Minimizing Costs For its beef stew, Betty Moore Company uses aluminum containers that have the form of right circular cylinders. Find the radius and height of a container if it has a capacity of 45 in.3 and is constructed using the least amount of metal. (Round your answers to two decimal places.) radius in height in

Q: r(t) = (−2 cos (2t), 3 sin (3t), In (2t)), then the fr(t)dt is equal to 3 Cos cos 4 where C is a…

A: Given:    rt=-2cos2t,3sin3t,ln2t then  ∫rt dt =∫-2cos2t,3sin3t,ln2tdt…

Q: J7 -dz 21-8

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Q: = 2√/16 - x² - y2, then the domain of D = {(x, y) x² + y² ≤ 16}. 2

A: We have to choose the correct option from the given options according to the given information

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A:

Q: Let z = (y - 2x) ³, where x = s′ s²t and y = st². Use the Chain Rule to dz find when s = 2 and t =…

A:

Q: f(x, y) = 6√x - y'e a) b) -3xy + Find f and fy. Evaluate fazy (4,-1).

A: Given f(x,y) =6x -y2 e-3xy+3y

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Q: Determine whether the series Σ or divergent. +∞0 (-1)" 4" 100 is absolutely convergent,…

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Q: f(x, y) a b) = 4x²+2y² Find the domain of f. Show that the limit does not exist lim f(x,y) (x,y) →…

A: Here, the given function is: f(x,y)=3xy4x2+2y2

Q: Let z = √7xy +9y, and x = s³ and y = 1². Use Chain Rule to find dz when t = 1 and s = 2.

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Q: If f(x, y) = sin (xy) - yer, then f (0, 1) = -1. Select one: O True O False

A:

Q: Work Problem You must provide a clear and detailed solution for the question. Let 2 = (y - 2x) ³,…

A: To find out the partial derivative.

Q: A road perpendicular to a highway leads to a farmhouse located a = 1.5 km away. An automobile…

A:

Q: For the limit, sin(x² - y²) x² - y² if we approach along y-axis, we will get 0. Select one: O True O…

A: We know :- If we approach along y axis the x=0

Q: Given the function f(x, y) = √2x + y = 1 - x + 1 Select one: O None of those O D= {(x, y)]y > 1 +…

A: To find out the domain of the given function..

Q: If z = x - 2y, dz and x = 2t, y = 5t, then the value of at dt t = 3 is equal to -8. Select one: True…

A: To determine whether the given statement is True or False.If z=x-2y, and x=2t, y=5t, then the value…

Q: graph 10 5 0 answer 5

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Q: The admission fee at an amusement park is $1.50 people entered the park, and the admission fees…

A: Given: The admission fee at an amusement prk is $1.50 for children and $4 for adults.On centrain…

Q: Question 23 Find the length and width of a rectangle that has an area of A square centimeters and a…

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Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

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Q: Vector A has a magnitude of 8.0 m, South and vector D has a magnitude of 10.0 m, 530 W of N. Find…

A: To find out the vector product.

Q: For the following telescoping series, find a formula for the nth term of the sequence of partial…

A: Here we have to find the limits and then state whether it diverges or not.

Q: Find the limit of the following sequence or determine that the sequence diverges. (-1)^) 4n+3

A: The given sequence,       -1n4n+3

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A: This question can be solved using the concept of the stated theorem 13.9

Q: S sin² 2xcos² 2xdx

A: This question is based on indefinite integral using Trigonometric formula.

Q: What is the equation of the tangent live the When X = 4 √(x) = ² -6√x cheve f(x) = 3/

A: Given ::fx=8x-6xx=4

Q: If f(x, y) = 2√/16 - x² - y², then the domain of f is the set D = {(x,y)|x² + y² ≤ 16}. Select one:…

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Q: If then fyy = Select one: O True O False f(x, y) = 2(x² + x) (x - y)³ x² + y x - y

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Q: Evaluate the geometric series or state that it diverges. 5k E •(-4)* Σ 5 k=1 Select the correct…

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Q: Is the scalar valued function f(x)=(x^2-1)/(x+1) continuous?

A: This is a problem related to limit and continuity of the function. Please follow the procedure given…

Q: Question 1 function r(t) = (tª In 1, ¹2³, −3e¯³¹). a) Find the integral r(t)dt. b) Find parametric…

A: Here, r(t)=t4ln t, t-32,-3e-3t

Q: A y=1 x=y² B y=x² C (1, 1) X=1 X (0,0) Region A is bounded by the parabola x = y², the line y = 1,…

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Q: Find the limit, if it exists, or show that the limit does not exist. 2 x² - 3y² lim (x,y)→(0,0) x² +…

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Q: Evaluate cosh² x dx }(sinh2n +2) + 0 +x + C O2e²x +4z + C 8 O None of the choices cosh(z)sinh(2)++C

A: We can solve this as follows:

Q: π/2 The integral f/2 So sin drde is equal to cos 0 O-1/2 O 1/2 0 1 00 10

A:

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Given f(x) (x + 21 -x² 4 x < -1 -1 < x < 2 x ≥ 2 a. Evaluate f(-3) b. Evaluate f(-1) c. Evaluate…

A: We need to find values of function.

Q: A heart-shaped graph in a 2D plane is defined by the equation (x² + y² - 1)³ = 4x²y³ Determine dy/dx…

A: See this solution in below

Q: None of the other choices 7 The curve y = f(x) has the horizontal asymptote y = Select one: 00 1…

A: Given function:- f(x) = (x+35)/(x-5)  To find:- Horizontal asymptote of f(x)

Q: If In (x² - y) -x+y+1 then the domain D of the function f is given by the set Select one: f(x, y) =…

A: Given function:- f(x,y)=lnx2-y-x+y+1  find domain of f(x,y)

Q: 1. Find the domain of the vector function r(t) =

A: 1. Given Vector Function,rt = lnt+2, t1-t2, 2tt2 -4

Q: 4. Evaluate (²52³Vl-Pax

A:

Q: C What is f" (x) of f(x) = x Arc sin(x) + √1 − x²? Arc sin(x) 2 √1-2² √1-7² ◄ Previous + Arc sin(x)

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Q: If and x = 1², y = 1² then Select one: 2t √xy(21) 41 None of them √xy (21²) dz dt =? z = √√√xy,

A: Please see the below picture for detailed solution.

Q: If you can only answer one, please answer 99. The questions asks whether the series converges or…

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Q: z = e Select one: True False In (2-y), dz and x = s² - 6t, y = t - s, then the value of when t = 4…

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Q: If the line y = 2 is the horizontal asymptote of the curve y = f(x), then /(2) is undefined. Select…

A: To find whether given statement is true or false.

Q: if u=f(x,y), x=g(w) and y=h(w), using chain rule, what is ∂u/∂w?

A: Silution : Given that u = f(x,y)

Q: Consider the function f(x)=5/x^2 - 9/x^7 Let F(x) be the antiderivative of f(x)with F(1)=0 then…

A:

Q: 1/4 1 1/12 √√x (4x + 1) √x (4X - dx

A: See the details solution in below