A triangle-shaped sheet has a surface mass density of 1.5 grams per square centimeter. Suppose that the corners of the sheet are located at the points P(2,1,2), Q(1,1, -3) and R(2,3,1) and that all the Coordinates are in centimeters. What is the mass of the sheet?

Q: Evaluate the definite integral by the limit definition. [²5 Step 1 5 dx To find the definite…

A:

Q: Use polar coordinates to evaluate the integral vẻ ty dxdy where R is the region in the xy-plane…

A:

Q: Let G be the group of integers under addition, and H the group of even integers under addition. Is G…

A: In group theory, two groups G and H are said to be isomorphic if there exists a bijective map ϕ:G→H…

Q: Let the following predicates be given. The domain is all mammals. L(x)= "x is a lion." F(x)= "x is…

A: 4. The domain is all mammals." is a lion"" is a fuzzy"The aim is to translate the following…

Q: Use appropriate Riemann sum (re-writing as a definite integral) to evaluate (a) n lim Σ nx n² + k²…

A:

Q: The torus obtained by rotating the circle (x − a)² + y² = b about the y-axis, where a > b.Hint:…

A: Given equation of the circle We have to find the volume of the torus using shell method.

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Here we have to verify that x1, x2, x3 are the solutions of x'=Ax.

Q: Newton's Law of cooling states that the rate at which an object cools over time is directly…

A: Advance maths

Q: The matrices listed in Eq. (11) are used in some of the exercises that follow. 12 ^-[13] B-[23].…

A:

Q: Solve the following allocation problem. The cost of warehouse space is allocated to three…

A: Given Information:Raw materials use one-third of the space.Work-in-progress uses one-sixth of the…

Q: Prove the converse Pythagorean Theorem

A: In this question, we will prove the converse of the Pythagorean theorem.

Q: First verify that the given vectors are solutions of the given system. Then use the wronskian to…

A:

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A:

Q: The procedure for obtaining a minimized function in product-of-sums form follows from the basic…

A: Given Informaton:Boolean Function is given as .To find:a) Sum of the Product form (SOP form).b)…

Q: Determine the largest t-interval on which Theorem 3.1 guarantees the existence of a unique solution:…

A:

Q: Find an interval in which the value of the series must lie if you approximate it using ten terms of…

A:

Q: Using Discrete Mathematics and language. Determine whether the statement is true or false. Prove the…

A: The given statement, " For all integers  and , if  then  and .The aim is to check whether the…

Q: Prove that there exist open subsets U, VCR such that x EU, y E and U = 0.

A: As we know that  is a metric space,where  . .Let  be two distinct points.And .Define .

Q: 33. Is it possible to have a combination of nickels, dimes, and quarters that add up to $4.72?…

A:

Q: Problem 3: For the 2 x 2 linear, constant coefficient, homogeneous system 1 v-(a-2 3-a)" = 23

A: We will find the eigenvalues and corresponding eigenvectors of the coefficient matrix.

Q: Use the method of Frobenius to solve for the following expressions: a) xy"+y=0 b) y"+ xy' - 2x2y = 0

A:

Q: Of an initial amount of 8000 g of lead-210, how much will remain in 160 years? Lead-210 decays at a…

A:

Q: 2 cm 2 mm 2 cm

A: The inner radius of the cylinder in mm is;r=2 cm=2(10 mm)=20 mmThe outer radius of the ring is the…

Q: A rectangular box with no lid will be made of cardboard and have a surface area of 24 square feet.…

A: Let  be the length  be the width and  be the height.The surface area is

Q: 1. Allina opens an exotic bakery. Her capacity for the month is eight hundred (800) Love Cherry…

A: Let's break down the problem step by step:Variables:Let C represent the total cost function.Let R…

Q: Se aplican las fuerzas F1 = (1, -1,2) y F2 = (6,2,b + 1) y F3 = (3,-b,5) a un punto situado en el…

A: If two lines are parellel then these lines will be scalar multiples of each other.

Q: Larry has 5 different books on his shelf which he wants to distribute to his 3 students so that each…

A:

Q: (16) Solve for the matrix 1 -2 3 4 S the matrix XGM ₂ (R): 1-12 L 5 X = 7 0 8 f 1 4 1 3

A: (.) Given,        where  .(.)  Gauss - Jordan method: Let  be an matrix. We write  where  is an…

Q: The Maclaurin series of the function f(x) = 2x²e 5x 00 can be written as f(x) = where the first few…

A:

Q: Let D be the distance from the origin to the point at which the tangent plane of z=3x² +#sin(y)+ay…

A: The equation of the given surface is .The given point is P.Suppose the point where the tangent plane…

Q: Use Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If…

A:

Q: x = 2x y = x + y

A:

Q: Express the following invertible matrix A as a product of elementary matrices: You can resize a…

A:

Q: Question 1 Evaluate the limit. Note: two 'o's make infinity (oo). sin(t) ‚ († — 1)²) lim t-0 11…

A:

Q: Find all of the subgroups in A4. What is the order of each subgroup?

A: A4 is the alternating group of order 12, which consists of the even permutations of 4 elements.The…

Q: If income is continuously collected at a rate of f(t) dollars per year and will be invested at a…

A:

Q: 8. Evaluate the following integrals using the residue theorem: r sin r dr. x² +1 x² +1 2+1 -8 dr. x…

A: Since there are many questions, find the solutions to the first three parts of the first question.

Q: Using Discrete Mathematics and language. Give a reason for your answer. Assume that all variables…

A: Given that .The aim is to determine does divide .

Q: 1. The Area of the region is 2. The Centroid of the region has an x-coordinate of 3. The Centroid of…

A: The region is bounded byNote : According to the guidelines we are allowed to solve three subparts at…

Q: A and B aren X matrices. Check the true statements below: A. The determinant of A is the product of…

A: We check that given statement is true or false.

Q: Assume we are working in R³. Rewrite the equation 2x1 + 3x2 4x3 5 in the parametric vector form ₁ +…

A:

Q: A differential equation and a nontrivial solution fare given below. Find a second linearly…

A:

Q: II. Find the Particular solution indicated. 27. (2x + 3)y' = y + (2x + 3); when x = −1, y = 0 Ans.…

A: For given differential equation we have to find the solution.

Q: e. lim 5r3 +8r _4 10x³ +3x+1 g. lim x² sin x→0+ ( (Hint: Use the Squeeze Thm) f. lim ∞0-7x 16x³ +7x²…

A:

Q: A singular value decomposition -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 0.5 A = UEVT = -0.5 0.5 0.5…

A:

Q: Use the graph of each equation to test for symmetry with respect to the x-axis, y-axis, and origin.…

A:

Q: Consider the following three simple statements: o: The oven is on. c: Some cookies are baking. s:…

A: As you have asked only first problem that is "to translate statement ".I will do only first…

Q: Consider a hyperplane H = {(w, x, y, z) E R4 | 2w + 3x - 4y + z = 10} and a line ((t) (1,-1,1,-1)…

A: (a) Given hyperplane is  and a line Observed that direction ratio of normal to the hyperplane is…

Q: The population of bacteria in a culture grows at a rate proportional to the number of bacteria…

A:

Q: 3.9 Find y=10 area between of z - X + X that is в ус region these functions. = x²²+19x enclosed

A: We have given two curves:,First draw the both graph at same axis as follows: is cubic function with…