Given planes P₁ : 2x - 3y + 5₂-6=0 and P₂ : 2x -y - z 2 +9 =6 equation of the line of intersection @ Find an plans PI and P₂ Find am quation of the plane orthogonal to of intersection of the Planes P, and P₂ through the poin't Q (4₁ -2,5) line Find the point on the plane 1 P₂ that closest to the point R (7,3,4) is

Q: sin(x) |_sin(x)+cos(x)dx=?

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Q: Solve the following linear program using the general formulas z = -2x1-x2 x1 + x₂ ≤ 5 2x1 + 3x2 ≤ 12…

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Q: For each ordered pair, determine whether it is a solution to the system of equations. -2x+7y=3…

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Q: Find the order of Z=0 for the following functions: 1) 1+2-e² 2) 6 sin(z ³) + z9-673 3) (e²²-1-7²)…

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Q: 1. Show that if the Wronskian of Y₁ and Y₂ is nonzero then so is the Wronskian of 2Y₁ and Y₁ + Y₂. 2…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Determine whether each of these proposed definitions is a valid recursive definition of a function…

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Q: Let f: Z → Z be given by f(n) = n² - 5n+6 (a) Is fone-to-one? Justify. (b) Is fonto? Justify. (c) Is…

A: Since you have posted multiple questions with multiple sub parts, we will provide the solution only…

Q: 5(c): The function is defined implicitly by the equation 2 + y² = 1. 1-7² ,0<x<2 .-1≤x≤0

A: When  0&lt;x&lt;2,  we have          y= f(x) = sqrt(1-x2)  or,            y2 = 1-x2    or,…

Q: Find 1(2), (3), (4), and (5) if fis defined recursively by f(0) = -1, f(1) = 2, and ƒ (n + 1) =…

A: fn+1=fn2fn-1, f0-1 and f1=2. We have to find the value of f2, f3, f4 and f5.

Q: For the function f whose graph is given, determine the limit. Find lim f(x). x-3 24

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Q: Problem #8: Consider the following initial value problem. 0 1 ≤ 3 3 < t < 5 0 5 <1 00 Problem #8(a):…

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Q: lim f(x) = 0, x →1 lim F(x) = 2, 2-1 which, if any, of A. lim f(x)g(x), B. lim f(x) 9(2), x →1 g(x)…

A: Determination of indeterminate forms.

Q: Let K[x] is the polynomial ring over the field K  be a field and let F be a subfield of K. If F is a…

A: Kx is the polynomial ring over the field K is a field and F is a subfield of K.F is a perfect field…

Q: Use an artificial variable (xo) and auxiliary problem to verify that the following problem is…

A: Given: Problem is: maximise x1-x2+x3subject to:x1-5x2+5x3≤-5x1+x2+2x3≤4x1, x2, x3 ≥0. To do: We need…

Q: b) Is 1 -2 an eigenvector of 1 367 337 565 ? (say why). If so find the eigenvalue.

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Q: 1. Find the Fourier Series on [-, π] of the following functions: sin² x, sin x cos x, sin³ x, and…

A: Even function- A function is said to be an even function if f-x=fx. Fourier series expansion of the…

Q: Problem #4: Let y(t) be the solution to the following initial value problem. "-8" +12y = fet, y(0) =…

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Q: 6. How many permutations of {0, 1, 2, 3, ..., n,} leave at least two numbers fixed?

A: How many permutations of {0, 1, 2, ...., n} , leaves at least two number fixed ?

Q: Now H= [² 2 id 2² H эрг = Ho 2² [Ho Sin (Kr_wt)] ar 2 [2 Ho Sin (Kr- wt) Ho 2/ [cos (kr-wt) x] K Ho…

A: They have derived the partial derivative. Our aim is to explain the derivative rule.

Q: 1.) god (+n₁ fn + 1) = 1 VAZI

A: Kindly note, as per the office rule, we are supposed to solve the first problem from a set of…

Q: Let N be the set of natural numbers, A = {1, ½, ½, ½, ...}, B = {1:1 ≤ x ≤ 10, where x N} 111 E (10)…

A: 10. Given that, B={1x:1≤x≤10,where x∈ℕ} For x=1,1x=11=1 For x=2,1x=12 For x=3,1x=13 And so on we get…

Q: 6. Using your favorite method for numerically approximating derivatives, compute the Jacobian of a…

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Q: K6. What is the solution to the inequality: x = (-∞, -8) U (-3, ∞) Ox€ (-8,-3) XE Oxe (-∞, -8]U…

A: Just write the inequality as one quotient on the left side and zero on right.

Q: Determine if the line r = (1, 3, 1) + s(5, 1, 1), SER is intersecting, parallel to, or coincident…

A: The equation of the line is given as          r = (1, 3, 1) + s(5, 1, -1)    Then, any point on the…

Q: Minimize subject to C = 18x₁ + 2x2 4x₁ + x₂ ≥17 3x₁ + x₂ 24 X₁, X₂ ≥0 a. Form the dual problem.…

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Q: i had a typo can you also find the eigenspace for the given matrix

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Q: a) Is λ = −2 an eigenvalue of ( 7 3 3 -1 ? Why or why not?

A: As per our guidelines, we have to solve the first question if multiple questions are posted at a…

Q: 3. Sketch the graph of the reciprocal function. Find its intercepts.

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Q: Consider the problem of computing the Riemann-Stieltjes integral S a(x) = x¹/5 We will use the…

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Q: 9. Which of the following statements about convergence of the series 30 (A) Σ h=] (Β) 1 In(n + 1) 1…

A: We have used comparison test

Q: Consider the following. (a) Compute the characteristic polynomial of A. det (4-1)--(2-2)(2+1)(2-2)…

A: Eingvalues found by finding characteristics equation.

Q: Analytically determine the highest point on the curve of intersection of x² + y² + z² = 64 and 2x+y…

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Q: (2) Calculate the flux of F(x, y, z) = (x², y², z²) outward across the boundary of the domain D =…

A: Here S is the boundary of a sphere which is closed so we can apply Gauss Divergence Theorem.

Q: (B) Suppose that g(x) is a real analytic function such that: Find g(7) (-3) (derivative of order 7).…

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Q: In a sideshow game. A player gets 3 balls to place into a Clown's mouth. Each ball is swallowed by…

A: The given slot numbers are 1,2,3,..,9. The 3 balls given to the player ends at three of the given…

Q: Let P₂(x) = {ax² + b | a, b e R and a #0}. If p(x) = ax² +b and g(x) = cx² + d are elements of…

A: In the given problem we have to show the the set p2(x) is a group with respect to the binary…

Q: 1. Graph a) lim f(x) = x-0 b) lim f(x) = c) lim f(x) = x-2 - per d) lim f(x) = 1+3+ e) lim f(x) =…

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Q: (b) Show that if gcd(m, n) = 1, then σ₁ (mn) = σt(m)ot(n). In other words, show that function. Is…

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Q: Suppose A, B and Care 3 x 3 matrices with det (A) = 3, det (B) = -2, and det(C) = 3. Find det…

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Q: A company y has two categories of workers (Grade A and Grade B) in each department. In department 1,…

A: A company has two categories of workers (Grade A and Grade B) in the department. In department 1,…

Q: Let P(n) be the statement that 13+2³+33 + ... + n³ = What do you need to prove in the inductive…

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Q: Joe takes out a home loan for $100,000. It will be repaid with 360 monthly installments beginning at…

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Q: -2 5) Are following functions Sin²x, sin (x²), lux, (x² +1) J ^ even or odd or xe tanx neither even…

A: 5) We need to determine whether the following functions are even, odd or neither: (i) f(x)=sin2x,…

Q: 1. Cos 5. cos 17. cos 2. arccos 3π 37 = 0 6. cos 14. √3 2 || ان | ته 2 3. cos 18. arccos 0 = 7. 2π…

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Q: II. Given: F(s)= s²+2s-4 4e¯) (s²+4)² s(s²+4) Find the inverse Laplace, f(t) +

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Q: Recall from Section 5.1 that the differential equation for the instantaneous charge q(t) on the…

A: Laplace transform

Q: Q10. In this problem we will solve a recurrence using generating function an = 5an-1-6 an-2, ao=1,…

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A: From the given conditions, the following linear system of equations can be obtained: There are a…