Basic Math question and answers for August 11, 2023
- Q Related rates Part A:1. Consider a right triangle with hypotenuse of (fixed) length46 cm and variable legs of lengths x and y,respectively. If the leg of length x increases at...
- Q Sketch the region in the first quadrant enclosed by y=2/x ,y=3x, and y=1/3x. Decide whether to integrate with respect to x ory. Then find the area of the region.Area =Find...
- Q 1)How much more area does a 18-inch rim have compared to a16-inch rim on a car? Round the answer to 2 decimal places.2)The area of a sector is 110.60 sq...
- Q Use Euler's method with step size 0.5 to compute the approximatey-values y1, y2,y3 and y4 of the solutionof the initial-value problem. y' = y − 5x, y(3) = 1.y1 =...
- Q The radius of a sphere is measured to be 6 inches, with apossible error of 0.02 inch. Using differentiation, approximate themaximum possible error in calculating the volume of the sphere.
- Q If money is flowing continuously at a constant rate of $2, 000per year over 5 years at 6% interest compounded continuously, findthe following.1. The total money flow over the 5-year...
- Q Look at these two functionsf(x) = -x^2-x-6g(x) = (x+1)(x^2+6x+9)a. Which function changes direction more times and by howmuch?b. Which function touches the x-axis more times and by howmuch?c. At what...
- Q A plane flying with a constant speed of 19 km/min passes over aground radar station at an altitude of 14 km and climbs at an angleof 20 degrees. At what...
- Q Use spherical coordinates.Evaluate(x2 + y2) dVE,where E lies between the spheresx2 + y2 + z2 = 1 andx2 + y2 + z2 = 9.
- Q Exercise 2 2.1. Write each expression as a single logarithm and,if possible, simplify. ln (x - 4) - ln (x+ 2); ln (x) - 3 [ln (x -5) + ln...
- Q f(x)= 2x^4 - 4x^2 + 1a. Indicate where the function is increasing or decreasing.b. List the coordinates of where extrema occur.c. State where the graph is concave up or concave...
- Q Verify the Divergence Theorem for the vector eldF(x; y; z) = hy; x; z2i on the region E bounded by the planes y+ z = 2,z = 0 and the...
- 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 2.(a) Find an equation of the tangent plane to the surfacex4 +y4 +z4 = 18 at (2, 1, 1). Find aderivative in direction (2,2,1) at point (2,1,1). (b) Use Lagrangemultipliers...
- Q Solve the following system of equations using Gaussian or​Gauss-Jordan elimination.w + x + y + z = -22w +2x - 2y - 2z = -123w - 2x + 2y +...
- Q A particle moves from point A = (0, 0, 0) to point B = (2π, 0,2π), under the action of the force F = xi +yj − zk .a. Calculate...
- Q 2.  The profit function from manufacturing and sellingxx BabCo Lounge Chairs is:P(x)=30x−140−0.2x^2a. Find the exact additional profit for manufacturing and selling10 chairs instead of 9 chairs.b. Find the marginal profit at...
- Q Suppose a company's revenue function is given byR(q)=−q3+320q2R(q)=-q3+320q2 and its cost function is given byC(q)=290+20qC(q)=290+20q, where qq is hundreds of unitssold/produced, while R(q)R(q) and C(q)C(q) are in total dollars ofrevenue...
- Q (t-1)^3(t+4) find increasing decreasing , concave up down and iflection
- Q Find the inverse of the matrix[ 1 1 4 ][ 3 2 4 ][ 1 1 6 ]It is a 3*3 matrix
- 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 5. The population of certain small organism grows according tothe model: dy/dt = 5y where y=20 when t=0t is measured in months. a) Construct the specific function fory. b) Find...
- Q Use a triple integral to find the volume of the solid under thesurfacez = x^2 y and above the triangle in the xy-plane withvertices (1.2) , (2,1) and (4, 0).a)...
- Q Check all of the following that are true for the series∑n=1∞(n−8)cos(nπ)/(n^2).Converge, diverge, integral test, comparison test, limitcomparison, ratio test, and alternation test.Same with ∑n=1∞8^n/((4^n)-1)
- Q A car rental agency rents 420 cars per day at a rate of ​$40 perday. For each ​$1 increase in​ rate, 10 fewer cars are rented. Atwhat rate should the...
- Q Find the mass, the center of mass, and the moment of inertiaabout the z-axis for the hemisphere x^2+y^2+z^2=1, z >(greaterthan or equal to) 0 if density is sqrt(x^2+y^2+z^2)
- Q A spring with a mass of 2 kg has a damping constant 14 kg/s. Aforce of 3.6 N is required to keep the spring stretched 0.3 mbeyond its natural length....
- Q Series Solutions of Ordinary Differential Equations For thefollowing problems solve the given differential equation by meansof a power series about the given point x0. Find the recurrencerelation; also find the...
- Q Determine if each of the infinite series belowconverges or diverge. State the criteria used to make thedetermination, and show the work.(7 pts)     n=1∞sin(1/n)(7 pts)n=1∞ln(n)/n(7 pts)    n=1∞2n/n!
- Q Find the third MacLaurin polynomial for the function f(x) = e2xsin(3x)
- Q 1. (8pt) Consider the function f(x) = (x + 3)(x + 5)^2 √ (7 − x)whose first and second derivatives are f'(x) = ((x + 5)(139 + 12x −7x^2))/2 √...
- Q Find the solution ofy′′+5y′=100sin(5t)+250cos(5t)with y(0)=7 and y′(0)=3.
- Q Find the relative extrema, if any, classify as absolutemax/min.a.) f(x)= x+1/x-2 on [2,4]b.) f(x)= x^(2) -2x-3 on [-2,3]c.) f(x)= x^(2/3) (x^2-4) on [-1,3]Solve for x:a.) 6^(2x) =36b.) 2^(2x) -4 *...
- Q Find the volume of the solid generated by revolving the regionbounded by y = sqrt(x) and the lines and y=2 and x=0 about:1) the x-axis.2) the y-axis.3) the line y=2.4)...
- Q Find the absolute maximum and absolute minimum values of thefunction, if they exist, on the indicated interval. 6) f(x) = x 4 -32x 2 + 2; [-5, 5]
- Q Evaluate (please answer all of them)1) ∫ 1.67 ?^(1/3) ?? =2) ∫ [(?^3+ sin(4?)) / (?^4−cos(4?)+4)] ?? =3) ∫ ???^8(4?)cot(4?) ?? =4) ∫ sec^2(4?) ???^5(4?) ?? =5) ∫ (4x^3) /...
- Q A rectangular box is to have a square base and a volume of 40ft3. If the material for the base costs $0.35 per squarefoot, the material for the sides costs...
- Q Show that at every point on the curver(t) = <(e^(t)*cos(t)), (e^(t)*sin(t)), e^t>the angle between the unit tangent vector and the z-axis is thesame. Then show that the same result holds...
- Q 4) A company manufactures and sells x lime scooters sets permonth. The monthly cost and price-demand equations areCx=16,000+75xp(x)=200-x/30 0≤x≤3,000a) Find the maximum monthlyrevenue.b) Find the maximum profit, theproduction level that...
- Q Let f(x)=(x^2+1)*(2x-3)Find the equation of the line tangent to the graph of f(x) atx=3.Find the value(s) of x where the tangent line is horizontal.
- Q What are the basic facts about?a- Sums, differences, and products of power series?b- Substitution of a function for x in a power series?c- Term-by-term differentiation of power series?d-Term-by-term integration of...
- Q 3) A company manufactures and sells x cellphones per week. Theweekly cost and price-demand equations areCx=5,000+84xp(x)=300-0.2xa) What price should the companycharge for the phones, and how many phones should be...
- Q What should be the dimensions of a rectangle inscribed in asemicircle of radius 5 centimeters so that the recatangle has amaximum area
- Q Find the particular solution to the equation.y''-4y'+5y=(e^(2t))(sec(t))
- 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 please explain simpson's rule and how i can use it forapproximation
- Q 1) Let P(x) = 3x(x − 1)3 (3x + 4)2 . Listthe zeros of P and their corresponding multiplicities.2) Let f(x) = −18(x + 3)2 (x − 2)3 (x +71)5...
- Q Find the general solution of the given system.dx/dt=6x-ydy/dt=5x+4y
- Q “Find the critical values at which each of the following cubicfunctions is optimized and test the second-order conditions to seeif the function is at a relative maximum, relative minimum,inflection point,...
- Q Initially 10 grams of salt are dissolved into 35 liters ofwater. Brine with concentration of salt 4 grams per liter is addedat a rate of 5 liters per minute. The...
- Q f(x) = 10/cos-1(x). Use calculus to determine:a) all critical valuesb) any local extremac) any absolute extremad) the intervals where f is increasing/decreasinge) any points of inflection rounded to the thousandths...
- Q 1A) Let ?(?) = 3? + 2. Use the ? − ? definition to prove thatlim?→1 3? + 2 ≠1.Definition and proof.1B) Let ?(?) = 2?^2 − 4? +...
- Q Which interest rate and compounding period gives the better return?-8% compounded semianually- 7.85% compounded continuosly
- Q Consider the function below. (If an answer does not exist, enterDNE.)h(x) = (x+ 1)9 − 9x − 2(a) Find the interval of increase. (Enter your answer usinginterval notation.)Find the interval...
- Q Estimate the slope of the line from its graph.
- Q Find T(t), N(t), and B(t) for r(t) = t^2 i + (2/3)t^3 j + t k atthe point P ( 1, (2/3) , 1)
- Q The curve C is given by the parameterization ⃗r(t) = <−t , 1− t^2> for −1 ≤ t ≤ 1.a) Choose any vector field F⃗ (x, y) = 〈some function...
- Q 1. Consider the cubic function f ( x ) = ax^3 + bx^2 + cx + dwhere a ≠0. Show that f can have zero, one, or twocritical numbers...
- Q Suppose that in a given store, customers are willing to buy ypounds of coffee beans per day at $x per pound, as given by theprice-demand equation y=10+(180/x) for 2 (is...
- Q 3. Suppose a bird takes off from the top of a lamp post with itsaltitude (in m) given byp(t) = (1/3)t3 - (1/2)t2 -6t +15(a) Calculate the bird’s velocity and...
- Q Use spherical coordinates.Evaluate(4 − x2 − y2) dV, where H isthe solid hemisphere x2 + y2 + z2≤ 9, z ≥ 0.H
- Q If x 1 and x 2 are the number of items of two goods bought, acustomer’s utility is U ( x 1 , x 2 ) = 2 x 1...
- Q Use the method of undetermined coefficients to find one solutionofy′′+4y′−3y=(−7x2+7x+7)e4x.
- Q 1. Differentiate the following functionsA. y=ln(x+sqrt(x^2 -1))B. y=ln(sinx)C. y=xlnx-xD. y=e^x(sinx)
- Q Series Solutions of Ordinary Differential Equations For thefollowing problems solve the given differential equation by meansof a power series about the given point x0. Find the recurrencerelation; also find the...
- Q Find the center of mass of a thin plate of constant densitydeltaδcovering the region between the curvey equals 5 secant squared xy=5sec2x​,negative StartFraction pi Over 6 EndFraction less than or...
- Q 1. Denote I =∫10  (1/(1+4x2)) dxa. Find the exact value of I (for example, by finding anantiderivative of the integrand).b. For a generic positive integer n, we partition the interval[0, 1]...
- Q 1:Given that f(4) = 6 and f'(x) = 2/x2+9 for all x.a) Use a linear approximation or differentials to estimatef(4.04)b) Is your estimate in part (a) too large or too...
- Q You just won $900 in the lottery and you decide to invest thismoney for 10 years. Three accounts pay as follows:Account A pays 14% interest per year.Account B pays 13.4%...
- Q The estimated monthly sales of Mona Lisapaint-by-number sets is given by the formula q =105ep −3p2/2,where q is the demand in monthly sales and pis the retail price in yen.(a)...
- Q Solve the following using a generating function:Elizabeth is hosting a party inviting 7 friends. She boughtgifts as the following: 8 teddy bears, 8 books, 5 watches. If shewants to give...
- Q Consider the parametric curve given by the equationsx = tsin(t) and y = tcos(t) for 0 ≤ t ≤ 1Find the slope of a tangent line to this curve when...
- Q Find the mass and center of mass of the solid E withthe given density function Ï.E is the tetrahedron bounded by the planesx = 0,y = 0,z = 0,x +...
- Q 1. Find the average value of the function f(x)= 1/ (x^2-9) onthe interval from 0 ≤ x ≤ 12. Find the arc-length of the function f(x)= x^2 from 0 ≤...
- Q Find a polynomial p(x) with zeroes at 1,-2, and -1 and such thatp(2) equals 6 ?What is the remainder when the polynomial p(x) equals (x^101 -x^50 - 3x^9 + 2)...
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