Basic Math question and answers for August 07, 2023
- Q 1. F=xi+yj+ (xz+yz)k, and Sis the part ofx+y+z= 1 in the firstoctant, oriented upwards. Compute∫∫Scurl(F)·dSdirectly.2. Compute∫CF·drdirectly (3 curves to parameterize).
- Q Find a solution of the following differential equationssatisfying the given initial conditionsy''+y'+y=x2 , y(0)=1, y'(0)=1
- Q 1. You’ve been hired by a company that makes rectangular storagecontainers. Each container has a square base and each containermust have a volume of 10 m^3. The material for the...
- Q What is the relation between definite integrals and area (ifany)? Research and describe some other interpretations of definiteintegrals.
- Q a)Find the value or values of c that satisfy the equationf(b)-f(a)/b-a = f′​(c)in the conclusion of the Mean Value Theoremfor the function and interval. Round to the nearest thousandth.f(x) ln(x-3),...
- Q The number of new businesses established in the US since1990 can be modeled by the functionNx=110.8x^3-5305.5x^2+76,701x+332,892 where x = 0 represents 1990and the domain is [0, 25].Use the First Derivative...
- Q Outside temperature over a day can be modeled as a sinusoidalfunction. Suppose you know the high temperature of 92 degreesoccurs at 3 PM and the average temperature for the day...
- Q Estimate the area (A) between the graph of the functionF(X)=3/XÂ Â and the interval [1,2]. Use an approximationscheme with N= 2, 5 rectangles. Use the right endpoints.If your calculating utility will perform...
- Q From a thin piece of cardboard 4 in. by 4 in., square cornersare cut out so that the sides can be folded up to make an open box.What dimensions will...
- Q A quantity of air (γ = 1.40) expands adiabatically from aninitial pressure of 2 atm and volume of 2 L at temperature 20 ° Cto twice its original volume. Find:a)...
- Q The number of snowplows needed by a town is given bys(p)=0.5p−0.01p^2. snowplows where p is the population (inthousands).The projected population of the town t years from now isp(t)=150(1+12e^−0.02t)^-1 thousand people.(a)...
- Q Let f(x) = (x2 + 8) / 2xa) Find all local minimum and local maximum values of f.b) Find all intervals on which f is concave up/concave down.Does f have...
- Q 1.A student takes out a college loan of $5000 at an annualpercentage rate of 3%, compounded monthly.a. If the student makes payments of $1000 per month, how much,to the nearest...
- Q Consider the function below. (If an answer does not exist, enterDNE.)f(x) =12x4 − 4x2 + 6(a) Find the interval of increase. (Enter your answer usinginterval notation.)Find the interval of decrease....
- Q Solve the exponential equationsa) log4(x-4)+ log4(x-10) = 2b) (1/4)x = 18c) 34x-1 = 14
- Q Find the approximate area under the curve by dividing theintervals into n subintervals and then adding up the areas of theinscribed rectangles. The height of each rectangle may be found...
- Q Find the general solution of the differential equation y'' + 4y'+ 4y = (e-2t/t2)
- Q Let ?(?)= (sqrt ?)The local linearization of ? at 49 is ? (subscript) 49(?) = ?(subscript)0 +?(?−49) is __________where ?= __________ and ? (subscript) 0= _____________Using this, we find our...
- Q ) Find the VA / HA / maximum and minimum values of f(x) = x^ 2 +1/ x^ 2 − 3
- Q 11.A man invests his savings in two accounts, one paying 6 percent andthe other paying 10 percent simple interest per year. He puts twiceas much in the lower-yielding account because...
- Q Show the feasible region by shading of the following system oflinear inequalities and show all the intersection points (labelyour graph carefully): Hint: Use the guidelines shown in lecturesand show all...
- Q You are looking to spruce up your garden by making a rectangularenclosure using a wall as one side and 160 meters of fencing forthe other three sides. You want to...
- Q A ship embarked on a long voyage. At the start of the voyage,there were 400 ants in the cargo hold of the ship. One week intothe voyage, there were 700...
- Q You are looking to spruce up your garden by making a rectangularenclosure using a wall as one side and 160 meters of fencing forthe other three sides. You want to...
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