Basic Math question and answers for July 16, 2023
- Q The count in a bacteria culture was 800 after 20 minutes and1100 after 30 minutes. Assuming the count grows exponentially,What was the initial size of the culture?Find the doubling period.Find...
- Q The price of a product in a competitive market is $200. If thecost per unit of producing the product is 80 + 0.1x dollars, wherex is the number of units...
- Q Use Laplace transforms, solve the differential equation y'' +16y = 4 sin 4? , where y(0)=2. y?(0)=0.
- Q 1. The Arizona Fish and Game department has a lottery for elktags in an effort to control the population of elk in NorthernArizona. There are two proposed methods of deciding...
- Q Use differentials to approximate the value of the expression.Compare your answer with that of a calculator. (Round your answersto four decimal places.)326
- Q solve using the multiplication principle first. Then add1/3x+3/2y=5/61/4x+1/2y=3/8
- Q Solve this system of equations. Write the solution as an orderedtriple.6x + 3y + z = 36x - 3y + 2z = -1217x - 2y + 3z = 80
- Q A heavy rope, 40 feet long, weighs 0.3 lb/ft and hangs over theedge of a building 110 feet high. Let x be the distance in feetbelow the top of the...
- Q use the method of Lagrange multipliers to find the absolutemaximum and minimum values of the function subject to the givenconstraints f(x,y)=x^2+y^2-2x-2y on the region x^2+y^2?9 andy?0
- Q 1)Let y be the solution of the equationy ? = 4(x^4)*sin(x^4) satisfying the condition y ( 0 ) = ?1.Find y ( pi^1/3 ).2)Find the largest value of the parameter...
- Q A business that produces color copies is trying to minimize itsaverage cost per copy? (total cost divided by the number of?copies). This average cost in cents is given by?f(x)equals=0.00000093x^2?0.0146+60?,where x...
- Q Use Green’s theorem in the plane to evaluate?C(4x+1)x2ydx+x(x3?y3)dy where C is the circle whose equation is x2+y2=2x transversed once in an anti cloickwise direction.
- Q The following exercise is designed to be solved using technologysuch as calculators or computer spreadsheets.Interest paid on a home mortgage is normally tax deductible. Thatis, you can subtract the total...
- Q Find the general solution of this differential equation:y'''+y''+y'+y=4e^(-t)+4sin(t)
- 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...
- Q 1. Consider the region bounded by the graph of y^2 = r^2?x^2(a) When this region is rotated about the x-axis a sphere ofradius r is generated. Use integration to find...
- Q 1-Prove the identity.cosh(x) + sinh(x) = excosh(x) + sinh(x)=12ex + e?x+12 =12 =2-Prove the identity.sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y)sinh(x) cosh(y) + cosh(x) sinh(y)=12(ex ? e?x)12 +12(ex + e?x)12 =14 + ex...
- Q Answer all the question below.Table 2:13579111315171921232527293133353739414345474912.237355142457911.770844025303811.311403319470011.098109024134510.991753287142610.963344962387010.932898518690411.060912318277011.144715012471311.299424341353311.469941187953311.586258096908611.788705567858811.927783392672111.933232561717212.002775422895712.045519181787011.989507604459712.116149224795711.914299990240611.952344538473811.844471664317711.832557268184511.639478255493611.4409836766153 Visualize data in table 2 in a 2-dimensionalplot using Matlab. Interpolate data in table 2 to determine avalue of temperature when t = 8...
- Q A piece of wire 28 m long is cut into two pieces. One piece isbent into a square and the other is bent into an equilateraltriangle. (Give your answers correct...
- Q EvaluateRC F·dr where F = hyzexz,exz,xyexzi and C : r = ht2 +1,t2 ?1,t2 ?2ti, 0 ? t ? 2. Hint: Check whether F is conservative.If so, the Fundamental Theorem...
- Q Consider a region R bound by the coordinate axes and y = ( 9 + x2 ) ? 1 2 on 0 ? x ? 4.a. Find the area of...
- Q An economy is based on three sectors, agriculture,manufacturing, and energy. Production of adollar’s worth ofagriculture requires inputs of $0.30 from agriculture, $ 0.30frommanufacturing, and $0.30 from energy. Production of a...
- Q find the riemann sum f(x)=x^2 +3x over the interval [0,8] wherex0 =o, x1=1 , x2=6,x4=8, and c1=1, c2=2,c3=4, c4=6
- Q Arguments & Standard FormFind an article from google scholar (topic isirrelevant just need something that will be easy to understand).Examples might be college drinking, overcrowding in prisions, Applephone issues, really...
- Q the table gives a total U.S expenditure for health services andsupplies selected years from 2000 and projected to 2018.year $(billion)2000 12642002 14982004 17332006 19762008 22272010 24582012 27462014 31072016 35562018 4086a....
- Q 5 + (3 * 4)^2 - 2 = 147 (5 + 3) * 4^2 - 2 = 126 (5 + 3 )* (4^2 – 2) = 112 5 + (3 * 4^2) -...
- Q American General offers a 8 -year annuity with a guaranteed rateof 6.73% compounded annually. How much should you pay for one ofthese annuities if you want to receive payments of...
- Q Calculate an approximate value of the area of the place insidethe curve. (So if you sketch it up (by using WolframAlpha orsomething else) then you will see that what is...
- Q DefineInstructions:After reading Chapter 4 of the textbook, define the followingterms:-System of linear equations-Solution to a system of equations-Consistent system of equations-Inconsistent system of equationsWrite a good paragraph with at least...
- Q The populations of termites and spiders in a certain house aregrowing exponentially. The house contains 110 termites the day youmove in. After four days, the house contains 195 termites. Threedays...
- Q Is this true or false? The foci for the hyperbola((x-2)^(2))/(36)-((y+1)^(2))/(64)=1 are (2, -1 +4sqrt(7) and (2,-1 - 4sqrt(7)
- Q 1) Find the velocity and position vectors of a particle that hasthe given acceleration and the given initial velocity andposition.a(t) = 7i+4j, v(0) =k, r(0) =i2) Find the tangential and normal components...
- Q a) Calculate the maximum MaxDisk value of the function f (x,y) =9 ln * (x^2+(1+1)y^2+(0.5+0.5)) on the circle disk with the centerof origin and radius 4.b) Also calculate the maximum...
- Q Find the equation of the circle ((x-a)2 +(y-b)2 = r2 ) that goes through the points(1, 1), (0, 2), and (3, 2). [Hint: subtractequations.]
- Q 1. Given parametric equations below, find dy/dx , equations ofthe tangent and normal line at the given point.(a) x = t^2 , y = t^3?3t at t = 1(b) x...
- Q 1. Given parametric equations below, find the values of t wherethe the parametric curve has a horizontal and verticaltangents.a) x=t^2 - t, y= t^2 + tb) x= e^(t/10)cos(t), y= e^(t/10)sin(t)2....
- Q Consider the function below.f(x) =ex3 + exFind the interval(s) where the function is decreasing. (Enteryour answer using interval notation. If an answer does not exist,enter DNE.)Find the local maximum and...
- Q The following DEs are not solvable as written. Perform the givenvariable change to turn them into something that you are equippedto solve (e.g. either linear, separable or exact) and then...
- Q Shane (famous Western movie name of the star character) settlesdown in Wyoming Territory. He lives the same distance from GeneralStore (-78,202), the Saloon is (111, 193) and the Courthouse (202,-106)....
- Q a)Find the value of the Wronskian of the functions f =x^7and g = x^8 at the piont x = 1.b)Let y be the solution of the equation y ? ? 5 y ?...
- Q Solve the inequality. (Enter your answer using intervalnotation.)(x + 5)2(x + 2)(x ? 1) > 0
- Q A lamina occupies the region inside the circle x^2 + y^2 = 6x,but outside the circle x^2 + y^2 =9.Find the center of mass if the density at any point...
- Q perform a rotation of axes with a suitable angle of rotation (noxy term) and identify the related conic.1. x2-xy+y2=22. x2-3y2-8x+30y=60
- Q A manufacturer estimates that production? (in hundreds of?units) is a function of the amounts x and y of labor and capital?used, as f(x,y)=[1/3x-1/3+1/3y-1/3]-3. Find thenumber of units produced when8 units...
- Q if two parallel planes, vector n1* vector x = a, vector n2*vector x = b. How to describe their distance?
- Q In this assignment, we will explore four subspaces that areconnected to a linear transformation. For the questions below,assume A is an m×n matrix with rank r, so that T(~x) =...
- Q A lamina occupies the region inside the circle x^2 + y^2 = 6x,but outside the circle x^2 + y^2 =9.Find the center of mass if the density at any point...
- Q A man gets a job with a salary of $38,900 a year.He is promised a $2,430 raise each subsequent yearDuring a 9-year period his total earnings are________
- Q A firm produces two commodities, A and B. The inverse demandfunctions are:pA =900?2x?2y, pB =1400?2x?4yrespectively, where the firm produces and sells x units ofcommodity A and y units of commodity...
- Q Solve the following initial value problem.y(4) ? 5y??? + 4y?? ?=?x, y(0) ?=? 0,y?(0) ?=? 0,y??(0) ?=? 0,y???(0) ?=? 0.
- Q Approximate the area under the graph of f(x)=0.03x4?1.44x2+58over the interval [2,10] by dividing the interval into 4subintervals. Use the left endpoint of each subinterval.The area under the graph of f(x)=0.03x4?1.44x2+58...
- Q Determine the slope of the tangent line, then find the equationof the tangent line at t=?1 .x= 9t,y=t^2
- Q g(x, y) = 2x 3 + 9xy2 + 15x 2 +27y2Find all the critical points of the following functions. Foreach critical point of g(x, y), determine whether g has a...
- Q Suppose you want to have $500,000 for retirement in 35 years.Your account earns 4.3% interest. How much would you need todeposit in the account each month?Round your answer to the...
- Q When a 6?kg mass is attached to a spring whose constant is24?N/m, it comes to rest in the equilibrium position. Starting at?t = 0, a force equal to ?f?(t) ?=?42e?7t?cos?4t...
- Q find the dimensions and volume of the right circular cylinder ofmaximum volume inscribed in a sphere with radius 50cm
- Q A frog is climbing out of a well that is 31 feet deep. The frogcan climb 3 feet per hour but then it rests for an hour, duringwhich it slips...
- Q A water tank is spherical in shape with radius of90 feet. Suppose the tank is filled to a depth of140 feet with water. Some of the water will bepumped out...
- Q The equation of the line that goes through the point (3,2) ( 3 ,2 ) and is parallel to the line going through the points (?2,3) ( ?2 , 3...
- Q A Ferris wheel is boarding platform is 3 meters above theground, has a diameter of 76 meters, and rotates once every 7minutes.How many minutes of the ride are spent higher...
- Q State two characteristics of line integrals of scalar field
- Q (1 point) Two chemicals A and B are combined to form a chemicalC. The rate of the reaction is proportional to the product of theinstantaneous amounts of A and B...
- Q 1. (a) Evaluate the integral: ?0 to 2 16 /x^2+4 dxYour answer should be in the form k?k?, where k is an integer. Whatis the value of k?Hint: d/dx arctan(x)=1/x^2+1k=(b)...
- Q A. Use the Product Rule or the Quotient Rule to find thederivative of the function.g(x) = x3 cot(x) + 6x cos(x)B. Use the Product Rule or the Quotient Rule to...
- Q Joe leaves an intersection traveling west in his car. He is 20feet from the intersection 4 seconds later. At the same time,Joshua leaves the intersection heading north in his car...
- Q Q1) Velocity and acceleration: a ball is thrown verticality upword from the ground level with initial velocity of 2 feet persecond and initial position 10 feet. Use a(t)=2cos?(2x+3) Find the...
- Q Solve the following integral ? (x^2 + x + 2) / (x +1)(x^2 + 1) dx. Use partial fraction decomposition. Show all workand steps to get to solution.
- Q Question 4: Homogeneous Second Order Differential equationSolve the following equation for the particular solution.i. 2??? + 5?? + 3? = 0; ?(0)=3, ??(0)=?4ii. 4 (?2?/??2) + 8 (??/??) + 3y...
- Q Question 3: Exact Differential Equationi. Test to see if the following equation is exact, if exact solvefor the general solution(??/??) +(2? ????+?^3?^?)/(?^2cos?+3?^2?^?)=0ii. Solve (?+????)??+(??????2?)??=0iii. Solve (?^2+?)??+(?^???)??=0iv. (2??3?)??+(2??3?)??=0I am sorry I...
- Q Solve cos^2(x)-cos(x)=0 for x,
- Q A bath tub with a volume of 400 liters at first is full of 100liters of water with a bath salt concentration of 10 grams perliter. During some time, water...
- Q Suppose A*B*A? holds(B is between A and A') and D ?Int(?ABC). Prove that C ? Int(?A?BD).(a) Prove that C ? H(D,line A?B).(b) Prove that C ? H (A?, line??BD). Use point...
- Q Respond to the following in a minimum of 175 words: How will yougraphically represent data in your future career? What types ofgraphs are typically used in that industry? What types...
- Q solve completely(complementary function and particular integral)pdes1 (1+D^2-D')z = -8siny2 (D-D'-D'^2)z =132xy^10+504x^2y^63 (D^2-4DD' +4D'^2)z = x + y4 (D^2-2DD'+ D'^2)z = e^2x-2y+x^2
- Q we were looking at lives some men mathematicians. But women madevery serious contributions to mathematics as well. One of the mostimportant people in the history of mathematics was Emmy Noether.Please...
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