Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O <7,-8, 0> O <- 7, 8, 0> O <3, 1, - 5> <- - 3, -1, 5>

Q: 5) Examine the characters of the following Series using the Comparison tests. DO a) = 2n²+3n+1 n=1 2…

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

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A: Given that outside temperature over a day can be modeled as a sinusoidal function. Suppose you know…

Q: 22. Represent the graph of the following functions using a sine and cosine function. 323 124 10 8 m…

A: The general form of the function is f(x) = Asinkx+M or f(x) = Acoskx-π2+M Where M is the midline, A…

Q: Q1: If acoshx + bsinhx = c, find the value of x when c² = a² - b².

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Q: 69=y"+y = f(t) where: (0)=0, y₁ (0) = 1 0₁ 0≤+ 2π ។ 1 f(t) ] 1 0,

A: We use definition of Heaviside function then solve by Laplace transform.

Q: - - simplify the following: 3(6-x) + 4(2x − (m — 2))

A: Use the given information.

Q: 1. Let S be a nonempty set. (a) Give the definition for: "a is not an upper bound of S." (b) Give…

A: As per our guidelines only first three subquestions are solved. For remaining question kindly…

Q: Consider Quadrilateral EFGH with vertices E (-10, 8), F (8, 8), G (10, -6), and H (-6, -10). The…

A: Consider Quadrilateral EFGH with vertices E (-10, 8), F (8, 8), G (10, -6), and H (-6, -10). The…

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A:

Q: Provide an example of a function f(x) which has all of the following properties: - it is periodic…

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Q: k It is known that ( + (₁ ²₁₂) + (k) = (²+¹) (k + 1). Prove that r - 2 (k) + ( k + ¹ ) + ( k + ²) +…

A: We will use given formula and value of nr . nr=n!r!×n-r!

Q: the following "quation sutisfied Cauchy - Rieman equation es .4 W = Z

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

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Q: In this problem, x = c1 cos t + c2 sin t is a two-parameter family of solutions of the second-order…

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Q: (8) Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if…

A: (8) To Find: Infimum, minimum, supremum, and maximum of the given sets S: 1. S=1-1n| n∈ℕ 2. S=x∈ℝ |…

Q: Let U= {1, 7, 6, 14, 5, 10, 20, 18) A = {1, 20, 18} C = {7, 6, 14, 5, 10} Find A U C'.

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Q: 3. Show all your steps to evaluate 3 -0.5 -2 -2 a) 16 (16)² + 2² - (²) ² - b) +3

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Q: Three states have the following populations: State Population A 10,040 B 8000 C 2050 A house of…

A: State  Population Quota Initial A 10040 8.4958 8 B 8000 6.7695 6 C 2050 1.7347 1 Total 20090…

Q: 5. Let A= (a) Find the inverse of A, and (b) Express A as a product of elementary matrices,

A: Elementary matrices: Let E(k×i+j) denote the elementary matrix obtained from identity matrix I by…

Q: Using spherical coordinates calculate ſezsqrt(x²+y²)dV where E={(x,y,z) | x²+y²+z²0,y>0,z>0}

A: To find- Use spherical coordinates calculate ∭Ezx2 + y2 dV where E = x, y, z | x2 + y2 + z2 ≤ 4, x…

Q: Explain why the integral is improper. 49 1 dx 1.6 1.4 1.2 Y 0.81 0.6 0.4 0.2 10 20 O At least one of…

A: We Know that  An improper integral is a definite integral that has either or both limits infinite or…

Q: Prove that if c=12n+4 where n in Z then c is not a linear combination of 27 and 18

A:

Q: Suppose there are approximately 2.0 x 10° asteroids in the asteroid belt that have a diameter larger…

A: Given Asteroids in the asteroid belt = 2.0×106  Diameter larger than =0.5 km Asteroid belt stretches…

Q: Problem five : Find all maps : (Z, +) → (Q*, ×) satisfying (a + b) = o(a) X (b) Va, beZ

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Q: For a given set of populations and house sizes, different methods of apportionment may lead to…

A: Answer is true.

Q: Give negations of the following statements using formal mathematical language. negations must not…

A: To find: the negation of the given statements.

Q: find serious solution of differential equation (x+3)^2y''-9(x+3)y'+25y=0

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Q: For which real r> 0 does the series n=1 converge, and for which real r> 0 does the series diverge?…

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Q: Assume the X NY are both differentiable functions of tea find the required value X squared plus Y…

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Q: Problem 3 (A) Solve the matrix equation Ax-b where A- (B) Is it possible to solve Ax b for any given…

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Q: 12. The half-life of strontium-135 is 2 years, and its mass. A. is modelled by, where A, is the…

A:

Q: ne blanks and b = -2x+9y, write

A: Given: a⇀=3x⇀-5y⇀ and b⇀=-2x⇀+9y⇀ We should write the given vector5a⇀-8b⇀in terms of x⇀ and y⇀

Q: 12. Solve the following system of equations using either the substitution method or the graphing…

A: Introduction: The equations belonging to a system of linear equations represent a line in Euclidean…

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A: We have to Set up a difference equation that describes this situation, where x0 is the initial…

Q: Max (Z) = 3 X + 5Y Constraints: 2X +3Y≤ 30 5X +4Y≤60 By Condition X, Y20

A: Given LPP is max z=3x+5ysubject to2x+3y≤305x+4y≤60x,y≥0   So, graph of  function

Q: 11) The solid is generated by rotating R about the x-axis. 12) The solid is generated by rotating R…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: X = 1 + 6t y = 2 + 4t, ter z = 2t A line is defined by the parametric equation L : If the point (a,…

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Q: e linear approximation of the function of the function O, then use it to approximte f(5.9, 2.06).

A: Introduction: The formula of linear approximation of two variables function f(x,y) is given by,…

Q: (30) Prove the following inequalities: log x 1 (a) Vr € R \{1}, X - 1 - √x (b) Vn € N, e- e − ( 1 +…

A: Given,a) log xx-1&lt;1x , ∀x∈R*+\ 1b) e-1+1nn≤ e2n+1 , ∀n∈NWe will use Mathematical Induction…

Q: 10. Using 5x5 grids, determine the equation for steady state temperature distribution at T21, T22…

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Q: find the length of the remaining part of the y = x³/12 + 1/x curve between the x = l and x = 2 apfog…

A: We have to find the length of the remaining part of the curve y=x312+1x between x=1 and x=2

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Q: The diagram shows part of a logo design. There is one known angle of 142°. Calculate the sizes of…

A: Law of sines for the triangle △ABC. sin Aa=sin Bb=sin Cc

Q: [2 2 sinx cosx + 3cosx7 2 cosh 3 X 1 D²+ 4 D3 D³ -27

A:

Q: Solve using Power Series Centred Around Zero. (x² − 1)x²y" — (x² + 1)y² + (x² + 1)y= - - = 0

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Q: Suppose that f is a function given as f(x) = 2x² + 7x - 2. Simplify the expression f(x + h). f(x +…

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Q: 34. m,n pozitif tamsayılar, m,n are positive integers, m.n - положительные целые числа, m,n sind…

A: Solution :  Given that Let m , n are positive integers  m * n = m +(m+1)+(m+2)+...+(m+(n-1))

Q: Graph. Given the discrete-time signal sequence, plot the following into graphical form. 1. x[n] =…

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Q: D Solve the given initial-value problem. The DE is a Bernoulli equation. y¹/2 dy +y³/2 = 1, y(0)…

A: