GIVEN: In Figure 7.24(a), isosceles ARST with RS = RT = 15, and ST = 18; medians RZ, TX, and SY meet at centroid Q. FIND: RQ and QZ R 15 Y I S (a) (b) Figure 7.24 N

Q: If KN=2x+1 and NJ=3x+5, what value of x makes point N the centroid? K, J M

A: (1).   If in the given triangle N is the centroid then the point N divides the line HL, JK and LM in…

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A: z=13-x2-y2 Partially differentiating with respect to x, we get zx=0-2x-0=-2x Partially…

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Q: Find the y coordinate of the centroid of the region shaded in the following diagram. 9 in. -27 in.

A: Here the figure has drawn for our convenience.  To find the centroid, the rectangle indicated in x…

Q: 18. Show that the centroid of the sector in Figure 13 has y-coordinate 2R sin o (0, y) R FIGURE 13

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Q: If point N is the centroid of AHIJ, IM = 18, KN = 4, and HL = 15, find JN. %3D %3D %3D K /N/

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Q: Evaluate fpxV47x² + 47y² dA, where D is the shaded region enclosed by the lemniscate curve r? =…

A: To find the value of the double integral         ∫∫Dx47x2+47y2dA where D is the region enclosed by…

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Q: 1. Evaluate SSSE z dV where E lies between the spheres x2 + y? + 2² = 1 and a? + y² + z² = 4 in the…

A: Given, ∫∫∫EzdV where E lies between the spheres x2+y2+z2=1 and x2+y2+z2=4 in the first octant.

Q: 1) Find the outward flux of F across the region D where F= (6x² + 2xy, 2y + x²z, 4x² y³ ) and the…

A: The vector field is,F¯=6x2+2xy, 2y+x2z, 4x2y3The region D is cut from the first octant by the…

Q: The plane z =0 separates region 1 (z 0), which is a dielectric material with ɛ, = 4, from region 2…

A: The complete solutions are given below

Q: In AQUW, point T is the centroid, and VT = 5 . Find QT and VQ. W V QT= VQ =

A: We know centroid divide each median in 2:1 ratio.

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Q: | eョで)) dV=

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Q: Problem 52. Use Stoke's theorem to evaluate fy°dx – x³dy + z³dz where C is the trace of the cylinder…

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Q: • SSS ²³² x² + y² = 2, and the xy plane. Evaluate e² dV where E is enclosed by the paraboloid z = 6…

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A: Yes , we can solve using stokes theorem. Note that all the cases z = 0

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Q: 1. Evaluate fL, 2 dv where E lies below the plane z = 2+ 3x + 4y and above the region in the…

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Q: The area of the region defined by Il æ| – |y|| < 1 and a + y < 1 in the xy plane is a. T b. 27 С. Зт…

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Q: 1. Evaluate I = D xy dA, where D is the triangular region with vertices (0,0), (0, 1), and (1,1).

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 5/10 Determine the coordinates of the centroid of the shaded area. y * = ky? a b.

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A: Given problem:- The given integral is ∫∫D1+cosy2dA, where D is the triangular region with vertices…

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A: Solution-

Q: Question 3. Compute the integral - dz 8+z where y is the rectangle with vertices +3+ i with the…

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Q: 1. Compute the average height of the cone z = a> 0. r² + y² above the disk x² + y² ≤ a² for

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Q: Consider the following. C: line segment from (0, 0) to (4, 8) (a) Find a parametrization of the path…

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Q: Consider the surface: S:z = 4 – a?, in the first octant and bounded by x² +y°, as shown in the…

A: The equation of the surface given is as follows: z=4-x2 The surface is bounded by the curve x2+y2=4.…

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Q: (1) Find the area of the curved surface of the upper half of the sphere x2 + y² + z² = a²(a > 0) on…

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Q: Example 6: Evaluate ez dz dy dx E Where E is enclosed by the paraboloid Z = 3+ x? + y² , the…

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Q: In AFGH, M is the centroid. If FM=20 find FK. G J K F H L

A: Given: In △FGH,  M is the centroid of the triangle. FM = 20

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Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Let D be the solid region in the first octant bonded above by z-3 and below by 2= 2++y. Then the…

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Q: where E is the region bounded by the paraboloid y= r+ z2 (Figure 15.4. %3D y = x2 + z?

A: Please rate and feel free to ask any query about any part of the question .

Q: Which one of the following is the parametric equa- tions of the line that is normal to the surface…

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Q: Consider the solid Q shown in the following figure 2.x + 3y + 3z = 6 S y? + x = 2 2 If S: 2x + 3y +…

A: The given surface is as follows: 2x+3y+3z=63z=6-2x-3yz=136-2x-3yz=2-23x-y The projection of the…