Find the area of the triangle with vertices P(1,3, –3), Q(0,0,0) and R(4, 5, 1). NOTE: Enter the exact answer. A = ||

Q: What is the area of the region bounded by the graph of r2 16 cos 20? (Choose all applicable…

A: The curve r2=16 cos 2θ

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

A: Given problem:- Determine the volume of the tetrahedron with vertices P(-4,4,0), Q(2,1,-3), R(1, 0,…

Q: Find the vector component of v = (4, -1,7) along b = (1, 2, –2) and the vector component of v…

A: The vectors v=4,-1,7 and b=1,2,-2

Q: . Use separable equations to find the general and particular solution of xy dx – (x +

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Q: Find an equation of the plane through(-4, 4, – 4) that is perpendicular to the planes 9x – y + z = 9…

A: Given,            The plane passes through -4,4,-4 that is perpendicular to the planes…

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 7/3 and whose components have…

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Q: 10. Maximize f(x, y) = 25 – ² - y² subject to 2x + y = 10

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Q: 2. Evaluate the following limits. x²-6x+9 b. lim X-3 x-3

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Q: Find an equation of the plane that passes through the points (3, 3, 5), 2, 2, —1), аnd ( —5, 3, 4).…

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Q: Consider the points A(1, –1,4), B(2, –3,2), C(-1, –2, 2), and D(4, 3, –6). (a) Find the volume of…

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Q: Use Lagrange multipliers to find the indicated extrema of f subject to two constraints, assuming…

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Q: x² + y2 + z? = 26, (1, 4, 3) (b) Find a set of symmetric equations for the normal line to the…

A: Let f(x,y,z)=x2+y2+z2-26

Q: 1 Using u = 1 + 2x6, then the integral | x°(1+ 2x6)5 dx becomes 12 us du- This evaluates as 5+1 1 12…

A: Follow next step

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 6j as…

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Q: 2. x = 3

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Q: Find an equation of the plane through the origin that is parallel to the plane 4x-3y+5z+13=0

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Q: 1 Verify if y = -+; xy + y = x² is a solution of a differential equation.

A: We have to verify the solution

Q: 4. Let f(x) be a function that satisfies f(3x) dx = 1 and 3f(x) dx = 15. Calculate f(x) dx. Show all…

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Q: Are the lines = 7+12t, y = 12–10r, z = 1+2t, and.x = 6+13t, y = 8+2t, z = 10–5t parallel? O No O Yes

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Q: dx 3. 5 Sinux

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Q: diong the X-dXIS WiLII all dll and t is in seconds. If you know that the initial velocity is 6 m/sec…

A: According to our company's guidelines I can only answer first three subparts of the question. For…

Q: Solve for x in terms of a and b. log x = - 10(log a + log b) + 8 log b° + 5(log b – log a) = x Write…

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Q: Determine whether the lines Lj and L2 are parallel. L: x = 1– 2t, y = 4 + t, z = 6 – t L2: x = 4 –…

A: L1:x-1-2=y-41 =z-6-1=tdirection ratio: V1=(-2, 1, -1)L2:x-4-6=y+23 =z-7-3=tdirection ratio: V2=(-6,…

Q: (c) f(0) 4 (d) lim f(x) X-0 (e) f(2) (f) X-2 lim f(x) (g) f(4) lim f(x) X-4 (h)

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Q: 3" Σ 2. Use a direct comparison to test the convergence of 4" +n

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Q: Determine whether the lines Lj and L2 are parallel. L1: x = 3 – 4t, y = 5 + t, z = 8 – t L2: x = 5 –…

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Q: Now, let f"(x) =0 and solve for x. Remember that f"(x) = - sin is a periodic function, and thus…

A: use the equation above for solving the equation for x.

Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

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Q: 1. Budgeting for least cost. A manufacturing company pro- duces two models of an HDTV per week, xr…

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Q: Determine the folowing integrais: 32+8 1.1 4x+6 1.2 +3r-10 1.3 se (sin Sx)cos Sx dr

A: In this question we have to find the Integration. Note: As per our policy we are suppose to do only…

Q: If F(u,v) = (u-v) / (u+v), Find r(금금)+ F(x)

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Q: Find an equation of the plane through (-3, 8, – 7) that is perpendicular to the planes 6x – y +z = 4…

A: We need to find equation of plane.

Q: Eind the conorel ond norticulor solution of the linoor first order oguot

A: Given query is to find the solution of the differential equation.

Q: Evaluate. (Be sure to check by differentiating!) 1 dx, x# - 3 + 3x 1 dx = 9+ 3x (Type an exact…

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Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x2 - 2xy + y²,…

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Q: The graph at right shows a function g(x) a) Where is the function decreasing? b) Where are the local…

A: Given query is to find intererval where function is decreasing and local minimum location.

Q: y² = x y = x³

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Q: s+2 s(s-3) 25 s(s-2)

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Q: Find constants a and b so that the minimum for the parabola f(x) = x2 + ax + b Occurs at the point…

A: The given parabola is : f(x)=x2+ax+b We need to find the values of a and b so that the minimum for…

Q: 3. y = V x - 1. х — 5. у — 0. теvolved at u aris

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Q: Find the vector component of v = 2i – j+ 3k along b = i + 4j + 8k and the vector component of v…

A: Vector

Q: Use the Chain Rule to find- af when r = 2, t =-1 of the function ar f(x, y, z) = e3xyz cos 2xyz ; x…

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Q: Find Duf at P. f(x,y,z)=4x^3y^3z^3;  P(1,−2,1);  u=13i+23j−23k

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Q: Use the properties of logarithms to expand the expression as a sum, difference, and/or constant…

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Q: 1. Given: - 4r? with f'(x) = (x+2)2 (r+8)(r - 2) (x+2)3 8(7r-4) (r+2)4 f(r) = and f"(x) = %3D %3D…

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Q: Determine whether the sequence is divergent or convergent. If it is convergent, evaluate its limit.…

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Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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Q: Tutorial Exercise Find the sum. 4(k + 1)²(k – 4) k = 0 Step 1 Recall the definition of summation…

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Q: Find the limit of the sequence whose terms are given by 4.9 1 Cos In =

A: Let's find.

Q: Use the triple integral to find the volume of a solid G enclosed by surfaces x = y*2 and planes…

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