The rectangle shown here has one side on the positive y-axis, one side on the positive x-axis, and its upper right-hand vertex on the curve y = (ln x)/x2. What dimensions give the rectangle its largest area, and what is that area?

Q: A factory produces Q(L) = 9L²/3 items each day, where L is the size of the labor force in…

A: The solution is given below in detailed

Q: Find the length of the graph of y = (1/2) cosh 2xfrom x = 0 to x = ln 25.

A: Length of the graph y=f(x),a<x<b is given by L=∫ab1+dydx2dx Here,  y=12cosh 2x⇒dydx=122sinh…

Q: 2. A hemisphere of radus 12 nches and base up is full of water that runs out through an orifice of…

A: Dimensions of a hemisphere tank are: Radius R=12 inches or 0.3048 mHeight of tank H1=Radius of tank…

Q: 2. The amount of heat H (in joules) required to convert one gram of water into vapor is linearly…

A:

Q: An object hangs from a string in a stable position and is represented by the function y = 4 sin (3x)…

A:

Q: The cost of certain piece of machinery is $ 700 and its value is depreciating with time according to…

A: We have to find the value after 6 years.

Q: 5. For y = -ln(x), find the value of x where the slope is a) x = − 6 b) -In(6) d) Does Not Exist

A:

Q: The half-life of Palladium-100 is 4 days. After 12 days a sample of Palladium-100 has been reduced…

A:

Q: A population of yeast cells can double in 6 hours. Assume an initial population of 4,000 cells.Write…

A:

Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

A:

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from vertical…

A:

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: A company finds that the total cost of manufacturing a units of a certain product is given by C(x)…

A: We will find the required information as shown below

Q: An investment earning interest at the rate of 10%, compounded continuously, will double in tyears.…

A: Let's solve,

Q: A cylindrical can, open at the top, is to hold 490 cm33 of liquid. Find the height and radius that…

A:

Q: I need some help with this optimization problem

A:

Q: #2. Researchers have descried the maximum growth rate of a phytoplankton as a function of the cell…

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Q: If we put a cool object into a preheated oven, Newton's law of heating tells us that the difference…

A: Given: A potato initially has a temperature of 75 degrees and the oven is preheated to 375 degrees.…

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from horizontal…

A: Graph of y = lnx

Q: Find the absolute maximum value of ƒ(x) = x2 ln (1/x) and say where it occurs.

A: We need to find the absolute maximum value of the function

Q: Start with the graph of y = ln x. Find an equation of the graph thatresults from vertical stretching…

A: Start with the graph of y = ln x.

Q: Find one real root of g (x) = ln(x4) = 0.70 between 1 and 2. How many number of iterations were…

A:

Q: The graph of the acceleration a(t) of a car measured in ft/s is shown. Use Simpson's Rule with n = 6…

A: Given, a=0b=6n=6

Q: a) Determine whether the equation is exact. If it is exact, then: (b) Solve the equation.  (c) Use…

A: Given differential equation dydx=-4x+2y2x+3y To find: (a) To determine whether the equation is exact…

Q: In a study of eating behavior, the cumulative intake (in grams) of one individual was found to vary…

A: In a study of eating behavior, the cumulative intake (in grams) of one individual was found to vary…

Q: (d) If the ornithologists observe that birds of a certain species reach the shore at a point 3 km…

A:

Q: A cylindrical can, open at the top, is to hold 470 cm3 of liquid. Find the height and radius that…

A:

Q: Find one real root of g(x) = ln(xª) = 0.70 between 1 and 2. How many number of iterations were…

A: Before starting the solution, let we explain the False Position Method.Intermediate value theorm: A…

Q: a). A drug in the blood stream decays by according to the equation y'=ky, where y is the…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: The sum of the reciprocal s of Rehman's ages (in years) 3 years ago and 5 years from now is -. 1…

A: Age Related Problem

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: Solve parts a,b, and c.

A: Here we need to apply some basic concepts of derivatives to find the answers

Q: Evaluate the integral: t² ls teu du ds dt

A: Let's evaluate given triple integral.  There is no need to draw the graph.

Q: A radio active element (x) has a half-life of 38 hours. Initially, X = X0 %3D . Determine the amount…

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Q: The population of a certain country is growing at a rate of 1.4% per year. How long will it take for…

A:

Q: Find the absolute maximum and minimum values of ƒ(x) =10x (2 - ln x) on the interval [1, e2 ]

A: The given function is  ,fx=10x2-lnx on interval 1 , e2. To find the absolute maximum and minimum…

Q: A cylindrical can, open at the top, is to hold 160 cm³ of liquid. Find the height and radius that…

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Q: A pedestrian crosses diagonally from one corner of a two kilometer by three kilometer City Park to…

A: Consider the provided question, Given a city park has dimension 2 km x 3 km. Here, width (b) of the…

Q: Find a quadratic function with a root at X 5i that also includes the point (2, 14).

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Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A: Topic-basic maths

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: linear density of a rod of length 16 m is given by p(x)=25square root x+4 measured in kilograms per…

A: Explanation and solutions is given below....

Q: A cylindrical can, open at the top, is to hold 470 cm of liquid. Find the height and radius that…

A:

Q: 4. The profile of the cables of a suspension bridge may be modeled by a parabola. The central span…

A:

Q: The half-life of Palladium-100 is 4 days. After 16 days a sample of Palladium-100 has been reduced…

A:

Q: The half-life of bismuth-210,210Bi, is 5 days.(a) If a sample has a mass of 200 mg, find the amount…

A: Given : The half-life of bismuth-210, 210Bi, is 5 days.

Q: An exponential fuction is given by the equation y=3^× Using the points x and x+1 show that the y -…

A:

Q: The half-life of bismuth-210, 210Bi, is 5 days.(a) If a sample has a mass of 200 mg, find the amount…

A: a) Given  N15 (amount remaining after 15 days) = 200(0.5)^15/5= 200(0.5)^3 = 200 × 0.125 = 25 mg

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.