1. Use the following diagram to prove analytically that the diagonals of a rhombus are perpendicular. B (a, b) a A (0,0) Z C D(a.o) c'

Q: 23-32 Determine whether the geometric series is convergent or divergent. If it is convergent, find…

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Q: Show that f(x)=x\power{2}-3 is the minimal polynomial of \sqrt{3} over Q,

A: Let            We  have to  find the  minimal  polynomial of  the    over Let Then,  Suppose  that

Q: Question 2 Solve exactly the following integrals. (a) ¹*(¹+2) dx (b) fxsin2x dx (c) So (2x+3xx-1)dx

A: From  the guidlines i can solve only one question with three subparts.Consider the given integral

Q: 1. reasons. Evaluate the limits if it exists. If not, give (a) lim x → 0+ 2 x² −1+ sin(cos¯¹x) x³…

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Q: Consider the following initial value problem. y" + 10y' + 41y = 8(t) + 8(t - 7π), y(0) = 1, y'(0) =…

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Q: Determine whether the Existence and Uniqueness Theorem guarantees the existence of a unique solution…

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Q: Find the equation of the plane in the figure, which is tangent to the graph f(x, y) = 0.2x4+ 1.4y6 -…

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Q: The demand equation for your company's virtual reality video headsets is p = amounts to $110 per…

A: As given in question, Demand equation, Where q is the total number of headsets that your company can…

Q: Find a power series representation for the function. (Give your power series representation centered…

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Q: y′′′ + 14y′′ + 49y′ = 0, y(0) = 0, y′(0) = 1, y′′(0) = −10 y(x)=

A: The given differential equation is:The auxiliary equation is:So, either:So, the roots of the…

Q: 3. If k € Z, then {n €Z:n k} = {n €Z:n|k²}.

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Q: A Swiss watchmaker wants to create a production plan for the next 4 months. Projected orders for the…

A: To formulate a linear program to determine the optimal amount to produce in each month while…

Q: Fast pls solve this question correctly in 5 min pls I will give u like for sure Anu Let f(x) =…

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Q: K Dan borrowed $1580.00 today and is to repay the loan in two equal payments. The first payment is…

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Q: a) Find the area under the curve Y = sinx and the x-axis on the interval [0, 4л] in the figure 1.…

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Q: If dim. W = m and is T - cyclic subspace of V, then dim. Tẫ(W) is m – k for all k≤m.

A: If dim. W=m and is T-cyclic subspace of V, then our claim is the the dim. Tk(W) is m-k for all  .

Q: K Scores on a standardized intelligence test are normally distributed with a mean of 100 and a…

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Q: s = f(t) = t³ - 12t² + 36t ds v(t) = 3²- - 24t+ 36 dt = The velocity after 2 s means the…

A: As per the guidelines I am answering first three parts only.We have

Q: 1. Suppose x € Z. Then x is even if and only if 3x + 5 is odd. 2. Suppose x € Z. Then x is odd if…

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Q: Let -8 -2 -9 +1- 6 4 4 0 4 True False A = Is it true that w is in Nul(A)? 8 and w= 1 H

A: Our objective is given below:

Q: 5. y"- y = xex, (0) = 1, y'(0) = 1

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Q: Given that f(x) = 3x - 4 and g(x) = x² - 2x + 2, find unsimplified AND simplified versions of the…

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Q: Use integration by parts with u = -5lnz and du = zdz to find Do not include +C. -5zln z dz. Give…

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Q: Create an excel program using this non-linear equation using the following methods: (b) COSX = 0 xex…

A: The equation given to us is as follows:(a) We are asked to create an excel program to find the…

Q: Find the matrix (AT)-1 -4 2 -3 -8 4 -3 1 -3 4 -2 3 8 3 -1 - 3 8 -2 1 0 1 -1 -4 - 3 -3 -1 3 9 3 8 -3…

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Q: Find the number of distinguishable arrangements Of the letters of the Word Sex Decillion There are…

A: In the word of "Sex Decillion", there are 12 letters in it.But these letters e,i,l repeated 2…

Q: Solve the linear programming problem. Maximize and minimize z = 4x + 5y Subject to 2x + y ≥ 30 x +…

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Q: a) Draw y = f(x) -3√↓ i) At what value/s of x is the graph of y=undefined and what does that mean in…

A: The value of  is undefined when  clearly from the given graph we can see that  is defined for every…

Q: Solve equation in R, log₂ (x) + logx(9) = log₂ (x + 9)

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Q: Solve the given initial-value problem. y(x) = y" + 4y + 4y = (7 + x)e-2x, y(0) = 5, y'(0) = 8

A: We have to solve the given initial value problem.

Q: Draw y² = f(x) 1+ (1,-1) 2 (2.5,1)

A: We have draw the graph of y2=f(x)The procedure is given below

Q: solve the IVP 54y"+36y'+6y=0, y(0)=1, y'(0)=1

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Q: If Te A(V) is nilpotent, then aoT + a₁T+...+amTm, where a; € F, is invertible if a, # 0.

A: If is nilpotent, then we have to show that , where , is invertible if .

Q: (6. let aiseendn (coreen + cotu) == f(n) + C Of (eseen cot use su asien-cotu) ² f(n) = ? = (cosecn+…

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Q: 7.2.17 Show that To Ta dx (x² + a²)² = Л 4a³' a> 0.

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Q: Solve the given differential equation by undetermined coefficients. y""y" - 16y' + 16y = 6 - e* + ex…

A: The  given differential equation is,homogenous equation becomes,

Q: Problem 3: Given the function For given vectors f(x, y, z)= xy² - x²z+yz². v = (1,2,3), u:=…

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Q: Determine if the vectors 0 3 HOO -4 2 3 4 O 1 O -5 and are linearly dependent or independent. Also…

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Q: Suppose you want to decrease the margin of error by a factor of 5-for example, from 15% to 3%. By…

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Q: In V = R³. Let W₁ be the xy - plane and let W₂ be the z zxis: 2 and Show - W₁ = {(x, y, 0) : x, y ≤…

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Q: Find the general solution of the given higher-order differential equation. y"" + 3y" - 16y' - 48y =…

A: The given differential equation is .We have to find the general solution to the differential…

Q: Let F be a field, and let a be an algebraic element  of degree n and of minimal polynomial p(x) over…

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Q: A company will manufacture a tent that will have a square, 15-ft by 15-ft base, 4 vertical walls,…

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Q: 3. Given an integer a, then a³ + a² + a is even if and only if a is even.

A: To prove that for any integer 'a', is even if and only if 'a' is even, we need to show two…

Q: 1- Compute dy/dx, a) y = xtan x b) y = ex³+cosx c) y = ln (x+1) 2000 (sinx) 300 (3x+2)" d) y =…

A: Due to Bartleby answering guidelines I have solved only first question with first three Subparts.

Q: Show that the function f(x,y)= x¹/3y1/3 is not differentiable at (0,0) by showing that it does not…

A: A function f(x,y) is said to be differentiable at (a,b) if the following relation satisfy…

Q: (a) (b) Bisection method (200 iterations) Regula Fasi / False-position Method (200 iterations)

A: The equation given to us is as follows:(a) We are asked to create an excel program to find the…

Q: Solve the given boundary-value problem. (If an answer does not exist, enter DNE.) y'' − 2y' + 2y =…

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Q: A = 1 0 -1 Lo 0 -2 -3 -2 -2 1 3 3 -2 4 4 0 0 -1

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Q: 4. Suppose d € Z with d > 1. This ensures that √-d & Q. Prove that Z[√-d]× = {±1}. (Hint: use the…

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