Basic Math question and answers for August 02, 2023
- Q (1 point) The region in the first quadrant bounded by y=4x2 ,2x+y=6, and the y-axis is rotated about the line x=−2. The volumeof the resulting solid is: ____
- Q Given the first derivative of a function isf'(×)=2x^2-8x+10 , find the intervals of increasing and decreasingbehavior of the function.
- Q A cable runs along the wall from C to P at a cost of ​$3 per​meter, and straight from P to M at a cost of ​$5 per meter. If...
- Q L'Hospitals rule find the limitsa) lim  (tanx−secx)x→π/2-(b) lim   (lnx-1) / (x-e)    x→e(c)  lim      x^(1/lnx)      x→0+
- Q Please answer both parts of the question:a. Use linear approximation to estimate the value:12.03/3.99b. Find ∂z/∂z: z3= x2sin(xyz)
- Q Prove series 2, (-1/2), (2/9), (-1/8) is convergent by thealternating series test and find the number of terms required toestimate the sum of the series with an error of less...
- Q                     1                            -3                                 11(a) Suppose ∫     f(x)dx= 7 and∫   f(x)dx= −5. Evaluate ∫    3f(x)dx.                     -3                          11                                 1                       e^x(b) Find d/dx ∫      (t^3+4)dt                      0                    2(c) Evaluate ∫  3x/(3x+3)dx using u-substitution.                    0
- Q Considerthecurvex(t)=t2,y(t)=t3 −3t,for−∞<t<∞. 2(a) Find all t that give x intercepts and y-intercepts, and plotthem.(b) Find all t which give horizontal or vertical tangents, andplot the corresponding points, with a short...
- Q The Z-score bankruptcy model uses balance sheet and incomeinformation to arrive at a Z-Score, which can be used to predictfinancial distress. The Model follows:Z= ((Working capital / Total assets) x...
- Q The total revenue​ (in hundreds of​ dollars) from the sale of xspas and y solar heaters is approximated byR(x,y) = 11+196x+218y−8x^2−7y^2−4xy.Find the number of each that should be sold to...
- Q A rectangular box with a square base is to be constructed frommaterial that costs $6/ft2 for the bottom, $14/ft2 for the top, and$5/ft2 for the sides. Find the greatest volume...
- Q Why don’t we memorize a definite integral table?
- Q What are related rates? How related rate is useful in solvingphysical problems?
- Q Multivariable Calculus: Surface Area and Change of VariablesFind the surface area of the surface given by z=18−2x−3y over the triangle with vertices: (0,0), (2,3), (4,1).Since this is not a type...
- Q A conical tank has height 9 m and radius 4 m at the base. Waterflows at a rate of 3 m^3/min. How fast is the water level risingwhen the level...
- Q In 2007, (when t = 0), world solar photovoltaic (PV) marketinstallations were 2826 megawatts and were growing exponentially ata continuous rate of 48% per year.†(a) Define the variables.Let S be...
- Q A tank contains 200 gallons of water that has 5 lbs of saltalready in it. A brine containing .5 lbs of salt per gallon isentering the tank at a rate...
- Q A swimming pool whose volume is 10,000 gal contains water thatis 0.02% chlorine. Starting at t = 0, city water containing 0.001%chlorine is pumped into the pool at a rate...
- Q In 2010, (when t = 0), the population of acountry was 1.16 billion people and increasing at a rateproportional to its population. If the population is measured inbillions of people...
- Q An airliner passes over an airport at noon traveling 510 midivided by hr due west. At 1 : 00 p.m.​, another airliner passesover the same airport at the same elevation...
- Q Find and classify the local extrema of the function f(x,y) =(x^3)y+12(x^2)+16(y^2).
- Q An aquarium pool has volume 2 ·106  liters. The pool initially contains purefresh water. At  t = 0 minutes, watercontaining 20 grams/liter of salt is poured into the pool at a rateof...
- Q Thepopulation  P(t)  ofmosquito larvae growing in a tree hole increases according to thelogistic equation with growthconstant  k =0.5  days−1 and carryingcapacity  A = 1000.Find a formula for the larvaepopulation  P(t),assuming an initial population of  P(0)= 50  larvae.P(t) =__________After...
- Q 1. Determine the area of the area bounded by: curvature :y = x2- 7x + 6 and x-axis.2. Calculate the area of the area bounded by curves: y = 9...
- Q abaseball player bats a ball straight up with an initial speed of109 miles. it reaches a height of s = 0.03t-0.003t ^ 2 miles aftert seconds. What is the speed...
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