Find the area enclosed by the curve y=x⁴ and y²=9x
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- Find the y-component a force, 100N, acting 45 degrees to the right of the negative y-axis.Use a triple integral to find the volume of the given solid. The solid enclosed by the cylinder x2 + y2 = 9and the planesy + z = 11andz = 2.Determine the dimension b of the square cutout so that Ixy=0 for the region shown.
- It can be show that a plane area may he represented by a vector A=A, where A is the area and represents a unit vector normal to the piano: of the area. Show that the area vector of the parallelogram formed by the vectors a and b shown in the figure is A=ab.The second moments of area about z-axis, /z, and the second moments of area about y-axis, ly, can be calculated as Select one: O 1. I = Iz ○ 2. Ly ○ 3. ○ 4. ○ 5. = = Iz = *D' 64 I₁ = D, Iz Ly Ly = 32 *D' = = 3 Iz = *D' 32 = *D' O 6. Iy=D, Ly = D², Iz = 32 O 7. Ly = Iz D = 64 32I am struggling with this question
- 4. The composite area is composed of a triangle and a quarter circle as shown in the figure. Which of the following best approximates the first moment of the composite area about the x-axis? y 1.500 m → X r = 1.500 m-3.25- 2.937 Find the distance x when 20 = 49 30. K-1.375 4.5n this question, you will calculate the second moment of area for a 4 ✕ 6 piece of lumber about the x − x and y − y axes, as shown. A rectangle with height h and width w > h is centered on the origin of the x y-coordinate plane. The left and right sides of the rectangle, having height h, are parallel to the vertical y – y axis and the top and bottom sides, having width w, are parallel to the horizontal x – x axis. Visit a hardware store and measure the actual dimensions of a typical 4 ✕ 6 piece of lumber. (Enter your answers in inches.) h = in w = in Calculate the second moment of area about the x − x and y − y axes using the measured dimensions. (Enter your answers in in.4.) Ix – x = ______in4 Iy – y = ________in4
- Find the component of the force F = -7i + 8j – 9k lb along the line through the origin makingequal acute angles with the coordinate axes.For the section to the right, find the neutral axis due to the applied moment. (a) First work the problem in x'- y coordinate system. (b) Then work the problem in x-y coordinate system and show the final location of the neutral axis is the same. 5 mm M = 400 N·m 18.57 mm 30° 5 mm 50 mm 5 mm 50 mm ODetermine the second moment of area for the quar- with respect to ter circle shown in Fig. The x-axis. R