Basic Math question and answers for July 15, 2023
- Q Explain and state the formula of (a) Trapezoidal rule, (b) theMidpoint Rule, and (c) Simpson’s Rule and the error formula ofeach
- Q Find the maximum area of a rectangle inscribed in a triangle ofarea A.(NOTE: the triangle need not necessarily be a right angledtriangle).
- Q Matilda makes specialized chocolates. Her two best-sellingchocolates, the chocolate heart and the chocolate flower, are madeby pouring milk chocolate into a mold. A heart requires 3.5 ouncesof milk chocolate and...
- Q Thesum of two integers is 54 and their different is 10. Find theintegers
- Q DO NOT DO THE GRAPH OR THE DOMAIN OR RANGE PART. THOSE DO NOTCOUNT. WE ARE NOT DOING THEM IN MATH 1003.Find the factors that arecommon in the numerator and...
- Q Find the charge on the capacitor in an LRC-series circuit at t =0.05 s when L = 0.05 h, R = 3 ?, C = 0.008 f, E(t) = 0...
- Q Letf(x)=x • 3^xa) Find formula for f^(n) •(x) for natural n (the n orderderivative).b) Write the Taylor series generated by f(x) in 0.
- Q 1. Dealing with vector fields is very common in engineering andscience applications. Vector fields are often used to model amoving fluid throughout space, magnetic or gravitational force, andetc.a. Provide two...
- Q I don't understand how to use beats using sum-to-productidentity, or this assignment at all.
- Q A couple is deciding to invest in the laundromatbusiness. There are two laundromat stores available for sale. Theycan only afford to buy one of them. The annual flow of income fromeach...
- Q 4x-2y-2z=2-x-5y+2z=-84x-5y+z=11Please make sure you show all steps numerically,becuse I want to be sure I know how to arrive at the samenumbers.
- Q Given the following rational function: F(X)= (2X^2 - 20) / [( X - 5 )^2]Find all horizontal and vertical asymptotesFind the first derivative of F(X) andsimplifyFind the critical values for X...
- Q this as a whole question 1, answer all parts pleasea)Show that the derivative of f(x) = 6+4x^2 is f(x)'=8x by usingthe definition of the derivative as the limit of a...
- Q Evaluate the line integral ?CF?d r where F=?4sinx,cosy,xz? and Cis the path given by r(t)=(t^3,3t^2,3t) for 0?t?1 ?CF?d r=
- Q The function f(x, y) = 10?x 2?4y 2+2x has one critical point.Find that critical point and show that it is not a saddle point.Indicate whether this critical point is a...
- Q Test the series for convergence or divergence.??n=1(?1)nn4nIdentify bn.
- Q proof a circle is divided into n congruent arcs (n ?? 3), thetangents drawn at the endpoints of these arcs form a regularpolygon.
- Q What is the partial fraction decomposition of5x^2/((x+1)(x^2+3x+2)(x^2+4))
- Q The rate of growth of the population of rabbits in China isproportional to the current rabbit population. The population aftert years is R(t). Write the differential equation for which R(t)...
- Q Explain how to use derivatives to find the top of a hill or thebottom of a valley on a graph?What does it even mean for a derivative to not exist...
- Q Differentiate.1a) p(x) = 4th root of (2x-3/x^3)b) q(x)= (2 sinx)/(1-cosx)c)r(x)= sin(csc^3(x^4))d) U(x)= ((cube root of x^2) sinx -2x-3)/sq. rt. x
- Q A 600?-room hotel can rent every one of its rooms at $90 perroom. For each? $1 increase in? rent,3 fewer rooms are rented. Each rented room costs the hotel? $10to...
- Q Someone explain and show how finding a subspace works andknowing how it is one with a matrix example.
- Q Sketch the region enclosed by the given curves and find itsarea.a) y=4/x,y=4x,y=(1/4)x,x>0b) x=y2?4y,x=2y?y2
- Q A leaky 10-kg bucket is lifted from the ground to a height of 12m at a constant speed with a rope that weighs 0.5 kg/m. Initiallythe bucket contains 36 kg...
- Q An investment pays 8% interest compounded continuously. If moneyis invested steadily at the rate of?$16,000?, how much time is required until the value of theinvestment reaches $160000?2) Given f'(t)=-0.5t-e^-2t, compute...
- Q The temperature , u(x,t), in a metal rod of length Lsatisfies del u/ del t= k del squared u / del x squared limit 0 less than or equal to,...
- Q Sugary drink tax/soda taxandMammography are different levels of prevention,please categorize them from the three options below and explainwhy.Primary level of prevention.Secondary level of prevention.Tertiary level of prevention.Explain (Sugary drink tax/soda...
- Q In the figure below you see an ellipse which is enclosing arectangleThe equation of ellipse is givenbyx^2/4 + y^2 = 1Find the length(L) and width (W) ofthe the rectangle which...
- Q Problem 7. Consider the line integral Z C y sin x dx ? cos x dy.(Please show all work)a. Evaluate the line integral, assuming C is the line segmentfrom (0,...
- Q Next, let’s suppose a rancher wants to fence off a rectangularshaped enclosure that has two identical sections. You can think ofthis as a rectangle with an additional fence dividing the...
- Q Given that f "= - 12 (x-2) ^ 2 + 4, estimate the error obtainedby approximating the integral of f (x) on the interval [1.5,2.5]with n = 4, using trapezoids.Find...
- Q Under ideal conditions a certain bacteria population is known todouble every three hours. Suppose that there are initially 100bacteria.(a) What is the population after 15 hours?(b) What is the population...
- Q Find the Taylor series for f(x) centered atthe given value ofa=1fx=6x^-2
- Q A tank has the shape of a sphere with a radius of 5 m. It is filled with water up to 9 m.(i) Let x be the height in meters...
- Q Find the absolute maximum and minimum values of the function, ifthey exist, over the indicated interval.Where no interval is specified, use the real line.a)?(?)=?8x^3 + 9x^2 + 6x - 5;...
- Q Let C be the boundary of the quarter circle with radius 1,oriented counterclockwise (Figure 1). Evaluate H C(ex + y2) dx +(ey + x2) dy
- Q Consider the following function. (If an answer does not exist,enter DNE.) f(x) = x2 + 5 ? x(a) Find the vertical asymptote(s). (Enter your answers as acomma-separated list.)x =Find the...
- Q There are three boxes in front of you. They are as follows: –BOX A, which has the following statement written on it: “Box C isempty.” – BOX B, which has...
- Q Danica and Darrelle have developed a lucrative business sellinghandmade silver bracelets. Darrelle makes the more complexbracelets and Danica makes the simpler ones. It takes Darrelle 4hours to make 3 bracelets...
- Q Net income for the company for the year was $300,000,and 100,000 shares of common stock were outstanding during theyear. The income tax rate is 30%. For each of the followingpotentially...
- Q For the following pair of functions, ?(?) = ? 2 ? 2, ?(?) = ?? ?3 Find each of the following, and State its Domain: a) Find (f +g)(x)b) Find...
- Q 1) Find the following indefinite integrals. a) (4-3xsec^2 x)/x dx b) (5 sin^ 3 x ) / (1+cosx)(1-cosx) dx2) A particle starts from rest and moves along the x-axis fromthe...
- Q 1. ?11-3x/(x^2+2x-3) dx2. ?4x-16/(x^2-2x -3 )dx3. ?(2x^2-9x-35)/(x+1)(x-2)(x+3) dx
- Q A business owner needs to run a gas line from his business to agas main as shown in the accompanying diagram. The main is 30-ftdown the 12-ft wide driveway and...
- Q A baseball pitcher throws a baseball with an initial speed of 91feet per second at an angle of 5 degree to the horizontal. The ballleaves the pitcher's hand at a...
- Q Solve 4 questions of quiz. each of them gives 0.25 point1. Show that the following sets of elements in R3form subspaces. (a). The set of all (x, y, z) such...
- Q QA: (inspired by a problem from Stewart’s textbook) Suppose thatthere is some function f whose _derivative_ is f ’ =sin(x)/x, withf ‘(0)=1 by definition rather than DNE. Draw that, on...
- Q Evaluate the following integral ? ? R 4x + y (3x ? y)?ln(3x ? y)dA where R is the region bounded by the graphs of ?y ?=? 3x ? e7,?y...
- Q Let f(x) = cosh(x) and g(x) = sinh(x), a = 0 and b = 1.A) Find the volume of the solid with base on the xy plane,bounded by the region...
- Q find the equation of tangent line to the curve r=1+3sin? when?=?/3
- Q The height of a rock thrown upwards on the planet Mars with aninitial velocity of 60 m/s is 2 approximated by h(?) = 60? ? 1.86?. Fill in the average...
- Q 1. Find answers that meet the first-order optimizationconditions, identify the shape of the function graph to determinewhether these answers are maximum value or minimal value.(a) f(x) = e^x + e^-x(b)...
- Q Sketch the graph of the curve ? = 1 + sin ? for 0 ? ? ? 2? ? b)Find the slope of the tangent line to this curve at...
- Q In the new Mission Impossible movie, Ethan Hunt must save theworld from an evil genius who is going to release a computer bugthat will shut down the whole power grid....
- Q The position of a particle moving along a line (measured inmeters) is s(t) where t is measured in seconds. Answer all parts,include units in your answers.s(t)=2t^3 +6t^2 ?48t+7 ?10<t<10(a) Find...
- Q For the following u(x, y), show that it is harmonic and thenfind a corresponding v(x, y) such that f(z)=u+iv is analytic.u(x, y)=(x^2-y^2) cos(y)e^x-2xysin(y)ex
- Q MINIMIZATION BY THE SIMPLEX METHODconvert each minimization problem into a maximization problem,the dual, and then solve by the simplex method.1>.Minimize z = 6x1 +8x2subject to 2x1 + 3x2 ?74x1 +...
- Q A company can extract silver and gold from a particular site.It receives $8000 per unit of silver extracted and $12000 per unitof gold extracted. It has a fixed number of...
- Q 1. compute the least non-negative residue of 4^n (mod 9) forn=1,2,3,4,5.... prove that 6*(4^n)=6 (mod 9) for every n>0.2. find nice tests for divisibility of numbers in base 34 byeach...
- Q What does it means for a set of vectors a1; a2; : : : ; ; an tobe linearly independent?What is the span of the set?This question is about linear...
- Q A savings bond offers interest at a rate of 8.8% compoundedsemi-anually. Suppose that a $1500 bond is purchased.a) Determine the value of the investment after 12 years.b) Describe how the...
- Q Find the surface area of revolution about the x-axis of y = 5sin ( 5 x ) over the interval 0 ? x ? ?/5
- Q Explain in great detail the mathematical concepts inNon-Euclidean Geometry.
- Q 1.What is the order of the DEy'''+3xy'-y=x2y(4)+1? Justify with a completesentence.2.Determine whether or not the equation y=(ln(x)+2)/x , wherex>0, is the solution to the IVP x2y'+xy=1, y(1)=2.Justify your final answer...
- Q 1. (a) Throughout Question 1 part (a), let f be the functiongiven by f(x, y) = 6+x^3+y^3?3xy.(i) At the point (0, 1), in what direction does the function fhave the...
- Q find the y-intercept of the tangent line to ( y= (-1.4)/squareroot 6+8x)(note 6+8x all of it under square root)at (3,?0.255603860169077) The y-intercept = ?????????
- Q Consider the following in Euclidean geometry:Suppose that you want to translate a figure in the coordinate planealong the vector ( 0 2020 ). Find, with a brief explanation, theequations of...
- Q Question No.1: Solve the following system of two linearequations with two variables x and y by “Equating the equations”method. ? = ?? ? ?? ??? ? = ?? + 5Question...
- Q Solve the problem.Let C(x) be the cost function and R(x) the revenue function.Compute the marginal cost, marginal revenue, and the marginalprofit functions.C(x) = 0.0004x3 - 0.036x2 + 200x +30,000R(x) =...
- Q Determine if the point (-1, -1, 0) lies in the planewith equation 2x + 3y -4z + 5 = 0.Find the scalar equation of the plane through the pointsM(1,2,3) and...
- Q ??9ln(x2?1)dx
- Q Answer the following questions thoroughly. Use correct grammarand punctuation.1) A student observes the following spinner and claims that thecolor red has the highest probability of appearing, since there aretwo red...
- Q Find the area of the region that lies inside the curver=1+cos(theta) but outside the curve r=3cos(theta)
- Q 4. [22 pts] For the function ?(?) = 2?5 ? 9?4 + 12?3 ? 12?2 +10? ? 3 answer the following:a. [2 pts] Determine whether the function represents apolynomial. Justify...
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