A straight line is drawn through the point P(2,3) and is inclined at an angle of 30\power{∘} with the x-axis.find the coordinates of two point on it at a distance 4 from P.

Q: 1. (X, d) is a metric space and A and B are subsets of X. Prove each of the following if the…

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Q: b. Identify the systems from task (2a) that demonstrate closure, i.e., the result of the operation…

A: b) in the answer provided, we see the systems S1 and S3 satisfy the closure property.      For…

Q: Consider the following differential equation. (2x - 1) dx + (7y + 5) dy = 0 Let M = 2x - 1 and N =…

A: Let M=2x-1 and N=7y+5   My=∂M∂y=0Nx=∂N∂x=0 Here My = Nx hence the given equation is EXACT…

Q: Suppose that a and b belong to a field of order 8 and that a2 + ab + b2 = 0. Prove that a = 0 and b…

A: Given: Suppose that a and b belong to a field of order 8 and that a2 + ab + b2 = 0. To Prove: a=0 ,…

Q: Solve the given differential equation by undetermined coefficients. y" - 14y' + 49y = 35x + 2 y(x) =

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Q: Solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of…

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Q: The APR for loans can also be approximated (however, not within the 1 of 1% accuracy required by…

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Q: Find the chromatic polynomial of the graph

A: The given graph is: We have to find the chromatic polynomial for the given graph.

Q: Find the following. (Round your answers to the nearest cent.) Finance Number of Charge Payments…

A: a)Unearned finance charge = (m * (m+1)) / (n * (n+1)) * F = (6 * (6+1)) / (12 * (12+1)) * $9.20 = (6…

Q: D Question 30 Consider the function h as defined. Find functions f and g so that (f. g)(x) = h(x).…

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Q: The price of crude oil during the period 2000-2010 can be approximated by P(t) = 6t+ 18 dollars per…

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Q: Rationalize the denominator. Assume that all variables represent positive real numbers. 64 1 x 64 X…

A: I have explained everything with in the solution .please go through that.

Q: Find a particular solution to the differential equation using the Method of Undetermined…

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Q: h is linear with constant coefficients. d²y dx² = we will work on solving the corresponding…

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Q: Solve the exact equation (+22) de +(+2y) dy = 0. The solutions are of the form F(z,y)=c, where…

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Q: Data released by the Department of Education regarding the rate (percentage) of ninth-grade students…

A: Given that Data released by the Department of Education regarding the rate (percentage) of…

Q: Which of the following is equal to: Ο 10 Ο 16 Ο 4 ΣΣ i_1 j1 20 Ο 25 Ο 30 040 None of the other…

A: INTRODUCTION In mathematics, summation (or sum for short) is a mathematical operation that adds a…

Q: Find u × v and show that it is orthogonal to both u and v.u = −5i + 19j − 12k, v = 5i − 19j + 12k

A: The given vector is u=-5i+19j-12k, v=5i-19j+12k We have to find u×v. Also, we have to show that u×v…

Q: An article by a researcher reported on a long-term study of the effects of hurricanes on tropical…

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Q: Suppose that a company has just purchased a new computer for $2400. The company chooses to…

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Q: 5 sandwiches and 3 drinks cost $52.00 3 sandwiches and 2 drink cost $32.00 What is the cost of each…

A: Sol:- Let the cost of one sandwich be "S" and the cost of one drink be "D". We can use these…

Q: Sue earns £8.30 per hour for a 35 hour week and time and a half after that. How much would she earn…

A: Given Data: Let us consider the given Sue earns £8.30 per hour for a 35 hour week and time and a…

Q: Three commuter trains and three express buses depart from city A to City B in the morning, and five…

A: For the trip from city A to city B, there are three trains and three buses, so in total 3+3, i.e., 6…

Q: When a factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the…

A: A factory operates from 6 AM to 6 PM, its total fuel consumption varies according to the formula…

Q: Find the eigenvalues and eigenvectors of A geometrically.

A: To find the eigenvalues and eigenvectors of matrix A, we can use the definition of eigenvectors and…

Q: How long will it take to triple your money at a nominal rate of 8% p.a. compounded a. Quarterly b.…

A: To calculate the period to triple the money, we need to determine the effective annual interest…

Q: Solve this Homogeneous First-Order Diff. Equation: Hint: Partial fractions may be required for this…

A: given (y2+yx)dx+x2dy=0____(1)⇒dydx=-(y2+yx)x2put y=vx⇒dydx=v+x.dvdxNow the given equation…

Q: B = {anbmcn | m, n ≥ 0}

A: To prove that the language B = {a^nb^mc^n | m, n > 0} is not regular. To do this, we use the…

Q: Decide whether or not the method of undetermined coefficients can be applied to find a particular…

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Q: A GIVEN: The three points in R³: B = C = - (-1,2,0) (1,0,1) (0,1,-2) FIND: a) the measure of ZABC,…

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Q: 4(x – 4) = 3(2x + 1) + 2     Solve for x  3                     5

A: The equation is defined as a mathematical expression that is made from two expressions and they are…

Q: A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate…

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Q: Use the graph shown to find the following. (a) The domain and range of the function (b) The…

A: A vertical asymptote of a graph is a vertical line x = b where the graph tends toward positive or…

Q: Let T be a linear transformation represented by T = -5 -5 - 4 1 5 -5 - Check ALL vectors which are…

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Q: Find y as a function of x if y(1) = 8, y′(1) = 6. y = x²y" — 6xy' – 8y = 0,

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Q: s the following linear transformation linear or not? If it is, what is matrix representation of the…

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Q: Quantifiers and Negations "All freshmen students are graduates of the K-12 curriculum." is a quant…

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Q: Let p be a prime and k a positive integer such that ak mod p = a mod p for all integers a. Prove…

A: Given: p is a prime and k is a positive integer such that ak mod p =a mod p for all integers a. To…

Q: A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3 aregiven. If x0 = 3, find the values of…

A: Given: A graph of ƒ and the lines tangent to ƒ at x = -3, 2, and 3. To Find: x1,x2, and x3 by…

Q: express L−1[F(s)G(s)] in terms of a convolution integral.

A: Given: Fs=4s3, Gs=s-1s2-2s+5. To Do: Express L-1FsGs in terms of convolution.

Q: In Problems 59-66, use the price-demand equation to find the values of p for which demand is elastic…

A: Price-demand equation f(p)=2,400-6p2 The elasticity of demand, E at price p is defined by…

Q: Data released by the Department of Education regarding the rate (percentage) of ninth-grade students…

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Q: (2) You've used a numerical method with second-order global error to estimate the value of a…

A: Sol:- If the numerical method used has a second-order global error, we know that the error decreases…

Q: Remark. This problem shows that Side-Side-Angle is not a valid congruence principle. 4. In this…

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Q: -2 2 D-0-0 V2 2 1 Compute the distance d from y to the subspace of R4 spanned by V₁ and ₂. Let y = d…

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given that Vx,y,z=4x2-5xy+xyz and point P(2,6,7). We have to find the rate of change of V at P in…

Q: x (t) 1 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13

A: We know that if a function f is periodic on [a,b] with period (b-a) then Fourier coefficients…

Q: Write the second example of compound statement which is "We will go to Camiguin island or we will go…

A: Sol:- Let p represent the statement "We will go to Camiguin island" and q represent the statement…

Q: 16. Solve, rounding to three decimals where appropriate, logx-4(3x + 1) = 2

A: Sol:- logx-43x+1=2Apply log rule:  logab=lnblnaln3x+1lnx-4lnx-4=2lnx-4ln3x+1=2lnx-4Apply log rule:…

Q: et T:R² R² be a linear transformation that maps x into X1V1+X2V2. Find a matrix A such that T(x) is…

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