my professor didn't use formula steps on all these problems but he only used answers...so please look at those all questions and include the formula steps on each of those questions.

1. Turn in: Use Geogebra, or a 3-D graphing tool of your choice to graph x - z' =I and match its graph with the 8 choices given below. If you do not have a printer, there is no need to print out your graph. The given equation matches Choice 2 2. Turn in: Use Geogebra, or a 3-D graphing tool of your choice to graph y= x - z and match its graph with the 8 choices given above. If you do not have a printer, there is no need to print out your graph. The given equation matches Choice 35. Turn in: Convert the following equation x - y -2z'- 4 to cylindrical coordinate system. Express your final answer as a function r, 0 . In other words, put: = = f(r, 0). Recall that in cylindrical coordinate system, an equation will contain r, z, 0 and you leave z alone. x = r cos 0 r cos' 0 -r sin? 0 -2z2 -4 r' cos 20-4 Using you get: y = rsin 0 r2 (cos? 0 -sin? 0) - 2= = 4' 2 r cos 20-4 It's OK to leave the answer as is, but if you want, you can go a bit further: = = t 23. Turn in: Use Geogebra, or a 3-D graphing tool of your choice to graph the 2 equations z= 5x2+ 4 . You z =5 will see that z = 5 is a horizontal plane slicing the top of the elliptical paraboloid z = 5x2 - 5y2 4 Rotate your graph to obtain the top-view looking down onto the xy-plane and identify the shape of the intersection curve between z = 5. and = = 5x2 + 5y - as viewed from the top. Be very specific and give key parameters for this curve (for example: if it is a circle, give its center and the radius) Confirm your finding by finding the equation of this curve using Algebra. If you do not have a printer, you do not need to print out the graphs. However, you are expected to draw the intersection curve with reasonably accuracy. At this point in time, you do not yet appreciate the underlying principle of this problem. Once we begin multiple integrations, it will become more meaningful. Think of it as a preview of things to come soon. 0Name: 6. Turn in: Convert the following equation z = x - y to spherical coordinate system. Express your final answer in the form p = f($, 0) . Simplify when possible. The essential conversion rules are: x = psin ocos 8 y = psin osine z = pcoso x2 + 1? + 2? = p- pcoso = p sin ocos' 0 - p' singsin e pcoso = p sin d( cost 0 - sin? e) coso = psin ocos 20 cos @ P= sin cos 20The graph clearly show that the intersection curve is a vertical ellipse; The center of the ellipse is at (x, y) =(0,0). The major axis lies along the y-axis with a = 2 units long and the minor axis lies along the x-axis with b = 1 units long. To find the intersection curve analytically, you equate the 2 equations and go from there: 5x2+ Sy =5 4 a = 2 ) which is the equation for the ellipse, center at (0, 0) and which, of course, is also 12 b =1 1 4 graphically confirmed.7. Convert the following equation x =16-2 to cylindrical coordinate system. Express your final answer as a in the form z = f(r, 0) when possible. Use trig identity, as needed, to simplify the answer. x = r COS 0 Using you get: , " cos 0 =16-22 cos' 0 y = r sin 0 z'=16-r cos 0 8. Convert the following equation x + y* + z* = 2: to cylindrical coordinate system. Express your final answer as a in the form z = f(r, 0) when possible. Use trig identity, as needed, to simplify the answer. x = r cos 0 r cos' 0+ r sin' 0 -= =2z Using you get: y = rsine 12 + z? =2z There is no convenient to explicitly get z. You can either leave the answer as is or: r = 2z -z9. Convert the following equation r = 9cos to rectangular coordinate system. r =9cos 0 From x =rcos 0 you get: cos 0 = - so : r = 9 r2 = 9x You then use: r = x + y to get: x"+ y" =9x > x -9x+y =0. Turn in: Use Geogebra, or a 3-D graphing tool of your choice to graph the plane defined by z - 2-x - 2y . x =0 (yz-plane) Then bound this plane by the 3 main planes: y =0 (xz-plane) . You should see the resulting solid is a z =0 (xy-plane) triangular prism. Rotate your graph to obtain the top-view looking down onto the xy-plane and identify the shape of the base of this solid and draw this shape clearly on the xy-axis graph. . The base should be a right triangle. Write the equation for the hypotenuse and put it in the form y = mx +b If you do not have a printer, you do not need to print out the graphs. However, you are expected to draw the base with reasonably accuracy. At this point in time, you do not yet appreciate the underlying principle of this problem. Once we begin multiple integrations, it will become more meaningful. Think of it as a preview of things to come soon. You can clearly see the triangular prism. And the base of this prism is the right triangle as shown. The hypotenuse goes from (0, 1) to (2, 0). Simple Algerbra will yield y = _x+2 2 Base