, and P another point onthe circle. Let M be the foot of the perpendicular from P to AB.Draw the circles which have AM...
- Q Let f(t)=5t2?t.a) Find f(t+h):b) Find f(t+h)?f(t):c) Find f(t+h)?f(t)/h: side note: (f(t+h)=f(t) is on top offraction and h is on bottom)d) Find f?(t):pls circle the 4 answers
- Q Biologists stocked a lake with 400fish and estimated thecarrying capacity (the maximal population for the fish of thatspecies in that lake) to be 7300. The number of fish grew to...
- Q Estimate the area under the graph off(x)=25?x^2from x=0 to x=5 using 5 approximating rectangles and rightendpoints.(B) Repeat part (A) using left endpoints.(C) Repeat part (A) using midpoints.
- Q Ali wishes to replace payments of $1050 due today and $1250 duein 22 months by a single equivalent payment 18 months from now. Ifmoney is worth 3.8% compounded monthly, what...
- Q 5. Solve equationy'+2y=2-e^-4t, wherey(0)=16. Use Euler’s method for a previous problem at t=0, 0.1, 0.2,0.3. Compare approximate and the exact values of y.
- Q 1.The position of a particle in rectilinear motion is given by s(t) = 3sen (t) + t ^ 2 + 7. Find the speed of the particle when itsacceleration is...
- Q Evaluate each integral using trig substitutions1.) Integral of (3x^5dx)/(sqrt(16-x^2)2.) Integral of (sqrt(x^2-16)dx)/x3.) Integral of (6dx)/(16+16x^2)
- Q Let g(t) = 5t ? 3 ln(t 2 ) ? 4(t ? 2)2 , 0.1 ? t ? 3.a. Find the absolute maximum and minimum of g(t).b. On what intervals...
- Q Does every polynomial equation have at least one real root?a. Why must every polynomial equation of degree 3 have at leastone real root?b. Provide an example of a polynomial of...
- Q Define vector addition as y_1? y_2=y_1+y_2-3 and scalarmultiplication as c ?y_1=cy_1-3c+3. Let V be the space of allsolutions of the equation in problem 3 that uses the abovedefinitions of vector...
- Q The figure shows four circles, each with a radius of 6 cm. Findthe area of the region between the circles. (Round your answer totwo decimal places.)cm2A student cuts out a...
- Q P= 16x -5y +66, subject to 7x +9y ? 63, 0 ? y ? 4, and 0 ? x ?5.The maxium value _____ occurs when x= _____ and y= ______.The...
- Q Have you ever hear about Banach Spaces? Chances are, you neverhad. Yet, they are an essential part of today’s mathematics. Pleasesearch some info about the person that first introduced them...
- Q Given two lines in? space, either they are? parallel, they?intersect, or they are skew? (lie in parallel? planes). Determinewhether the lines? below, taken two at a? time, are parallel,intersect, or...
- Q a. Verify that the given point lies on the curve.b. Determine an equation of the line tangent to the curve at thegiven point.9 (x2 y2)2 =100xy2 ;(1,3)
- Q Draw the graph, solid of revolution, one representative disk/washer.Set up and evaluate the integral that gives the volume of thesolid formed by revolving the region formed by a) when revolved about...
- Q Find the 5th Taylor polynomial of f(x) = 1+x+2x^5 +sin(x^2)based at b = 0.
- Q -3,7 11,-15A. Find Point Slope FormB. Find Slope InterceptC. Find X and Y interceptsSketch a graph
- Q Let R be a ring with at least two elements. Prove that M2×2(R)isalways a ring (with addition and multiplication of matrices de?nedas usual).
- Q Find the dimensions (in inches) of the rectangular package ofmaximum volume subject to the constraint that the sum of the lengthand the girth cannot exceed 192 inches (see figure). (Hint:Maximize...
- Q Consider the function on the interval (0, 2?). f(x) = sin(x)/ 2+ (cos(x))^2 (a) Find the open intervals on which the function isincreasing or decreasing. (Enter your answers using intervalnotation.)...
- Q a)Let y be the solution of the equation y ? =(y/x)+1+(y^2/x^2) satisfying the condition y ( 1 ) = 0.Find the value of the function f ( x ) = (y ( x...
- 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 Show that of all isosceles triangles with a given perimeter ,the one with greatest area is equilateral.
- Q An investor is considering three types of investments: a highrisk venture into oil leases with a potential return of 15%, amedium risk investment in bonds with a 9% return, and...
- Q Let f(x) = 1 + x ? x2 +ex-1.(a) Find the second Taylor polynomial T2(x) for f(x)based at b = 1.b) Find (and justify) an error bound for |f(x) ?...
- Q For the given polynomial, find all zeros of the polynomialalgebraically. Factor the polynomial completely. ?(?) = ?^4 ? 2?^3? 2?^2 ? 2? ? 3For the given polynomial, find all zeros...
- Q The demand equation for your company's virtual reality videoheadsets isp=1000/q^.3where q is the total number of headsets that yourcompany can sell in a week at a price of p dollars....
- Q prove using the definition of derivative that if f(x) and g(x)is differentiable than (f'(x)g(x) - f(x)g'(x))/g^2(x)
- Q state the discriminant of the quadratic formula anddescribe for which values of the discriminant a quadratic equationwill have real solutions, for which values it will have imaginarysolutions, and for which...
- Q Given a 2x2 matrix, A =1 42 -1Find its eigen values, eigen vectors. Can matrix bediagnolized?
- Q ** Using Calculus**We have a client asking for our recommendations on which storagecontainers are better for shipping and storing hazardous waste.Their requirements are as follows: The container should hold 50,000cm3...
- Q use the Rational Zeros Theorem to find all the real zeros ofeach polynomial function given below: f(X)=3X^3 + 6X^2 -15X -30f(X) = 2X^4 - X^3 - 5X^2 + 2X +...
- Q A cylindrical can is to be built to occupy a volume of 5000m3.The top and bottom of the cylinder cost $500/m2, wheras the cost tobuild the wall of the cylinder...
- Q Vector Analysis: Verify Green’s Theorem in the plane for ? ? =(?^2 + ?^2)??+ (?^2 ? ?^2)?? in the anti-clockwise direction aroundthe ellipse 4?^2 + ?^2 = 16.
- Q A bottle of white wine at room temperature (68°F) is placed in arefrigerator at 4 p.m. Its temperature after t hr is changing atthe rate of ?18e^?0.6t °F/hr. By how...
- Q Find the coordinates of the vertex for the parabola defined bythe given quadratic function.f(x) = x2 + 8x - 8
- Q List all possible rational zeros given by the Rational ZerosTheorem (but don't check to see which actually are zeros). (Enteryour answers as a comma-separated list.) Q(x) = x4 ? 5x3...
- Q y''-2y'+y=exx-1
- Q A boat leaves the harbor entrance and travels 27 miles in thedirection ??? ° ?. The captain then travels for another 16 miles inthe direction ??? ° ?, which is...
- Q Solve the following equation using the method of variation ofparameters :x2 y'' ? 2y = 3x2 ? 1, x > 0.
- Q Let P denote the vector space of all polynomials with realcoefficients and Pn be the set of all polynomials in pwith degree <= n.a) Show that Pn is a vector...
- Q Suppose a rancher wants to fence off a rectangular shapedenclosure. He has 2400 feet of fencing that he can use. What arethe dimensions that gives the enclosure the most area?(a)...
- Q The position function of an object moving along astraight line is given by the function t3 - 15t2 -48t -10, where sis in metres and t is in seconds and...
- Q Question: (a) Find parametric equations for the line ofintersection of the planes given by 3x ? 2y + z = 1 and 2x + y ? 3z= 3.(b) Find the...
- Q Find the local extrema of the following function.f(x,y)=108+7xy-5x2-6y2
- Q verify Stokes' thm.Assume that the surface S is oriented upwardF = 2zi - 3xj +4yk ; S that portion of the paraboloid z =16 -x2- y2 for z>=0. My primary...
- Q Find the arc length of the curve x^3 = y^2 between x = 1 , x = 4.
- Q ({s^3} + 6{s^2} + 15s + 15)=0Solve for s - please show all work
- Q Evaluate the following limits using l'Hopital's rule.(a) lim x?0 (sin(x)?x)/(x^2)(b) lim x?0 (1/x) ? (1/e^x?1)(c) lim x?0+ (x^? x)
- Q Use Laplace transforms to solve the following system ofdi?erential equations.
- Q I am stuck in Austin with a flat tire, and I need to get to myclass in Houston within 2 hours. The drive is 180 miles long, but Iwant to...
- Q Solve the following system of equations using the SubstitutionMethod.1.x + 3y = – 25x + 15y = 02. x – 4y = 103x – 2y = 103. 4a + 7b...
- Q Iodine 131 is a radioactive isotope that decays as time passes.The function M(t) = 200e-0.093t gives the mass of Iodine131 remaining in the sample measured in grams in terms oft...
- Q Use the Laplace transform to solve the given initial valueproblem.y(4) ? 4y''' + 6y'' ? 4y' + y = 0;y(0) = 1,y'(0) = 0,y''(0) = 0,y'''(0) = 1
- Q a)The functions y1 = x^2 and y2 = x^5 aretwo solutions of the equationx^2 y ? ? 6 x y ? + 10 y = 0.Let y be the solution of...
- Q This exercise is designed to be solved using technology such ascalculators or computer spreadsheets.You borrow $18,000 with a term of four years at an APR of 8%. Makean amortization table....
- Q When Cristina opens a bag of white and milk chocolate pieces,20% of the chocolate pieces are white. After Cristina eats 10 milkchocolate pieces, the ratio of brown chocolate to white...
- Q An electronics firm manufactures two types of personal computers(PC), a desktop model and a laptop model. The production of adesktop computer requires a capital expenditure of $400 and 40hours of...
- Q 1. You are given the graph of a function f. Determinethe intervals where f is increasing, constant, ordecreasing. (Enter your answers using interval notation. If ananswer does not exist, enter...
- Q 2. One week a computer store sold a total of 36 computers andexternal hard drives. The revenue from these sales was $25600. Ifcomputers sold for $1180 per unit and hard...
- Q y2 ? y ? 6
- Q Four marbles are drawn simultaneously and at random from an urncontaining 8 black, 7 white, and 5 red marbles.What is the probability that at least one of them is white?
- Q Data from an independent research company found that the annualcost per worker for insurance? (health, life,? liability, etc.) wasincreasing according to the function f(x)=64.91e^(0.34 ×), wheref(x) is the cost in...
- Q A small plane can fly 350 miles with tailwind in 1 3/4 hour. Inthe same amount of time, the same plane can travel only 210 mileswith a headwind. What is...
- Q Let T: R2 -> R2 be a lineartransformation defined by T(x1 , x2) =(x1 + 2x2 , 2x1 +4x2)a. Find the standard matrix of T.b. Find the ker(T) and nullity...
- Q 1. Describe the origin of exponents in 2-3 paragraphs(please cite)
- Q Find the two critical values of the functionf?(x) = x2/5?(5 ?2x).
- Q Whats is the proof for the long exact sequence incohomology?
- Q A ladder 25 feet long is leaning against the wall of a house.The base of the ladder is pulled away from the wall at a rate of 2feet per second.How...
- Q Let f(x)= cos3 – 1.25cos2x +0.225. Determine f ? (xo) at the pointxo at (?/2, ?) wheref(xo)=0Step by step procedure to understand the exerciseplease.The solution of the book is not acceptable,...
- Q 1. You have an annual salary of $62,000from which they deduct 3% for medical insurance and 18% for taxes.Your rent is $1200 a month. Your water bill comes every 3 monthsfor...
- Q la place transform of1. y´´+4y´+3y=0. y(0)=3, y´(0)=12. y´´+2y´+y=0. y(0)=1, y´(0)=1
- Q A projectile is fired at an angle of 28 degrees above thehorizontal with an initial velocity of 1800 feet per second from analtitude of 1,000 feet above the level ground. A)...
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