The amount of energy needed to increase the radius of orbit of a 500-kg satellite from its original orbit r - 10 000 of radius 10 000 km can be modelled by the function E = 2×100| where E is the energy, in r Joules, and ris the new radius, in kilometers.

Q: The rate (in mg carbon/m³/h) at which photosynthesis takes place for a species of phytoplankton is…

A: To find the maximum value, P''(I)<0. If this condition satisfies, then P will be maximum at I.

Q: Find the domain of the function. f(x) = ln ( 1/ (x + 1)

A: f(x)=ln1x+1

Q: The volume V of a right circular cylinder of height h and radius r is V = πr 2 h. If the height is…

A: Given: The volume of a right circular cylinder is, V=πr2h . Here, h is the height of the cylinder…

Q: The temperature of points on a plate x2 + xy + y? <1 is modeled by the function f(x, y) = 25(x² +…

A: Given: The temperature of point on a plate x2+xy+y2≤1 is model by the function is : f(x, y)=25 x2+y2…

Q: The number of bacteria in a culture is given by the function ?(?) = 350?^0.8?, where t is measured…

A:

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

A:

Q: The finance department of Tayitu Company conducted a study of their weekly sales in the past years,…

A: NOTE: Refresh your page if you can't see any equations. . here we want to find the weekly sales at…

Q: Differentiate and simplify this function g (y) = y3 / ln(2y)

A:

Q: Plot the function f(1) for -10 <xs 10. %3D 1+e5.5 – 1.5x 20

A: Graph of any function can be plotted by joining the points from which the function passes. So to…

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

A:

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given query is to find the maximum concentration of antibiotics in bloodstream.

Q: A spherical balloon with radius r inches has volume V(r) =Tr'. Find a function that represents the…

A: First, we are given the formula for the volume of a sphere…

Q: It was determined that the number of prey consumed by a predator over a period of time was a…

A:

Q: Approximate the function at the value of x to four decimal places.

A: f(2)=ln 2+1+e2=ln (3)+e2

Q: The number N of cars produced at a certain factory in 1 day after t hours of operation is given by…

A: Given problem:- The number N of cars produced at a certain factory in 1 day after t hours of…

Q: Let f(x)=xlnx+x. If f'(x)=0, solve for x. Round your answer to 4 decimal places.

A: So,  Given        fx = x lnx +x       f'x = ln x + xx+                = ln x +1  + 1…

Q: A pebble is embedded in the tread of a rotating bicycle  wheel of diameter 60cm. If the wheel…

A:

Q: Let L(x) be the linearization of the cube root function at x=8. When using L(x) to approximate the…

A:

Q: Find the domain of the function. f(x) = √(ln x)

A: To find domain of the function fx=lnx. Solution: Domain is the input value for which a function is…

Q: Determine the point(s) at which the graph of -8x f(x) 2x - 1 has a horizontal tangent. (x, y) = Need…

A:

Q: P = 6x + sq. root of x where x is the number of magazines you sell in a month. If you are currently…

A: Given p(x)=6x+x  where x is the number of magazines you sell in a month.

Q: Two ships leave port at the same time. One sails south at 9 mi/h, and the otiyer sails east at 12…

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Q: If L(x)=mx+b is the linearization of the principal square root function of x at x=900, then b= Use…

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Q: Two ships leave port at the same time. One sails south at 18 mi/h, and the other sails east at 24…

A:

Q: Find the equation of the line tangent to the graph of f at the indicated value of x. f(x) = Inx?;…

A:

Q: 2. Suppose the rate of growth of bacteria in a Petri dish is given by q(t) = 3°, where t is given in…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: The volume V of a right circular cylinder of height h and radius r is V= π r 2h. If the height is…

A: Volume of a right circular cylinder = V = π r2 h where r is radius of cylinder  and h is height of…

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: pressure

A:

Q: The marginal revenue (in thousands of dollars) from the sale of x gadgets is given by the following…

A: (a) The function representing the marginal revenue is R'(x)=4xx2+26,000-23 (in thousands of dollars)…

Q: d y is a function of tin

A:

Q: Find the function whose tangent line has the slope 3x² + 1 for each value of x and whose graph…

A: We have to find the function whose tangent line has the slope 3x2+1 for each value of x and whose…

Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: Given query is to find the maximum concentration of antibiotics in the blood during the first 12…

Q: The area of a disk as a function of radius is given by A = πr². How close must r be to 2.0 cm to…

A:

Q: A 2000-liter cistern is empty when waterbegins flowing into it (at t = 0) at a rate (in L/min) given…

A: It is given that   . Suppose a quantity Q changes over time at a known rate Q'. Then the net change…

Q: 5. Consider the population of bacteria grows according to the function f(t) 200e0.02t, where t is…

A: The solution of the problem is given in the next steps.

Q: For what value(s) of x does the graph of f(x)=10x^3 − 90x^2 + 240x +90 have a horizontal tangent?…

A: To find the slope of the tangent we find f'(x)

Q: The slope of the line tangent to the graph of f(x) = 18 – 5x² at the point x = -8 O 20 O 10 O 160 O…

A:

Q: Differentiate the function. y = In(12 + t – t31)

A: We have to find derivative

Q: The surface area of a hot-air balloon is given by the function S(r) 4Tr", where r is the radius of…

A: NOTE: Refresh your page if you can't see any equations. . the radius is increasing at a rate of…

Q: O For what value of x does the function f (x) = 4x2 – x +1 have a horizontal tangent?

A:

Q: The height, h, in ceneles, of a pis ton reoving up and down in an engine cylinder modelled by the…

A:

Q: 1. A truck that delivers essentials in remote areas can travel 85 kilometers. Which of the following…

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: Differentiate the function. y = In(12 + t – t³1) y' =

A: Here we differentiate the y with respect to t

Q: f(x) = In(x² + 1)

A:

Q: fx)= e? (ょ2 +メ-1) interval [o,

A: Given that: f(x)=e-2(x2+x-1) in the interval [0, 1]

Q: Let L(x) be the linearization of the cube root function at x=64. When using L(x) to approximate the…

A: The linearization L(x) for tge function f(x) at x =a is given as L(x) = f'(a) (x-a) + f(a)

Q: The rate at which blood pressure decreases in the aorta of a normal adult after a hearbeat is dp/dt=…

A: It is given that rate at which the blood pressure decreases in the normal adult is…

Q: Express the area A of a right triangle as a function of the height h if the base of the triangle is…

A:

Q: A ball is thrown into the air with an initial upward velocity of 48 ft/s. The height () of the ball…

A: Given, initial upward velocity = 48 ft/s h(t)=-16t2+48t+4