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Q: The purchases of a videogame can be represented by the exponential relation N = 400(1.8)t, where N…

A: To find the number of games sold after 3 weeks,  simply substitute t = 3 into the exponential…

Q: Find the Laplace transform of the given function: 0, t 0

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Q: Suppose T is a linear transformation on R² (i.e. T(x, y) = (ax + by, cx + dy) where a, b, c, d are…

A: Linear transformation

Q: O Show that the following set of matrices is closed under linear combina- tions. a + 2b a+b a b -{(a…

A: Since you have asked multiple questions, we will solve first question for you. If you want any…

Q: For the last question you will be finding a minimum distance spanning tree; take your graph from (1)…

A:

Q: An infinitely thin rod of length 1 m has density 8(z) = 1+kr² g/m, where k> 0 is constant and a is…

A:

Q: 17. Let S = {1,2, 3, 4, 5). The vertex set of a graph G is the set of 2-element subsets of S. Two…

A: The Petersen graph is a well-known and interesting graph with 10 vertices and 15 edges. It is named…

Q: The indicated function y₁ is a solution to the given differential equation. Use reduction of order…

A: Cauchy-Euler equation,: underline;" data-mce-style="text-decoration: underline;">Cauchy-Euler…

Q: Determine the approximate slope of the tangent to the curve f(x) at x = 2. Round intermediary steps…

A: Here we have to calculate slope of the tangent to the curve at x= 2.

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

A: Given:S is the surface .To Evaluate: .

Q: SSX² √64 - x³ dy dx

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Q: Using the inverse of matrix to solve the following system of linear equations

A: Introduction: In mathematics, a matrix is an array of numbers arranged in a rectangular pattern and…

Q: The Von Bertalanffy's equation states that the rate of growth in length of an individual fish is…

A: The rate of growth in length of an individual fish is proportional to the difference between the…

Q: The population of a community is known to increase at a rate proportional to the number of people…

A: From the given data the rate of change in growth is propotional to the rate at which present.…

Q: Consider a bipartite graph with edges in E connecting members of the vertex bipartition S, T, and…

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Q: 5. Given the following points (2,5), (4,6), (5,3) calculate the second order interpolation…

A: Formula for interpolation polynomial with Lagrange's formula is            Given,

Q: Find the total weights using edge-picking algorithm.

A: Given,                    .To find the total weights using edge-picking algorithm.

Q: A 1-kilogram mass is attached to a spring whose constant is 16 N/m, and the entire system is then…

A:

Q: 4.7 Let G= be a cyclic group of order 24. List all the elements in G that are of order 4.

A: Every element of G can be written as xa for some a between 0 and 23 (including both).  Suppose that…

Q: In the vector space of real functions on [-, π], let the inner product be defined by ㅠ (f,g) = f( […

A: Using the Gram-Schmidt orthogonalisation prosess to find an orthogonal basis.

Q: a. Find a particular solution to the nonhomogeneous differential equation y" + 16y= cos(4x) +…

A:

Q: The lives (in hours of continuous use) of 100 randomly selected flashlight batteries are: Interval…

A: According to the given data, first form the following table:IntervalFrequency(fi)Midpoint(xi…

Q: Q2. 600 people (250 less than or equal to 20 years old, and 350 greater than 20 years old) were…

A: Given: A survey was taken in which people (less than or equal to  year old, and  greater than  year…

Q: All members of our painting team paint at the same rate. If 20 members can paint a 1600 square foot…

A:

Q: Determine the interest and amount owed after 3 years on a 5,000$ car loan at 6% interest compounded…

A: A car loan of  at 6% interest compounded annually.The objective is to find the interest and the…

Q: SOLVE STEP BY STEP IN DIGITAL FORMAT 2. Find one of the two roots of the equation x² - 4x +2=0 using…

A: We have to find the root of the equation in fixed point iteration we first fix a point from where we…

Q: ate True or False and provide a proof or counter example. ) If n x n matrices A and B have the same…

A: As per the guideline, I am supposed to solve only first three subparts of the given question.

Q: he Laplace transform to solve the given system of differential equat d²x dt² d²y +y-x = 0 dt² x(0) =…

A:

Q: Show that the following equation is exact and then solve it. (5y-2x)y' - 2y = 0

A:

Q: Find an explicit description of Nul A by listing vectors that span the null space. A= 1-5 30 0 0 10

A: The given matrix is Now we solve the system of linear equation i.e., .................(1)…

Q: polynomial of a 3x3 matrix is not easy to do with just row operations, because the variable X is…

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Q: [19 -4 25 -4 A = -4 -8 -87 -4. Fir 19

A:

Q: Let F be a C¹ vector field and let W be a symmetric elementary region in R³ with boundary OW = S.…

A: Gauss divergece theorem

Q: A 2-D polygon has the following vertices in (x,y): A(2,1), B(3,5), C(8,7), and D(4,1). The polygon s…

A: In the given problem the coordinates of the four points of the polygon are given.A( 2,1) B( 3,5)C(…

Q: Given that x² + y² + z² = 6 and (055) w w³ + z³ 5xy + 12. Find for x=1, y=0 and z=7. ( ($).

A: Given,                   and To find the value of for

Q: A child is given 480 milligrams of cold and flu medicine. The concentration of the medicine decays…

A:

Q: The temp of water “T” in degrees Celsius after being heated for “t” seconds is illustrated by the…

A: In this question we will find the average rate and instantaneous rate of change.

Q: Using variation of parameters  x^2 y''-x(x+2)y'+(x+2)y=x^3 e^x given y1(x)=x ,y2(x)=xe^x

A: Solution is uploaded below

Q: Show that L{(1+e²t)²} = 4(s²-4s+2) s(8-2) (8-4)

A: Solution is uploaded below

Q: Compute the integral of the scalar function f(x, y, z) = 6xy +9z over r(t) = (cos (t), sin (t), t)…

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Q: Using integration by parts, [4x²2x dx

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Q: Let f(x, y, z) = x + yz and let C be the line segment from P = (0, 0, 0) to (4, 5, 5). (a) Calculate…

A: Given function is  and let  be the line segment from . We have to calculate  and for , .Since,…

Q: Determine the values of n and h required to approximate R02e2xsin(3x)dx to within 10−4 using the…

A: We use concept of trapezoidal and simpson's rule.

Q: When ax³ 2x² + cx- 4 is divided by x + 2, the remainder is 4. When it is divided by x-1, the…

A: We have, by the remainder theorem and according to the problem,we get,

Q: А понерне об mension of each ? A= 52 Зо -1322 Ч 21 з

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Q: Let A = [3 10 0-9 1-3] ܗ ܘܘ Find an orthonormal basis of the row space of A.

A: We have to find the orthonormal basis of the row space  of

Q: Find the nth partial sum of the sequence an = 1 n+3 n+4

A: Given that,

Q: 10. 2x"(t)-2x' (t) - 4x(t) = 2e²¹

A:

Q: Let F = (, , 2). Calculate div (F) and curl (F). (Use symbolic notation and fractions where needed.)…

A: We have to calculate  and .

Q: Let S be the quadratic surface given by S = {(x, y, z) | z = 4x² - y², z ≥ 0}, oriented with the…

A: