A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 200 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.04 cents per square centimeter. The top will be made of glued paper, costing 0.05 cents per square centimeter. Find the dimensions for the package that will minimize production cost.

Q: ders of integration. Use the more convenient order to evaluate the integral over the plane dA unded…

A:

Q: Please answer number 5. And how can we identify what kind of graph is that.

A: Topic:- function and it's curve

Q: y" + 5y' = 0

A: Use the homogeneous differential equation method to solve the second order differential equation.

Q: |r'(t) × r"(t)|| Use the formula k(t) to find k(t). ||r(t)||* r(t) = 11 cos(3t)i+ 11 sin(3t)j+ 7tk…

A:

Q: Solve the following system of IVP: -3 3 x' = Ax where A =-2 -1 1 and x(0) 21 %3D 3.

A:

Q: Determine how many terms should be used to estimate the sum of the entire series with an error of…

A: Use the  Alternating Series Estimation Theorem and solve the problem.

Q: Solve. y" + 36y = u;(t), y(0) = y'(0) = 0 %3D S f(t) 9(t) for t > 5* for t < 5 The solution can be…

A:

Q: The geometric series 4 5-2+ 5 16 + 25 8 32 125 625 is convergent. true false

A:

Q: Evaluate

A:

Q: dE 3D25-8t, where t is the number of hours the operator has been at work dt The rate at which a…

A: Given dEdt=25-8t To find E(t):

Q: S. Elli gives her son Paul 1¢ on his first birthday, 2¢ on his second birthday, 4¢ on his third…

A: Here, the amount doubles on every birthday starting from 1c. That is we have the sequence:…

Q: Find the surface area formed when the curve f(x)=x^3 between x=1 & x=3 is rotated around the x-axis

A:

Q: Consider the function f(x) 1 on the interval 4, 8]. Find the average or mean slope of the function…

A:

Q: A light shines from the top of a pole 20 m high. A ball is falling 10 meters from the pole, casting…

A: We sketch lines on the given image as below: Let us assume x = The height of the ball = BG.  y =…

Q: 2 -1 1 2 -2 3.

A:

Q: Rewrite the Cartesian equation x = 7y as a polar equation. r(0) = Use the math palette or type theta…

A: Solve the following

Q: 2. Let A = (1,0, 2) and B = (6, -2, 3). Solve for proja B. %3D

A:

Q: Set up a double integral that represents the area of the surface given by z = f(x, y) that lies…

A:

Q: 4. In each part below, give an example of a function which satisfies the given criteria. Justify…

A:

Q: Find the derivative f (x) = e3x+ x (csc x + sec x)² %3D

A: Using product rule of Differentiation we find the derivative of given function.

Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

A: This is case where critical points are not defined.

Q: show

A:

Q: ded above by surface z = 10 – x2, bou e planes y = 0 and y = 3.

A:

Q: The 3rd term of an arithmetic series is 34 and the 17th term is -8. Find the sum of the first 20…

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: 3) Which type of quadric surface listed in Table 2 below is 4x² + y² + 4z² – 4y – 24z + 36 = 0?

A:

Q: 1. F(x) ; (3, 7), [-6, 4], (-co, 0), (-5, +∞), [-5, +∞), [10, -5) %3D x+5 2. F(x) =: (0, 1), (-1,…

A: To find the domain of the function.

Q: 7. Test for relative maxı.na and minima and classify the critical points of the function f(x, y) =…

A:

Q: An environmental landscaping company wishes to run a pipeline from a pumping platform (R) located…

A:

Q: Problem 5 Find the general solution of the following equation: y" + 2y'- 15y = 0. Find the…

A:

Q: spherical coordinates arc

A:

Q: Use an iterated integral to find the area of the region bounded by the graphs of the equations. y =…

A: Given the equations are y = x32 y = 6x

Q: An airplane leaves City A and flies 132 km due north to City B. It then turns through an angle of…

A: Given problem:- An airplane leaves City A and flies 132 km due north to City B. It then turns…

Q: 5 – sin n Test the series for convergence or divergence. n=1

A:

Q: THe rate of U.S. per capita sales of bottled water for the period 1993–2003 could be approximated by…

A:

Q: f (x) = x²In x + sec x; find f"(x)

A: Given ,f(x)=x2ln(x)+sec(x)DIferentiate…

Q: For the functions f(x) = xeX 1. The minimum value of the function occurs when x = 2. A point of…

A: Note that, the function if decreasing when f'(x)&lt;0  it is concave upwards if f''(x)&gt;0.

Q: if f(x) dx=18 and F(X)dx=3.8 find 5 S F(x) dx

A:

Q: Determine the number at which h(x) = V16 – x² is continuous. %3D | Vx²-1 Determine the largest…

A: Note that: A function is said to be a continuous function on some interval when the function is…

Q: Find a formula for the slope m of the graph of f at the point (x, f(x)). Then use it to find the…

A:

Q: Compute the partial sums S2, S4, and S6. 9 9 + 9 + S2 = | %3D S4 = | S6 =[ %3D + +

A:

Q: (A) Find the dimensions of a rectangular box with square ends that satisfies the delivery service's…

A:

Q: Use the Definition of a Definite Integral or Theorem 4 from Section 5.2 to find the exact value of…

A:

Q: Approximate the area under the curve y = x from r = 2 to a = 5 using a Right Endpoint approximation…

A:

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 5- 5- 3 2- 1 3…

A:

Q: region bounded by f(x) = 3- X, y = 0, and x = 1 is shown. /hat is the volume of the solid formed by…

A: Follow next step

Q: Find a parametric equation for the path of a particle that moves halfway around the circle…

A: We have to find the parametric equation for the path of a particle.

Q: Determine Y for y= 5x²(1 + x²).

A:

Q: Problem 7 Using the method of undetermined coefficients, find a particular solution yp of the…

A:

Q: a. Determine "(®) if fx) = (8x² + x)³. Write your answer in simplified form. %3D b. Determine

A:

Q: Frank wants to know the length of a tunnel built through a mountain. To do so, he makes the…

A: Solve the following