Find the volume of the parallelepiped (box) determined by u, v, and w. u 2i+j V 4i-2j+ 4k The volume of the parallelepiped is units cubed. W i + 2k

Q: 2. Sketch the following polar curves by first sketching the graph of r = f(0) in Cartesian coordi-…

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Q: (b) A simple connected graph with 2,024 vertices is such that there are exactly two vertices, u and…

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Q: Determine if the given system is consistent. Do not completely solve the system. = 8 2X1 3 4x1 -3x2…

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Q: Find the effective interest rate re for investments with the following annual interest rates.…

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Q: Let a 0 for all x € [a, b]. Let A > 0, B > 0 be constants. functional S[y] = fºd dx f(x)√1+y¹²,…

A: Given functional is where  is continuously differentiable function on the interval so to get optimum…

Q: Let P = 28000 (1.04)* be the population of a town t years after the year 2000. Estimate in which…

A: The objective of the question is to find the year in which the population of a town will reach…

Q: Consider the lamina in the shape of the triangle whose vertices are (0, 0), (L, 0), and (0,L) for…

A: We have to find the moment of inertia of the lamina whose shape is a triangle with vertices  and…

Q: Solve the following differential equations. dy a) ce 3x y = 1-ce 3x b) y = √2 cos x + c dx dy dx =…

A: Note: As per our guidelines, we will solve the first three sub-parts. Please repost the remaining…

Q: Find the ratio. Then find and interpret the value of the ratio. A recipe is shown. The title is,…

A: We have to compare the club soda to the white grape juice.

Q: Let f be the continuous function defined on [-6, 6] whose graph consists of a quarter circle and…

A: given:f is the continuous function defined on [-6,6] whose graph consists of a quarter circle and…

Q: 1. Sketch the solution to the inequality y < -2(x-1)²-4.

A: The given inequality is .The aim is to sketch the solution set of the given inequality.

Q: Solve the initial value problem for t > -1 with y(0) = 17. y = 10(t+1) dy dt - 8y = 16t,

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Q: A population of beetles are growing according to a linear growth model. The initial population (week…

A: The objective of this question is to find an explicit formula for the beetle population after n…

Q: b) Calculate the Laplace transform of the piecewise function in figure 1. f(t) 2 0 0 1 2 3 Figure 1…

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Q: Marco is 450 m due east of the centre of the park. His friend Ray is 450 m due south of the centre…

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Q: Given cost and price (demand) functions C(q) = 150q+45,900 and p(q) = -2.9q +880, what price should…

A: From the given data,what price should the company set to earn $40,000 in revenue?

Q: Problem 12. Can you find a solution to the following system without knowing the number of variables,…

A: Suppose that  the  given system be of the form :…

Q: Problem: cot (x) csc (x) dx

A: We have to solve the integration.

Q: Let P(x) be a polynomial that interpolates f(x) at x; for i = 0, 1,...,l−1,1+1, ---, n (i.e.,…

A: Given Information:The polynomial  is a polynomial which interpolates  at ,  exclude .The polynomial…

Q: Part G Given the same coordinate system as the one shown in Part F, what are the components of C?…

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Q: Figure 4 ft C Part A 1 ft O UF 4 ft N uF = i +4k 17¹+ 17k O up = Choose the correct directional unit…

A: From figure, Force F has +ve x-component and -ve y and z-component both.So directional unit vector…

Q: Use the following expression for the gravity model and the table's hypothetical data to answer the…

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Q: Problem 2. independent in R³. Find all values of a such that the vectors {(2, a, 1), (1, 0, 1), (0,…

A: We have to find all values of  such that the vectors {(2, , 1),(1, 0,1),(0, 1, 3)} is linearly…

Q: MODELING REAL LIFE You open a donation center the same distance from each of the three stores shown.…

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Q: 4. Find the slope of the tangent line to the graph f(x) = 3x² +4 at the point (2, 16) and determine…

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Q: Which number line highlights all whole numbers that round to 470 if we are rounding to the nearest…

A: Rounding numbers to the nearest ten is a straightforward process. Here are the steps:Identify the…

Q: If M is the midpoint of AB in triangle ABΩ, prove that ∠A ≅ ∠B if and only if ∠AMΩ is a right angle.

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Q: Use the differential equation below to answer the following questions: y = -3y PART 1. Find the…

A: a.                y' = -3y          ⇒  dydx = -3y         ⇒  Integrating, we get      = -3x +…

Q: In Exercises 7-10, the augmented matrix of a linear system has been reduced by row operations to the…

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Q: Determine if the given system is consistent. Do not completely solve the system. 2x1 - 8X4 = 2x2…

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Q: The Ax = b system is "solvable" only if b is a (a) Explain why the linear system Ax=b where A = 4 4…

A: The  system is "solvable" only if  is a _______ of .(a) Explain why the linear system  where  and…

Q: Find the horizontal and vertical asymptotes of f(x). 2 4x² +5x-6 2 x+5x-14 f(x)= Find the horizontal…

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Q: G. Show that a set A in R² is open in the Euclidean metric it is open in the Manhattan metric. Hint:…

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Q: Consider the ODE: (e2xy² - 2x) dx - (6y² - e²xy)dy = 0 a. Show that the ODE is exact. b. Solve the…

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Q: Pay attention to the assumptions of each statement and select all statements that are correct. There…

A: The first statement is correctfor  a=2 we get

Q: The prime factorization of the number contains the factor 3€ for some nonnegative integer e. Enter e…

A: We want to find the number of  3's that appear in the prime factorization of  1667!…

Q: According to Newton's law of cooling, the temperature of a body changes at a rate proportional to…

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Q: Given a metric space M with metric d, verify that any e-ball is an open set.

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Q: Emily and her family are planning a trip to Hocking Hills for a weekend in either October or…

A: The objective of this question is to determine which month would be the most cost-effective for…

Q: In Exercises 21-30, find all scalars c, if any exist, such that the given statement is true. Try to…

A: The given parallel vectors are,21.  and .22.  and .23.  and .The objective is to find the value of .

Q: Suppose U and W are subspaces of a vector space V. Prove that if U C W, then U + W = W.

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Q: Use the differential equation below to answer the following questions: y' = 7y³ PART 1. Find the…

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Q: Problem 4. Let f and g be functions on [a, b], and assume that f(a) = 1 = g(b) and f(b) = 0 = g(a).…

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Q: a Ex let G fropirrazz H.W. Show this set for Ere Qircost √ =

A: We know that Dedekind cuts are defined as follows.A set  is a cut if: contains at least one rational…

Q: Are the data displayed in the graph above discrete or continuous? What is the level of measurement…

A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: Use the Pythagorean theorem to calculate the unknown si ength. Label each length, to one decimal…

A: The Pythagorean theorem states that in a right-angled triangle, the square of the length of the…

Q: Suppose you have a choice between receiving $5,000 today or $10,000 in five years. You believe you…

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Q: (3) (a) Find the smallest positive solution of the system of linear congruences x = 3 (mod 5) * = 7…

A: We solve this using Chinese Remainder Theorem

Q: You have just purchased a new car. The table below shows the value of the car after n years. n V 0 1…

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Q: Eli currently has 45 tulips in his yard. Each year he plants 9 more. (a) Which of the following is a…

A: The objective of the question is to find a recursive formula and an explicit formula for the number…