How would I find the equation of the plane that goes through the points (3,2,1), (4,4,1), and (4,6,2)?

Q: Find the simple interest paid on a $880 investment at 6.4% annual interest for 30 days. Use the…

A: given that  principal p=$880 , interest rate r=6.4% annual  and t=30 days  now by bankers formula we…

Q: Exercise 1.4.9 (Challenging): A number x is algebraic if x is a root of a polynomial with integer…

A: A number x is said to be algebraic number of x is a root of a polynomial with integer coefficients.…

Q: let (R₂ *) be a mathematical system * is defined as: FabER where axb=atbab prove that: □ is…

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Q: In Exercises 7-12, find all zeros of the given polynomial. 7. x³ + x² - x + 2 8. 3x³ - 7x² + 8x - 2

A: As student asked to solve 7. So,  here we solve question 7 only.  Here we have to find zeros of…

Q: 1. Let u = (1,2,3) and v= (1, x, 0) and w= (0,1,0). a. Find ||u + w||. b. Find (u, u + w) + ||u||.…

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Q: Let T(x) = Ax for the matrix A and [4 -4 -16] -16, b = A = 7 5 Lo 0 1 1 Select true or false for…

A: Given that  A=4-4-1675-16011, b=3-11, c=-451 Select true or false statement.

Q: The following matrix over GF(2) is used in the SubBytes Transformation in AES. Find its inverse. A…

A: In the Advanced Encryption Standard (AES), the SubBytes transformation is used to perform a…

Q: A linear differential equation is given below: y" + 2y' + y = 0 for 0 ≤ x ≤ 1 with two additional…

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Q: Let V and W be vector spaces with VC Vand WW subspaces. Suppose that T: VW is a linear…

A: A subset W of a vector space V is a subspace if and only if αw1+βw2∈W for all w1,w2∈W.

Q: Consider the Sturm-Liouville eigenvalue problem on 0 ≤ x ≤ 2, y" + 2y = 0, y(0) = 0; y(2) = y'(2).…

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Q: Solve the ODE

A: Given ODE is y3+2y-1dy=y2-4y+83dx

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A: Given: The number of varieties of doughnuts = 6 (apple cider vinegar, sour cream, cherry, caramel,…

Q: Let u(x, t) = e^(iwx). v(t) and v(0 = 1 be the solution of part differentail equation u_t=u_xxxSo,…

A: Since given that  u(x,t) =eiωxv(t) is solution of the partial differntial equation…

Q: 7. For the differential equation (1-2x)y" + 2y' + (2x − 3)y = e-ª - (a) Write the associated…

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Q: 2 The equation of three circles are given x² + y² -1, x² - y² − 8x + 15 = 0, x² + y² + 10x + 24 = 0…

A: We know that the point from which the lengths of tangents are equal in length is the radical center…

Q: ODE

A: we solve the ode by variable seperable method

Q: Let R1 and R2 be two 2 × 2 rotation matrices andlet G1 and G2 be two 2 × 2 Givens…

A: Given: R1, R2 are two 2×2 rotation matrices and G1, G2 are two 2×2 givens transformations.To find:…

Q: 1. Use the limit theorems to prove that the following sequences converge. 15n² 6 sin (2n + 1). ;…

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Q: Motor car takes 10 sec to cover 30 m & 12 sec to cover 42 meter. Find the velocity of car at the end…

A: I assume the initial speed of the motor is u m/s; then the motor car has traveled a distance of 30 m…

Q: 5)Find the terminal point of the vector that is equivalent to u = (1, 2) and whose initial point is…

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Q: a) Find the coefficient of the x³ term in the expansion of (x-2)7.

A: (a) To Find: The coefficient of x5 in the expansion of x-27. As per policy, we are solving only the…

Q: 4. The region bounded by the given curves is rotated about the specified axis. Find the volume of…

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Q: The figure below shows four named points A, B, C, and D on a grid generated by two vectors V₁, V2 in…

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Q: Example 2: A soda company is designing a new can that is more cost efficient. The base of the can…

A: This is an optimization problem. We will first find the cost function and then minimize the cost…

Q: The safe load, L, of a wooden beam supported at both ends varies jointly as the width, w, and the…

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Q: Find the value of intergration 1 1 So ' √₁²-X² in ¹(2xV/1-x²) dx

A: Given: An integral ∫0111-x2sin-12x1-x2dx To Find : The value of the above integral.

Q: For the system equation given below: [210x₁ = 0 2 1 002 Xz Determine the state variables' solution…

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Q: CONVERT THE FOLLOWING 1. 2. 3. 4. 5. 6. 4/1 4 rotation → deg 3.45 rotation → deg, min, sec 3πt 5…

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Q: 3. Solve differential equation y" - 3y + 4y = 0.

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Q: The number of food trucks in a city has been increasing by 50% annually. There were two food trucks…

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Q: 7. Answer the following questions that are related to the equation shown below: Ny -Qy: = exp N…

A: Given: NvN=exp-QVkT   Boltzmann distribution: The Boltzmann distribution is a probability…

Q: 1 Match the graph of each function in (a) (d) with the graph of its derivative in I-IV. Give reasons…

A: Graph of the functions and their derivative graphs are given, we have to match its graph.

Q: . Find solution of the initial value problem y" + 7y' +12y = 0, y(0) = 3, y'(0) = -1.

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Q: Use the method of cylindrical shells to find the volume V generated by rotating the region bounded…

A: To Find: Volume generated by rotating the region bounded by the curves  y=3ex, y=3e-x, x=1 about…

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Q: If H is a finite subgroup of a group G and x ∈ G, prove that |N(H)| = |N(xHx-1)|.

A: Given: If H is a finite subgroup of a group G and x∈G. To Prove : NH=NxHx-1

Q: 2. Prove the following implication: strong convexity → strict convexity → convexity. Is the converse…

A: Sol:- The implication "strong convexity implies strict convexity which implies convexity" can be…

Q: Find a rearrangement of Σ(-1)"+¹ that converge to.

A: The objective is to find a different rearrangement of ∑n=1∞-1n+1n such that it converges to 12. The…

Q: evaluate the given expression with u = (2,−2,3), v = (1,−3,4), and w = (3,6,−4). (a) ∥u+v∥

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Q: A cannon ball as fired horisontally at exactly the same time as a bowling ball is dropped straight…

A: we need to find and compare time taken by cannon ball and bowling ball to hit the ground.

Q: Find the maximum of the product of the sines of the three angles of a triangle, and show  that the…

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Q: 4π Suppose T: R² R² is a rotational linear transformation (about the origin) through radians 3…

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Q: f(x) *[32snx-05 cos x] x €3,4

A: The given function is  fx=e-x32 sinx-5 cosx, x∈3, 4 We have to find the solution using the false…

Q: Let A = -6 18 - 2 6 and w= 3 Determine if w is in Col(A). Is w in Nul(A)? Determine if w is in…

A: This question is about linear algebra.

Q: Find the general solution for the following differential equation: y = ******** General Solution:…

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Q: Kis T-invariant if. T(W) W

A: Given that T:V→V be a linear transformation .A subspace W⊆V T is T- invariant if T(W)⊆W.

Q: Test the series below for convergence using the Ratio Test. (-1)"6²n+1 (2n + 1)! ∞ n=0 The limit of…

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Q: 1) State whether the angle is acute or obtuse. State the height of the triangle. Determine how many…

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Q: Q1/ R,X' charts are used to control the yarn and the results of 25 samples as follows: 50 X'1 =…

A: To determine the control limits in the R chart, we first need to find the average range:…

Q: Find the initial point of the vector that is equivalent to u = (1, 1, 3) and whose terminal point…

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