The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000 + 90x - x2/3 . Find the marginal average cost at x = 20, C'(20) and interpret the result

Q: Give the implicit solution of y'my-x³-2 Oe-2x = y²(x²+c) Oe²-y²-c 2x Oe² = x²(x²-c) 0²¹-y²(x²-c)

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Q: A distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1. Find the…

A: Given that a distribution of values is normal with a mean of 22.3 and a standard deviation of 41.1 .

Q: Which of the following equations has a solution of the form F(x,y) = C A. 2x + 3y + (2y + 3x) dy dx…

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Q: On a part-time job, you are asked to bring a cylindrical iron rod of density 7800 kg/m³, length 88.6…

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Q: Evaluate the sum 50 Σ(2 · k + 5) = k=1 50 Σ5₁(2. k+5). k=1

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Q: Which of the following equations is NOT a variable separable differential equation? A 2xydx + (x² +…

A: See this solution in below.

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Q: Find the exact length of the curve. X = t 2 + t y = In (2 + t), 0≤t≤1

A: Given: x=t2+t, y=ln(2+t) We know that exact length of the curve is given by  s=∫t1t2dxdt2+dydt2dt

Q: 7x - 4 3 – – 4x 4x² dx

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Q: Write the function whose graph is the graph of y = x2 , but is shifted left four units and down 2…

A: The original function: y=x2 To write a function whose graph is the graph of original function but…

Q: Evaluate the following integrals: 2 5cos x - 3tan x COS X S- -dx

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Q: 9. Determine the convergence of the following series using the ratio test. If the ration test is…

A: Ratio Test

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Q: 4. Let sin² x + cos² y = x² + y². Find y' by using implicit differentiation. ។

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Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

A: Given, dy/dt = 5t4-3et+2 And conditions y= 1  and t=-2

Q: Find the exact length of the curve. x = 5 + 12t², y = 6 + 8t³, 0≤ t ≤ 3 12117-1)

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Q: II. Give the indicated derivative 1) find the 27th derivative of cos x

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Q: Can someone compute this into decimal form. f'(4)=-sin(4)-3sec²(4) Thank you

A: we already have f'(x)=-sinx-3sec²x so,f'(4) =-sin(4) -3sec2(4)

Q: (a) Find the distance from P1 = 1 - 2, - 32 to P2 = 13, - 52.(b) What is the midpoint of the line…

A: Given, P1=-2, -3 and P2=3, -5

Q: Evaluate S9 cos √2x dx using a substitution followed by integration by parts.

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Q: 1. Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

A: We need to find partial derivative. NOTE - As per Bartleby guidelines we can solve one question.…

Q: If f(x) f'(x)= -3x sin²(x) + 3x cos² (x) + 3 cos(x) sin(x) = 3x sin x cos x, find Find f'(4) =

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Q: Evaluate the following integral. 4x Jetz 4* sin(2x) dx =

A: The given integral is e4xSin(2x).

Q: 111 Solve for the actual solution of y''' = 2x + 1 when y(2) = 1, y'(2) = − 4, y''(2) = 7 X 12 6 X 4…

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Q: A B C D lim /(x) = 0 x+2+ lim f(x) = 2 x →-2+ lim /(x) = 0 x+2- lim f(x) = -3 x--2 -5-4-3-2-1 Y -3-…

A: Find limit of function

Q: Elimination of Arbitrary Contants 1. y = peax cosbx + yeax sin bx 2. y = c₁x + c₂ex ; a and b are…

A: we need to eliminate the arbitrary constants C1 and C2

Q: Let SS be the universal set, where: S={1,2,3,...,28,29,30} Let sets A and B be subsets of S, where:…

A: S={1,2,3,...,28,29,30}Let sets A and B be subsets of S, where:Set A={4,5,6,9,13,20,24,28,30}Set…

Q: 8. Use the limit comparison test to determine the convergence of the following series; state what…

A: See this solution in below.

Q: Which of the following is a non-homogeneous function? tan³y/x OxLnx-xLny O x³ − xy + y² (y² + v²)³/2…

A: homogenous function is f( tx,ty ) = t^n f(x,y) option a) f(x,y) = tan (3y/x) now,…

Q: A wooden beam has a rectangular cross section of height h and width w (see figure). The strength S…

A: Given :d=46 cm

Q: (7) sin √x dx. (First substitution, then by parts)

A: The solution for the given integral is as follow.

Q: The answer is incorrect

A: We have to find derivative value at the given x-value.

Q: Find the given limit (x² - 1)(y² - 4) lim (x,y) →(1,2) (x - 1)(y-2)

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Q: Find a unit vector in the direction in which f(x, y, z) + == Z y² increases most rapidly at P(1, 2,…

A: Given f(x,y.z)=xz+zy2,point (1,2,-2) The objective is to find the unit vector and rate of change of…

Q: 1. If an ((¹+√5) - (¹-√5)n), find a, and a₂.

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Q: If the slope m of the graph of a linear function is ,the function is increasing over its domain.

A: If the slope m of the graph of a linear function is _______, the function is increasing over its…

Q: Given f(x) = 4x¹n (x) " f'(9) _ answer the following:

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Q: 1. y peax cosbx + peax sin bx ; a and b are parameters

A: According to given ,1st is solved.y=ϕeaxcosbx+ψeaxsinbxhere 2 constant then 2 times derivative

Q: 1) Using the definition, calculate the derivatives of the functions. Then find the values of the…

A: Solve by derivatives

Q: Find the average rate of change of f1x2 = 8x2 - x:(a) From 1 to 2 (b) From 0 to 1 (c) From 2 to 4

A: Given: Given expression: f(x) = 8x2-x Formula Used: The Average rate of change ARC = f(b)-f(a)b-a

Q: Suppose that F(x) = √ (t +)dt where x < 0. Using the Fundamental Theorems of -4 Calculus, find the…

A: Given ; F(x)= integration of (t+1/t), t from -1/x to x2.

Q: Question 26 Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x =…

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Q: If f(x) = f'(x) = f'(2) = tan x 2 sec x 1 + 2 tan(x) sec(x)

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Q: Calculate the slope of the line that passes through (-11, -6) and (1, -4). O - 1 O -16 1 O 6

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Q: Find the directional derivative of f at the point P in the direction of a. P(4,0); f(x, y) = 4x³y³;…

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Q: Question 2 Determine the values of a for which the following system of linear equations has no…

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Q: Suppose f f(x) dx = 25, f f(x) dx = 10, f g(x) dx = 10 and h(x) = 0 3 the following: a. (5f(x) 6g(x)…

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Q: Use the Lagrange multipliers to find the maximum and minimum values of f(x, y) = 2x + y − 2z subject…

A: Given function fx,y,z=2x+y-2z Let gx,y,z=x2+y2+z-2025

Q: Use the disk method to find the volume of the solid obtained by rotating the region bounded by x = 1…

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