Find the distance from the point (-6,3,1) to the plane: x-2y-4z = 8.

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A: Given function:- fx,y=x2+xy+2x+5y-3

Q: Consider the following vector function.. r(t) = (2√2t, e²t, e-2t) (a) Find the unit tangent and unit…

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Q: Find the surface area of revolution about the x-axis of y = 5 5 ㅠ 0 ≤ x ≤ 5 sin(5x) sin(5x) ov over…

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Q: Find the vector equation of a line passing through (5,1,3) and perpendicular to the plane 3x - 2y +…

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Q: The region bounded by f(x) = −4x² + 16x + 84, x = 0, and y = 0 is rotated about the y-axis. Find the…

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Q: Find the average rate of change of f(x) = x² from x = 1 to x = 4. (a) 3 (b) 5 (c) 15 (d) 6

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. 8s² - 49s + 294 s(s² +49) Your…

A: given  Fs=8 s2 - 49 s + 294s  s2 + 49 and asked to find the inverse laplace transform of F( s ).

Q: For each cost function (given in dollars), find the cost, average cost, and marginal cost at a…

A: Given : a. at q = 1000 Average cost = 128000/1000 = 128 dollars / unit   Marginal cost for q=1000

Q: Find the arc length of y = 4x + 1 on 0 ≤ x ≤ 2.

A: Recall the formula: ddxconstant=0ddxx=1∫dx=x+C

Q: Consider the graph below. Which of the following is the correct setup for the area of the shaded…

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Q: Use the following three identities to evaluate S sin sx cos tx = sin sx sin tx = cos sx cos tx = ·S=…

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Q: A tepee has a circular floor with a diameter of 4 meters. What is the floor's circumference? typed…

A: Given :  A tepee has a circular floor with a diameter of 4 meters. Find :  What is the floor's…

Q: Obtain the particular solution satisfying the initial conditions indicated. 1. ³ (3x²y − x²)dx + ex³…

A: The given differential equation:ex33x2y-x2dx+ex3dy=0

Q: Find f'(x) and simplify. X x + 36 f(x) = Which of the following shows the correct application of the…

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Q: 4.4. Solve the equation ff(x) dx = sin x - 2 tan x + 7x HELP: Treat ff(x) dx as a variable and use…

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Q: Compute the surface area of revolution about the x-axis over the interval [0, 1] for y = e-5x (Use…

A: We draw the graph of the function and find the total area by integrating

Q: Find the area bounded by the curvey = x² + x +4, the x-axis, from x = 1 to x = 3. 16 14 12 10…

A: To find the area bounded by given curves.

Q: The area under the curve of the function f, using the Riemann sum, will be exact if we let the n or…

A: Solved below

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

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Q: d. f(x) = 3x4. 3x²-2 2x

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Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

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Q: f(x,y)=200(y + 2) represents the "population density" of a planar region on Earth, where x and y are…

A: Given: The population density is f(x,y)=200(y+2) Where x and y are in miles.   Curves are given as…

Q: Find parametric equations of the line that contains the point P(3, 1,-2) and intersects the line L:…

A: The solution is shown below-

Q: Q13 Use the limit definition of the derivative to find the derivative of the following function:…

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Q: Question 21 Suppose that is differentiable function and f'(r) 2 2r-1 for all are R. If f(0) = 1,…

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: Given curves: y=x4, y=1 To find: Volume of solid obtained by rotating the region bounded by the…

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Q: volume of the solid formed when the region bounded by y = x and y = = x¹ is rotated about the…

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Q: Complete the parametric equations of the line through the points (1,8,3) and (4,-6, (t) = 1 + 3t…

A: The parametric equation for the line through (x, y, z) and (a, b, c) is: (x, y, z)+t((a, b, c)-(x,…

Q: Given the function f(x)=x²-2, completo parts a through c (a) Find an equation for roo (b) Graph fand…

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Q: Find the volume of the solid generated by rotating about the x-axis the region bounded by y = 2.3*,…

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Q: 400 gallons of pesticide is accidentally spilled into a lake and uniformly mixes with the water. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of pesticide at time t…

Q: The figure shows a lamina that is shaded according to the given density function: darker shading…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Suppose that f is differentiable at 1 and f'(1) = 1 = f(1). Evaluate lim xf(x²+x-5)-16 22-4 (Hint:…

A: Given f is differentiable at 1 f'(1)=1=f(1) We are required to find limx→2x4fx2+x-5-16x2-4

Q: Consider the following problem: a farmer with 650 feet of fencing wants to enclose a rectangular…

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Q: Question 2. Consider the following linear programming problem. Min 7.505 + 9.00P s.t. 0.105 0.065 5.…

A: NOTE: Refresh your page if you can't see any equations. . for simplicity use the variables S=x and…

Q: Evaluate the integral. 37 sec 37 sec -2x tan ³x dx

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Q: [3-R] [CLO 14] Is the following set a function? Briefly justify your answer. M

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Q: (x)u[ S -dx 陇

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Q: Consider the following. Find r'(t) and r"(t). r' (t) r"(t) = K= r(t) = (4t², In(t), t In(t)) = Find…

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Q: For y = f(x) = 8x³, x = 3, and Ax=0.04 find a) Ay for the given x and Ax values, b) dy = f'(x)dx, c)…

A: We have, y=fx=8x3, x=3, and △x=0.04 To evaluate : (a) △y for given x and △x value (b) Expression for…

Q: Find the extreme values of f(x,y) = 4x + 6y subject to the constraint x² + y² = 13. 2 OA. The…

A: Question Find the extreme values of f(x,y) = 4x+6y subject to the constraint x2+y2=13

Q: 1. Find the surface area of the portion of the paraboloid z = x² + y² below the plane z = 1.

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Q: Write the equation of the tangent line to the curve at the given point. x² + y² + 6x - 3y + 7 = 0 at…

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Q: Find the absolute extrema of the function, if they exist, over the indicated interval. Also indicate…

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Q: 43 x

A: given diagram of polar region

Q: Consider the curve r(t) = (6 cos(t), 6 sin(t), e), 0 ≤ t ≤ π. Find r'(t). r'(t) = Consider the plane…

A: Given curve:- rt=6cost,6sint,et

Q: Determine if Rolle's Theorem can be ap plied to r²+3r-18 x+9 f(x) = on the interval [-6, 3), and if…

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Q: Consider the graph between two curves. Which of the following is the correct set up for the area of…

A: Application of derivative

Q: The gradient of f(x, y) = zy at (x, y) = (-1,1) is

A: The gradient of function f(x,y) is represented by ∇f(x,y) where:∇f(x,y)=∂f∂x,∂f∂y          Equation…