Let A be the point with coordinates (-3, -2, 3) and let B be the point with coordinates (2, 0, 0). Let / be the line passing through the origin and B. Let D be the midpoint of AB. What is the distance from D to the line /?

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A: Conservative Vector Field: A vector field F→ is said to be conservative if it can be written as the…

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Q: 2. Let S be the surface given by the equation y? = 9+ az. Find the point(s) on S that are closest to…

A: This is a problem of optimization and multi-variable calculus.

Q: Let F, and F2 be the Cartesian representation of the 75 N and 55 N forces, respectively. Which two…

A: We will find F1 and F2 by using component and then check all statements

Q: 6. Consider a control system given by 1 2 2 2 1 3 3 () u, ra, with r(0) (1,0,0). Find a control…

A: The solution is given below

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Q: The series 32n-54-1-2n is n=1 Select one: а. is a divergent geometric series. b. is convergent but…

A: Geometric series, find the series of converges

Q: Let i denote the square root of –1. For the two complex numbers z = 3e 3 and w = 6e'3 find z. w.…

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Q: Prove that an angle of θ radians is constructible if and only if the real number cosθ(sinθ)…

A: Since θ is constructible, by definition, (cosθ, sinθ) is a constructible point.

Q: Solve 4 2 x(0) - 2, y(0) = – 2 17 -2 20 -e (cos (5t) – i sin(5t)) × -3-5i -3+5 .2745098e* (cos (5t)…

A: To solve the below system of linear differential equations. x'y'=42−17−2xy, x0y0=−2−2

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x + ax + Bwith…

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Q: Give an example where the statement: If U and V are vector subspaces of Rn, then U ∪ V is also a…

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Q: How many different size of infinity are there? How does it relate to one-to-one correspondence?

A: There are actually many different sizes or levels of infinity; some infinite sets are vastly larger…

Q: (5) Solve the the definite integral (In(2))* dz indicating which integration techniques you are…

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Q: Prove that the number V7 lies between 1 and 2.

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Q: 3. (a) Let S be a two-dimensional subspace of R³. Let P be the projection matrix cor- responding to…

A: Every subspace of R^3 has an orthonormal basis. And this basis can be extended to the basis of whole…

Q: The function f : R → R defined by f(x) = cos(x ) is а. one-to-one and onto. O b. neither one-to-one…

A: A function f: A to B is one-to-one if for every different elements in A the images are different in…

Q: Find the first three terms of the expansion (4 – 2x)°. 4°(1 + 쫄 + 폴 + .) * + +..) Oc 4°(1-쪽 + 폭+ …)…

A: The solution is given as

Q: (-2 1 Consider the matrix A 2 1 and vectors x = |1 and y: (-1 Let vector v be defined as v = (A – A'…

A: Here given matrix  A=-210021-100 Then  AT=-20-1120010 Thus A-AT=-210021-100--20-1120010=011-101-1-10

Q: Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x - 6y + 2z = 5

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Q: If a line is parallel to the vector 3i +2j+ 1k and passes through the point P = (1,3,8), then the…

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Q: Express cos (a) in terms of cos(2a). Express sin (a) in terms of cos(2a). cos (a) Choose... sin (a)…

A: Trigonometric formulas

Q: Let A be the point with coordinates (7, 6, 3) and let B be the point with coordinates (6, 6, 4). Let…

A: The main objective is to determine the distance from the point to plane.

Q: D. Calculate volume enclosed by (z 8-x-y) and (z x +y). (Use order dx %3D dy dz).

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Q: Q3: How many angle and side conditions in each one of the figures below (the numbered angles are the…

A: We will observe the  both figures and answer this question

Q: if standard deviation equal 4 so the variance equal 6. 16 8 10 O O O O O 00

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Q: Use Lagrange Multipliers to solve the following: Maximize f(r, y, z) = 4x + 2y + z subject to r + y…

A: Solution :-

Q: Problem 8. Consider the 3 x 3 symmetric matrix over R 2 2 -2 A = 2 2 -2 -2 -2 6 (i) Let X be an mxn…

A: The main objective is to determine the rank of matrix A and also find the P and Q matrices.

Q: Employ Crout's decomposition to solve the system. 5x1 – x2 = 9 -x1 + 5x2 – x3 = 4 -x2 + 5x3 = -6

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Q: Give an example where the statement: If U and V are vector subspaces of Rn, then U ∪ V is also a…

A: The given is: If U and V are vector subspaces of ℝn; then U∪V is also a vector subspace of ℝn.

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Q: Use Simpson's rule with interval h = 1 to determine the approximate value of V(1 + x³ )dx. Give…

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A: In statement given, 1)The fertilized grass grew 2.9 inches in a week, were the unfertilized grass…

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Q: a particle is moving on the x-axis with a velocity of v(t) = t^2 - 3t - 18. For what values of t > 0…

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Q: Hello, thank you for your answer but where is the rest?

A: given figure

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Q: The voltage V(t) of a supply at regular intervals of At = 0.01 s, over a half-cycle, is found to be…

A: Given the voltage V(t) is {0,19.5,35,45,40.5,25,20.5,29,27,12.5,0} and ∆t=0.01 and…

Q: Can you shoe me how to prove this by the definition(without using the supremum property or whatever…

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Q: If f is just that = e*[- sin(x + y) + cos(x +y)] and =-e" sin(x + y) which if the dy %3D following…

A: Given ∂f∂x=ex−sinx+y+cosx+y and ∂f∂y=−exsinx+y. We have to find the function fx,y. Let us assume…

Q: 23 -31 7 7

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Q: Use the method of reduction of order to find a second solution to y'' – 16y : Given y1 (x) =…

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Q: 1 Let B be the surface with equation x = -1+ Y. (a) Provide a hand-drawn sketch of B. Label the…

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Q: Express the circle specified by x = 2 cos(0) y =1+2 sin(0) in Cartesian coordinates and find the…

A: Solution

Q: Determine the value of lim, 5x²+5 x²+3x+7 Answer:

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Q: Find the area of the region. Interior of r = 6 sin 0

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Q: 17. When the price of a laptop computer is $250, 10,000 people are willing to buy it. For each…

A: Given that when the price of a laptop computer is $250, 10000 people are willing to buy it. Also,…

Q: 1. 25 4

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