Prove that the equation ax + b = c has a unique solution where a, b, c constants and a≠0.

Q: 1. Find the coordinates of the focus, the equation of the directrix, and the length of LR for each…

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Q: Write the equation of each function shown below in vertex and standard form. Verify your equations…

A: Use shiting processes to right /left and top /bottom

Q: Find the real component if the nth root of a + bi is determined for a = 10, b = 8, and n = 5. Round…

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Q: 33. 2 ²² = ( ² ) ² + ( ² ) ² 4 8

A: (29) Given x2+y2-z2=1 n

Q: Draw Cay({2, 3}:Z6). Is there a Hamiltonian circuit in this digraph?

A: It is given that Cay2,3:Z6. we can calculate 2,3 in Z6. So, we have 2=0,2,4 and also 3=0,3. So, we…

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A: Given set is G = <a, b | a^6 = b^3 = e, b^-1ab = a^3>.

Q: 19. Use the Archimedean Property of R to prove that if z, M are real numbers such that 0≤x≤ for…

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Q: An exercise machine with an original price of $800 is on sale at 18% off. a. What is the discount…

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Q: Find approximate values for f' (x) at each of the x-values given in the following table. Use a…

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Q: Solve the equation. (x + 9xy¹) dx + ex²y³dy = 0 An implicit solution in the form F(x,y) = C is =C,…

A: The given differential equation is ,        (x+9xy4)dx + ex2y3 dy = 0 (.)  An equation of the form ,…

Q: a survey

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Q: What is 5/6 % of 600

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Q: Suppose ne Z. If n is odd, then n² is odd. Suppose ne Z. If n² is odd, then n is odd. Prove that 2…

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Q: Use the following table to answer the question: Risk Factor Exposed (E+) Not Exposed (E-) Totals…

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Q: 12 What is the coefficient of x in the expansion of (x + 2)¹8 + x²(x + 3) 2⁰? Preview

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Q: Faith observed that her product sales in a certain town is given by the function of M(u, v) = u²v²…

A: The given function is M(u,v)=u2v2 for (u,v)∈ℝ. The given region is bounded by lines passing through…

Q: 7 represents a reflection about the line x + y = 0 in R2. What trans- formation is the inverse of…

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Q: Use excel to solve the following linear program. Max. 3W + 4M s.t -1W + 2M ≤ 8 1W + 2M ≤ 12 2W + 1M…

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Q: Consider the second-order differential equation d²x dx + a dt² dt + b²x = 0 (a, b positive real…

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Q: 2. In a group G, (ab)³ = a³b² for all a, bEG, and that 3 does not divide order of G. Prove that…

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Q: Can we obtain a diagonal matrix by multiplying two non-diagonal matrices? Give an example

A: Yes, this can be possible. There exists two non-diagonal matrix, product of these is diagonal…

Q: Let Zn denote the set of integers {0, 1, ..., n-1}. Let be a binary operator on Z, such that a. b =…

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Q: Problems 5-6: Find the derivative of the function at the given point in the direction of A. ( 5)…

A: 5. Given,            f(x, y, z)=-2x-7y+8z, (-9, -8, 5), A=3i-6j-2k.

Q: Q1. f(x) = x³ + x² 12x - 18 (a) Use the factor theorem to show that (x + 3) is a factor of f(x). (b)…

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Q: John packages turkeys from a farm before they are sold to stores. To make them taste better, he…

A: Given equation 0.015x+0.05yx+y=0.035 Simplifying the equation  ⇒0.015x+0.05y=0.035x+0.035y⇒…

Q: 1. The input to a communication channel is a random variables x and the output is another random…

A: Given Data:   x=-1 x=0 x=1 y=-1 1/4 1/8 0 y=0 0 1/4 0 y=1 0 1/8 1/4 To Find: P(Y = 1 |X…

Q: PIA30 Show that the function 1,6 = (516) (3 cos 0 - 1) is normalized over the interval 0 ≤ ≤ man 0≤…

A: Given function is Y20θ,ϕ=516π1/23cos2θ-1. We have to show that the given function is normalized over…

Q: Using the Method of Undetermined Coefficients, determine the form of a particular solution for the…

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Q: Figure 14 Check Your Understanding 2.2 1. Make a good sketch of the function f(x) near the point…

A: 1. We have sketch the graph of fx at x=2 satisfies f2=5, f'2=1 and f''2=-3 Note:    Since you have…

Q: A brokerage firm has been tasked with investing $750,000 for a new client. The client has asked that…

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Q: Factor each polynomial and find the zeros. Then, sketch a graph using your knowledge of…

A: The given polynomial is: fx=x4-3x3+x2+3x-2 Factor the polynomial and find the zeros of the…

Q: K Write the percent as a decimal. 42.7% 42.7% = (Simplify your answer. Type an integer or a…

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Q: (Yi, X1i, X2i) satisfy the assumptions. You are interested in β1, the causal effect of X1 on Y .…

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Q: A population of willawonkar bats is modeled by P(t) which is an initial value problem. Assume t is…

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Q: . Function: f(x): 2x-1 (0,1) -1<2x-1<1 f^{-1}(x) = (x+1)/2 (-1,1) x belongs to the set A A={1,2,3},…

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Q: Transform the nth-order equationy(n) = a0y + a1y' +· · ·+an−1y(n−1)into a system of first-order…

A: The given differential equation is yn=a0y+a1y'+……+an-1yn-1 where yk is kth derivative of the…

Q: unit

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Q: Prove or disprove that Q(√3) and Q(√-3) are ring-isomorphic.

A: Here we have ℚ-3=a+b-3 / a, b∈ℚ Also ℚ3=a+b3 / a, b∈ℚ We know that, ring isomorphism is a bijective…

Q: Find the volume of the solid that lies within both the cylinder x² + y² = 4 and the sphere x² + y² +…

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Q: 2. Find the general solution for the system: y₁ = 3y₁ + y₂ y₂ = -2y₁ + y₂

A: Given : y1'=3y1+y2y2'=-2y1+y2 To find : General solution of given System

Q: 5. Assume the alphabet Σ = {0,1}. Give three different regular expressions (besides the one given)…

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Q: Show that the group Z13 is cyclic and give all of its generators. List all the distinct subgroups of…

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Q: Given a sequence x₁, x2,... of real numbers, show that cos(x₁) + + cos(xn) exists if and only if…

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Q: Balls, Inc. produces two products, Squid Balls (S) and Fish Balls (F), in two departments, the…

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Q: Consider the parametric equation x = 2 cost, y = sin t 9 " z = t². (a) Describe the curve in 3…

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Q: 1. Use Lagrange approximate places. interpolating polynomial to Answer up to 5 decimal f(8.4) if…

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Q: Consider the initial value problem y'(x) = y(x) V x = (0,2), y(0) = 1. When you apply Euler's scheme…

A: Given : y'x=yx   ∀x∈0,2  y0=1 We have to apply Euler scheme to find y0N,y1N,....,yNN∈R and…

Q: At age 30, you decide to deposit $150 at the end of each month into IRA that pays 4.5% compounded…

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Q: K A passbook savings account has a rate of 5%. Find the effective annual yield if the interest is…

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Q: Show that, the order of any subgroup of a finite group divides the order of the group. (This proof…

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