H.W: find the tangent plane and normal line of the surface f(x, y, z) = x + 2xy- y? + z2 = 7 at the point P,(1,-1,3) %3D 79
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- Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 1ᴀ 3" ᴅɪᴀᴍᴇᴛᴇʀ ꜱᴏʟɪᴅ ꜱʜᴀꜰᴛ ᴡɪᴛʜ ᴀ 0.375 ʀᴀᴅɪᴀʟ ʜᴏʟᴇ. ᴄᴏᴍᴘᴜᴛᴇ ꜰᴏʀ ɪᴛꜱ ᴍᴀxɪᴍᴜᴍ ᴛᴏʀꜱɪᴏɴᴀʟ ꜱᴛʀᴇꜱꜱ, ɪɴ ᴘꜱɪ, ɪꜰ ɪᴛ ɪꜱ ꜱᴜʙᴊᴇᴄᴛᴇᴅ ᴛᴏ ᴀ ᴛᴏʀQᴜᴇ ᴏꜰ 5852 ɪɴ-ʟʙ. ᴇxᴘʀᴇꜱꜱ ʏᴏᴜʀ ᴀɴꜱᴡᴇʀ ᴜꜱɪɴɢ 4 ꜱɪɢɴɪꜰɪᴄᴀɴᴛ ꜰɪɢᴜʀᴇꜱ. ʀᴏᴜɴᴅ ʏᴏᴜʀ ᴀɴꜱᴡᴇʀ ᴛᴏ 4 ꜱɪɢɴɪꜰɪᴄᴀɴᴛ ꜰɪɢᴜʀᴇꜱ.Can i have the method in vector mathematics 1.) On a three-dimensional cartesian plane, there are points A[ 1 1 0 ], B[ 1 10.713 0], C[ 5.156 1 0], and D[ 1 2.841 4.221]. Determine the x-component of vector AB. Find the resultant.
- The given curve is rotated about the y-axis. Find the area of the resulting surface. y = 2 − x2, 0 ≤ x ≤ 46 - Find the center of gravity M of the three-dimensional homogeneous wire ABCD in the figure using the (x, y, z) coordinate set. The dimensions of the wire are a = 24 cm, b = 36 cm. Which of the following is the correct coordinates of the BC part of the homogeneous wire in the x, y and z axes?A) (36; 12; 24)B) (18; 12; 0)C) (36; 24; 12)D) (36; 12; 0)E) (36; 24; 0)If an axis of symmetry for the cross-section exists, the shearthe center lies at a point on this axis.Is it true or false?
- Find the component of the force F = -7i + 8j – 9k lb along the line through the origin makingequal acute angles with the coordinate axes.ᴀɪʀ ᴜɴᴅᴇʀɢᴏᴇꜱ ᴀ ᴄʏᴄʟᴇ ᴄᴏɴꜱɪꜱᴛɪɴɢ ᴏꜰ ᴀ ꜱᴇʀɪᴇꜱ ᴏꜰ ɴᴏɴ-ꜰʟᴏᴡ ᴘʀᴏᴄᴇꜱꜱ ʟɪꜱᴛᴇᴅ ʙᴇʟᴏᴡ:1 – 2 ᴄᴏɴꜱᴛᴀɴᴛ ᴠᴏʟᴜᴍᴇ ʜᴇᴀᴛ ᴀᴅᴅɪᴛɪᴏɴ2 – 3 ᴄᴏɴꜱᴛᴀɴᴛ ᴘʀᴇꜱꜱᴜʀᴇ ʜᴇᴀᴛ ᴀᴅᴅɪᴛɪᴏɴ3 – 4 ᴄᴏɴꜱᴛᴀɴᴛ ᴠᴏʟᴜᴍᴇ ʜᴇᴀᴅ ʀᴇᴊᴇᴄᴛɪᴏɴ4 – 1 ᴄᴏɴꜱᴛᴀɴᴛ ᴘʀᴇꜱꜱᴜʀᴇ ʜᴇᴀᴅ ʀᴇᴊᴇᴄᴛɪᴏɴᴛʜᴇ ᴍᴀxɪᴍᴜᴍ ᴀɴᴅ ᴍɪɴɪᴍᴜᴍ ᴠᴀʟᴜᴇꜱ ꜰᴏʀ ᴘʀᴇꜱꜱᴜʀᴇ ᴀɴᴅ ꜱᴘᴇᴄɪꜰɪᴄ ᴠᴏʟᴜᴍᴇ ꜰᴏʀ ᴛʜᴇ ᴄʏᴄʟᴇ ᴀʀᴇ 30 ᴘꜱɪᴀ,15 ᴘꜱɪᴀ, 25 ꜰᴛ3/ʟʙ ᴀɴᴅ 12.5 ꜰᴛ3/ʟʙ. ꜰɪɴᴅ ᴀ) ʜᴇᴀᴛ ᴀᴅᴅᴇᴅ, ʙᴛᴜ/ʟʙ ᴀɴᴅ ʙ) ʜᴇᴀᴛ ʀᴇᴊᴇᴄᴛᴇᴅ, ʙᴛᴜ/ʟʙ.What is the moment of the force F = 595 N about line OC. Have the answer be in Cartesian form