Write the 3D Rotation Matrix that first rotates around the y-axis by 0, = 45° followed by a rotation around the x-axis by 0x = 180º Rows: 1 Columns: 1 C

Q: How is the nullspace N(C) related to the spaces N(A) and N(B), if C = [ A/B] ?

A: Given: N(C) is a nullspace and C=ABTo find: The relation between N(C),NA,NB matrix wise.

Q: Suppose an >0 and an diverges. Prove that n=1 n=1 an an +1 diverges.

A: Given that an>0, and ∑n=1∞an diverges. To prove that ∑n=1∞anan+1 diverges.

Q: Given f(x)=12x+8 Find ¹(2). Write your answer as a whole number or as a fraction. f¹(2)=

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Q: 1. If L{f(t)} = F(s), then

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Q: . Let F(t) = (et cost) î+ (e¹ sint) ĵ + et k. a. Find symmetric equations of the line tangent to the…

A: As per the question we are given the following vector valued function : F(t) = (et cos t)î + (et…

Q: x Y Consider the line integral 1 F. dr, where F(x, y) = ( √ C is the path along (x − 3)² + (y − 2)²…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: 91999 90992 The determinant of 4 0 050 A B C D -2 - 12 90390 60070 None of the given options 12

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Q: A sample of a radioactive substance has an initial mass of 761.7 mg. This substance follows a…

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Q: Write the 3 by 3 identity matrix as a combination of the other five permutation matrices! Then show…

A: Permutation matrix: A square matrix which has exactly one entry of 1 in each row and each column is…

Q: Let Q = (0, ∞) x (0, ∞) be the (open) first quadrant of R2 and define a map : Q→ Q by o(u, v) = (1,…

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Q: 2. Find and express the solution of the initial value problem in terms of a convolution integral…

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Q: b) the algebraic method 1. (Q-R) (R-S) = Ø 2. [(CND) U (D' n c')] = (CD)'

A: To prove the statements  1. Q-R∩R-S=ϕ 2. C∩D∪D'∩C'=C⊕D'

Q: What is the slope of the given slide? The slope of the slide is (Type an integer or a simplified…

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Q: Use integration by substitution to calculate the following integral:  ∫ x exp(-x2) dx

A: The idea is to note that the derivative of x^2 is 2x and we get an idea of what to substitute. The…

Q: Construct a graph with vertices L, M, N, O, P, Q that has an Euler circuit and the degree of N is 4.…

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Q: 1- (2x-y)dx + (7y-x-1)dy = 0 Then solve the equation using this form: M(x,y)+N(x,y)=0 And the…

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Q: B. Prove each item (Item 3 & 4) of the following by constructing a proof by element arguments 3.…

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Q: The range of sound intensities that the human ear can detect is so large that a special decibel…

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Q: Solve the following equations. 3 2x² - 6x = 5x² - 9 b) 4x 8x³ - 9x² + 18x = 0

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Q: B. Prove each item (Item 3 & 4) of the following by constructing a proof by element arguments 3.…

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Q: Question 4: Find the intervals on which f is concave upward or concave downward, and find the…

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Q: Find a rational and an irrational number between 71.8094 and 71.8095.

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Q: Use the definition of sinh and the formula for cosine of the sum of two angles to verify that π…

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Q: Temperature At time t = 0 minutes, the temperature of an object is 140°F. The temperature of the…

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Q: 2. Find the matrix A of T so that T ([]) = A[*].

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Q: Use integration by parts to calculate the following integral:  ∫ t cos t dt

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Q: Find the orthogonal projection of i - projw (0) = 22 33 9- 19 6 onto the subspace W spanned by

A: The given vector v=2233-19-6 and the subspace W spanned by 12-31,2-3-5-3,451-2. We have to find the…

Q: Answer the following questions: 1. Why are rational functions important? 2. How can rational…

A: 1)A rational function is a function of the form f(x) = p(x)/q(x), where p(x) and q(x) are…

Q: Suppose that $13,000 is invested in a bond fund and the account grows to $14,757.69 in 5 yr. Part: 0…

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Q: Solve the following integral:  ∫ (3/(x2 + 5)) dx

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Q: Let f(x) = cos(2), x=(0,x). (a) Find the Fourier COSINE series of f(x). (b) Use the convergence to…

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Q: How many ways can A, B, C, and D be arranged if B cannot occur before A, and C cannot be last?

A: To find: The number of ways A,B,C,D can be arranged if B cannot occur before A and C cannot be last.

Q: Class Scheduling   Enormous State University's Math Department offers two courses: Finite Math and…

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Q: A 25-ft ladder is leaning against a house when its base starts to slide away. By the time the base…

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Q: Let f(x) and suppose that this power series converges on n=0 (-R, R). Suppose that for all x = (-R,…

A: here we find an

Q: Consider the heat conduction in a metal rod 30 cm long, insulated on its lateral side as well as its…

A: The given problem is to find the temperature distribution by find the solution for the given partial…

Q: What lump sum do parents need to deposit in an account earning 12%, compounded monthly, so that it…

A: Let, the needed deposit is $P. Then, at a rate of 12% per annum compounded monthly, the lump sum…

Q: 1. Let 1 f(x, y) = 1-x² - y² (a) Find the domain D of f and show that f is of class C on D. (b) Show…

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Q: aph the solution set: x+3y>6 x2-3 1 X x+p 2033 ya ly 3 +2

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Q: Find a basis for the plane x -2y + 3z = 0 in R3. Then find a basis for the intersection of that…

A: Given an equation of plane x-2y+3z=0. To find the basis for the plane x-2y+3z=0 in ℝ3. Here vectors…

Q: 3. Let R be the region enclosed by the curve r(t) 27. Find the area of R. You may = (5 cost, - sint…

A: Given: r→t=5cost, -sint+cos4t , 0≤t≤2π To find: Area of R.

Q: Use the table below to estimate 3 [ƒ(2x)+2g(x)]dx by using a Riemann sum with 6 rectangles of equal…

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Q: 2 do

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Q: For each of the systems in Problems 1 through 12: (a) Find the eigenvalues and eigenvectors. (b)…

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Q: dy dx -2 y(0)=3 solve the initial value problem given above. y(x)=? OA) 2x+3 OB) x+2 OC) 2 OD) x+1…

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Q: explain the geometric relationship between the answer found in part b and the surface defined above

A: In part (b) we calculated gradient of F at (0, 1, 2).

Q: 3. Consider the problem of finding the point (s) on the plane 2x - 2y-z = 36 closest to the origin.…

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Q: unt. (Assume end-of-period deposits and compounding at the same intervals as deposits. Round your…

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Q: Consider the heat conduction in a metal rod 30 cm long, insulated on its lateral side as well as its…

A: The given problem is to solve the given partial differential equation with given initial conditions…