A homeware company has been approached to manufacture a cake tin in the shape of a "ghost" from the Pac-Man video game to celebrate the 45th Anniversary of the games launch. The base of the cake tin has a characteristic dimension / and is illustrated in Figure 1 below, you should assume the top and bottom of the shape can be represented by semi-circles. The vertical sides of the cake tin have a height of h. As the company's resident mathematician, you need to find the values of r and h that minimise the internal surface area of the cake tin given that the volume of the tin is Vfixed- 2r Figure 1 - Plan view of the "ghost" cake tin base. (a) Show that the Volume (V) of the cake tin as a function of r and his 2(+1)²h V = 2

Q: the answer is C, could you show me how to do it

A:

Q: please include radicals in answer

A:

Q: 1. Evaluate the integral f(x, y)dxdy, of function f R² →R over the domain DC R2, where: f(x, y) = 2x…

A: ∬D​f(x,y)dxdywhere  f(x, y) = 2x + y , and D is the triangular region with vertices at  (0, -1) ,…

Q: (2) (8 points) Determine normal vectors for the planes given by the equations x-y+2z = 3 and 2x + z…

A: Given:Plane 1: x - y + 2z = 3Plane 2: 2x + z = 3  Step 1: Normal Vectors of the Planes The equation…

Q: Q2/ verify that f grad = (h grad f- f grad h) h h₂ where and h are scalar factions. Solve in paper

A: For proving this relation, we will use product rule of gradients,∇(UV)=U∇V+V∇U        Eq (i)U and V…

Q: The OU process studied in the previous problem is a common model for interest rates. Another common…

A: Step-by-Step Manual Calculations: (a) Simulating the CIR Process using the Euler SchemeGiven the CIR…

Q: 60 फं + 2 T 2 -2 -3 2 4 5 6 The graph above shows the function f(x). The graph below shows g(x). फ 3…

A: Step 1: Identify Key Points in f(x) and g(x)By examining the graphs:Key points of f(x) (Original…

Q: Given the graph of f(x) below. Determine the average rate of change of f(x) from x = 1 to x = 6.…

A: We have to determine the average rate of change of f(x) from  x=1 to x=6 by using the given graph of…

Q: i need the solution of part d and bonus. THANK YOU

A:

Q: Draw the region bounded by the curves. y = 3x2, x = 0, and y = 3   Use the disk method to find the…

A:

Q: #4, #11, #25

A: 4 1125

Q: IV. Consider the function f(x) = esin 2x 1. Find the second-degree Maclaurin polynomial of f(x). 2.…

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Question 2 1 pts Let A be the value of the triple integral SSS. (x³ y² z) dV where D is the region D…

A: Now we can calculate sin(3A)By substituting the values :- sin(3A) = sin(3 * 25/8) ≈ -0.162…

Q: Find lim(x, y) as it approaches xy/(x2 +y2) if it exists.  If the limit does not exist, say so and…

A:

Q: Determine where the function is concave upward and where it is concave downward. (Enter your answers…

A:

Q: #22

A: Step 1: Step 2:

Q: A function f is even if f(x) = f(x) for all x in the domain of f. If f is even, with lim f(x) = 4…

A: Step 1: concept  Step 2: solution Step 3: Step 4:

Q: "P3 Question 3: Construct the accessibility matrix Passociated with the following graphs, and…

A: Step 1: Constructing the Accessibility Matrix PThe accessibility matrix (adjacency matrix) P…

Q: Given g = (-5, 10) and u = (5, 2), find -4ğ - 6.

A: If you have any questions let me know in the comment box thankyou.

Q: #39

A:

Q: Exercise 1 Given are the following planes: plane 1: 3x4y+z = 1 0 plane 2: (s, t) = ( 2 ) + ( -2 5 s+…

A: In the above diagram, the angle between the normal vectors α is what we are calculating using the…

Q: Find the equation of the line / in the figure below. Give exact values using the form y = mx + b. m…

A: Given the function  f(x)=10x and  Point : x=log⁡(9) Put the value of x=log⁡(9) in f(x),…

Q: 2. (i) What does it mean to say that a sequence (x(n)) nEN CR2 converges to the limit x E R²? [1…

A: Approach to solving the question:(i) Convergence of a Sequence in (R2)To say that a sequence…

Q: Sketch a graph of f(x) = 2(x − 2)² − 3 4 3 2 1 5 ས་ -5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 -5+ Clear All…

A: Key references:https://youtu.be/TxPDQfWeAUg?si=auU0w_nfOyr6mRyU

Q: I want the solution with all the details if L is of rank n

A:

Q: 5. Please solve this for me and show every single step. I am studying  and got stuck on this…

A: To find the area between two curves, we first need to find the points where the curves intersect.…

Q: 60! 5!.7!.15!.33!

A: The factorial of a non-negative integer n, denoted by n!, is the product of all positive integers…

Q: The integral of x2 dx with upper bounds of 2 and lower bounds of 0. Compute the integral exactly

A: The integral we are trying to solve is:∫02x2dx

Q: In the following exercises, evaluate each definite integral using the Fundamental Theorem of…

A: 170. To evaluate the integralget the antiderivative of each expressionx2 -> x3/3-3x ->…

Q: Determine the following limit. lim 35w² +8w+4 w→∞ √49w+w³ 3 Select the correct choice below, and, if…

A: Step 1:  Given Limit ExpressionWe must assess the following boundaries:…

Q: Determine the following limit, using ∞ or - ∞ when appropriate, or state that it does not exist. lim…

A: Step 1:Step 2: Step 3: Step 4:

Q: a C d 2 1 -1 0 1 2 3 -1 Graph of f'(x) (5) The graph of f'(x), the derivative of f(x), is shown in…

A: The question involves analyzing the graph of  f'(x) , the derivative of  f(x) , to determine which…

Q: 4c Consider the function f(x) = 10x + 4x5 - 4x³- 1. Enter the general antiderivative of f(x)

A: Step 1:Step 2: Step 3: Step 4:

Q: Test the series for convergence or divergence.

A: Step 1: Step 2: Step 3: Step 4:

Q: Write the given third order linear equation as an equivalent system of first order equations with…

A:

Q: 3. Evaluate. Leave your answer in simplest exact form: 8 x²+x+1 √x dx

A: Step 1:

Q: express the inverse transforms in terms of step functions, and then find distinct formulas the for…

A: I hope this is helpful.

Q: Please help me with these questions. I am not understanding what to do. Thank you

A: We will use the transformation below to transform the equation x2 + y2 = 2 into polar coordinates:x…

Q: A cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is…

A: Step 1:Step 2:Step 3:Step 4:

Q: (2) (4 points) Find all vectors v having length 1 that are perpendicular to both =(2,0,2) and j =…

A: We find all vectors v with length 1 that are perpendicular to both a = (√2/ 2, 0, √2/ 2) and j = (0,…

Q: Respond to this.

A:

Q: ints) A common representation of data uses matrices and vectors, so it is helpful to familiarize…

A: Let's analyze the problem step by step.We are given two column vectors:  Final AnswerRank of AAA:…

Q: 15. Please solve this and show each and every step please. PLEASE no chatgpt can I have a real…

A: The given function is F(r, s, t) = ln(r+t) * (r+s+t). This is a multivariable function, which means…

Q: 471 i want answered

A: Detailed explanation:490. ∫ (-1) dx To evaluate this integral, we simply need to find the…

Q: Question 3 1 pts By changing to spherical coordinates, calculate A = SSS, e(x²+y²+z²)³/2/2 dV, = 2x…

A:

Q: Find the average value gave of the function g on the given interval. gave = g(x) = 8√√x, [8,64] Need…

A: The average value gave​ of the function over the interval [8, 64] is 7180​.

Q: Complete the description of the piecewise function graphed below. 6 5 -7-6-5-4-3-2-1 2 3 5 6 -1 -2…

A: Identified points from the graph: 1. First segment: Points: (−6, −3), (-4, 0), (-2, 3) 2. Second…

Q: Derivation of the Laplace transform variational leration method in the same and simplified manner…

A: Derivation of the Elzaki Variational Iteration Method (EVIM) We will derive the Elzaki Variational…

Q: 6. Find the angle to the nearest degree between the two planes given by x-2y+2=0 and 2x+3y-22-0

A:

Q: The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at…

A: Note- open circle at any point means value of function at that point is not defined or not included…