HW12.1 Enhanced Assignment

Student: Jalen Wilson Date: 07/11/24 Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Assignment: HW12.1 enhanced assign 1. Give a geometric description of the set of points in space whose coordinates satisfy the given pair of equations. x = 4​, y = 2 Choose the correct description below. A. The line through the point (4,2,0) parallel to the​x-axis B. The point (2,4,0) C. The line through the point (4,2,0) parallel to the z​-axis D. The point (4,2,0) 2. Give a geometric description of the set of points in space whose coordinates satisfy the given pair of equations. 2 2 x + y = 4​, z = 5 Choose the correct description. A. The circle with center ​(2​,2​,0) and radius 5​, parallel to the​xy-plane B. The line that passes through the points ​(2​,0,5​) and ​(0,2​,5​) C. The line through (2,2,5)​, parallel to the​z-axis D. The circle with center ​(0,0,5​) and radius 2​, parallel to the​xy-plane 3. Give a geometric description of the set of points in space whose coordinates satisfy the given pair of equations. 2 2 x + z = 36​, y = 7 Choose the correct description. A. The circle with center ​(6​,0,6​) and radius 7​, parallel to the​xy-plane B. The line that passes through the points ​(6​,0,6​) and ​(0,7​,0) C. The line through (6,7,6)​, parallel to the​y-axis D. The circle with center ​(0,7​,0) and radius 6​, parallel to the​xz-plane 4. Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. 2 2 2 x + y + z = 16​, y = 0 Choose the correct answer below. A. The hollow lower hemisphere cut from the sphere x2 + y2 + z2 = 16 by the xz​-plane ​(the plane y = ​0); the hemisphere has radius 4 and is centered at​(0,0,0) B. The solid lower hemisphere cut from the sphere x2 + y2 + z2 = 16 by the xz​-plane ​(the plane y = ​0); the hemisphere has radius 4 and is centered at​(0,0,0) C. The circle x2 + z2 = 16​, y = ​0, together with its interior D. The circle x2 + z2 = 16 in the xz​-plane 5. Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations. 2 2 2 x + y + (z + 2) = 25​, z = 2 Choose the correct description. A. The circle with center ​(0,0,2​) and radius 9​, parallel to the​xy-plane B. The circle with center ​(0,0,2​) and radius 3​, parallel to the​xy-plane C. The line through ​(3,0,2​) and ​(0,3​,2​) D. The line through (3,3,2) parallel to the​z-axis 6. Describe the set of points in space whose coordinates satisfy the given combination of equations and inequalities. a. x = 0​, y ≤ 0​, z ≤ 0 b. x ≥ 0​, y = 0​, z ≤ 0 a. Choose the correct description below for the combination of equations and inequalities given in part​(a). A. The plane perpendicular to the x​-axis at x = 0 B. The third quadrant of the yz​-plane C. The line through the origin parallel to the x​-axis D. The half space consisting of the points on and below the yz​-plane b. Choose the correct description below for the combination of equations and inequalities given in part​(b). A. The line through the origin parallel to the y​-axis B. The half space consisting of the points on and below the xz​-plane C. The fourth quadrant of the xz​-plane D. The plane perpendicular to the y​-axis at y = 0 7. Describe the given sets with a single equation or pair of equations. The line through the point ​( − 4​, − 3​,2​) parallel to the a. ​x-axis b. ​y-axis c.​z-axis a. Choose the correct set of points. A. x = − 4​, z = 2 B. y = − 3​, z = 2 C. x = − 4​, y = − 3 b. Choose the correct set of points. A. x = − 4​, z = 2 B. x = − 4​, y = − 3 C. y = − 3​, z = 2 c. Choose the correct set of points. A. y = − 3​, z = 2 B. x = − 4​, y = − 3 C. x = − 4​, z = 2 8. Write the inequality that describes the​half-space of the set of points to the right of the xz-plane. The inequality that describes the set of points is ​(Simplify your​answer.) y>0 . 9. Find the distance between points P1 (0,0,0) and P2 ( − 3,5, − 6). The distance is 70 . ​(Type an exact​answer, using radicals as needed.) 10. Find the distance from the point (4,3, − 5) to the a.​xy-plane b.​yz-plane c.​xz-plane. a. The distance from the point to the​xy-plane is ​(Type an exact​answer, using radicals as​needed.) 5 . b. The distance from the point to the​yz-plane is ​(Type an exact​answer, using radicals as​needed.) 4 . c. The distance from the point to the​xz-plane is 3 . ​(Type an exact​answer, using radicals as​needed.)