Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w is u· (v x w)| to determine the volume of the tetrahedron with vertices P(-4, 3,0), Q(2, 1, –3), R(1,0, 1) and S(3, -2, 3). | NOTE: Enter the exact answer. V

Q: Find the centroid of the region bounded by the graphs of 512 y = x, x = and y = 16. NOTE: Enter the…

A: Given; y=x , x=512/y^2 , and y=16

Q: d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Consider the following planes. 5x + 2y – z =22 X- 4y + 2z = 0 (a) Find the angle between the two…

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Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the…

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Q: Evaluate the definite integral that represents the volume of the solid formed by revolving the…

A: Explanation of the answer is as follows

Q: Find the relative maximum and minimum values. 3 3. f(x,y) =x +y° - 15xy

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Q: Evaluate the iterated integral. 1 z y SS§ 9ze=v² dr dy dz

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Q: Two parallel sides of a rectangle are lengthened at a rate of 3 cm/sec, while the other sides are…

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Q: a) Consider the scalar function: f(x, y) = -4x*y³ – 2a*y? Find the gradient: Vf(x, y) = i+ Find the…

A: Given; f(x,y)=-4x^2y^3-2x^4y^2

Q: Find div F and curl F if F(x, y, z) = xz*i+ 6y°x*j+4z²yk. %3D div F= curl F=

A: To find the divergence and curl.

Q: h sin 2 xdx X COs 2

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Q: 33. The expression for the horsepower of an engine is P-0.4 n x^2 where n is the number of cylinders…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Question 13 2 Evaluate the iterated integral. yz dx dz dy

A: Evaluate the iterated integral .

Q: V4-x? 3-x2-y² Evaluate the iterated integral. x dz dy dx -5+x2+y? A 128/15 16/89 23/6

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Q: The value of the integral I = is required in the development of the normal probability density…

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Q: Determine the area of the region enclosed by y=x^2 and y=x^1/2 A) 1/3 B) 1/4 © 1/5 D 1/6

A: To find the area enclosed between the two given curves.

Q: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. O 4…

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Q: Find the area of the shaded region. r = Vcos 20 r = 14 cos 0 NOTE: Enter the exact answer. A =

A: Area of shaded region .

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Let's find.

Q: Find the exact arc length of the curve over the stated interval. 1 -2, from y = 1 to y = 2 1 49…

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Q: The graph of a function y (=) is shown At which point is the following true (Only type the letter of…

A: Topic:-   calculus

Q: uni vectors that stâtêd coi satisly th st cônditi NOTE: Enter the exact answers in terms of i,j and…

A: Given: u=-2i+7j

Q: lim x-00 1 with a a real constant different from 0, consider the Consider the limit following…

A: We have to find out the correct answer

Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: Evaluate the iterated integral. x dz dy dx 128/15 16/89 23/6 6.

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Q: Find a such that the line x = a divides the region bounded by the graphs of the equations into two…

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Q: Find the relative maximum and minimum values. f(xy) = e 6x2 + 4y2 + 8

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Q: Consider the vectors: a = -11î + 10j +–12k, b = 2î + -8j + -12K, c = -7î +-10j + 10k a) Find: bxc =…

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Q: Problem 6. The area A of a triangle is given by A=ac sin B, where B is the angle between sides a and…

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Q: Determine the surface area of the solid obtained by rotating y=v9-x from -2sxs2 about the x -axis.

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Q: Find f such that the given conditions are satisfied. 17) f(x) = 5x2 - 7x + 4, f(0) = 2 A) f(x) =x3…

A: Given f'(x)=5x2-7x+4,   f(0)=2To find f:

Q: 20. Find the area of the region bounded by the curver=8 cos 20. С. 12л A. 16π В. 32л D. 8t

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the area of the region inside the circle r = 12 sin 0 and outside the cardioid r = 4+4 sin 0.…

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Q: Use the properties of the derivative to find the following. r(t) = ti + 4tj + t?k, u(t) = 4ti + t²j…

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction to PQ

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Q: What is the period and domain of the basic tangent function y=tan(x)? @ *E, 2n, {x€R|x= (2k + 1)m…

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Q: Find the area of the region using a double integral. The region bounded by y = 2x³, 2x + y = 4, and…

A: To find the area of the region using a double integral.The region bounded by y=2x3, 2x+y=4, and the…

Q: Find the directional derivative of f at P in the direction of a. f(x, y) = 17 tan ; P(-18,18); а—…

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Q: A torus is formed by revolving the region bounded by the circle x? + y? = 49 about the line x = 8…

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Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 10 — 0. - - %3D -…

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Q: dy 18. Given y = 5t ( 3 - t), t = In p and p = e*. Find and simplify %3D dx

A: Given: y=5t3-t, t=lnp, p=ex   As we know from the chain rule; dydx=dydt·dtdp·dpdx    .....(1)   The…

Q: Find the length of the curve, L. y² = 4 (x + 5)* , 0 0

A: To find the length of the given curve

Q: For neN simplty 2-글 + 4-1 +8-금+16-습+. + +2"-그 2n

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Q: The point (– 1, 3) is on the terminal side of 0 in standard position. The exact value of cos(0)is…

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Q: find Fourier series on [0,2n] オーズ 0<x<T (12) f(x) = Tくx<2元

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Q: The total sales, S, of a one-product firm are given by S(L,M) = ML - L², where Mis the cost of…

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Q: r=1+ 3sino

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Q: Express the iterated integral as an equivalent integral with the order of integration reversed. r36…

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Q: Question 11 Find the approximate area under the curve of f (x) =cos from x = 0 to x = Tt, using 4…

A: We have to find it from Trapezoidal rule.

Q: Find the arc length of the parametric curve. x = e', y = et, z = V2t; 0<t< 4 L = 54.6

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