following equations in R3. (a) x2 + 2y2 + z2 − 8x + 12y − 2z + 35 = 0 (b) z = 1 − ex (c) x2/9 − y2/4− z2 = 1. Show the traces as well.

Q: 8. Which of the following functions represents the vertex form of y = x? - 12x – 18? a. y = (x - 6)2…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Use the equations y-11sin[6(x-4)]+26 to predict the month(s) when the average temperature if…

A: Given equation is y=11sinπ6(x-4)+26

Q: Find the quadratic y=ax2+bx+c that best fits the data points (−2,−37),(−1,63),(0,−43),(1,−5),(2,2) .…

A: To find the quadratic equation that best fits the given data points, we need to solve for the…

Q: Write y=2(0.5x-6)(6-24x) in the form y=k(x-r)(x-s) and give the values of k,r,s.

A: We have to factor out 0.5 and -24

Q: Solve for fx(-9, 9) and fy(-9, 9). f(x, y) = 5x2 + 8xy + 4y2 + 6x − 9y; (−9, 9)

A: Given:fx,y=5x2+8xy+4y2+6x-9yTo find:→fx-9,9→fy-9,9

Q: 2. A squirrel is 24 feet up in a tree and tosses a nut out of the tree with an initial velocity of 8…

A:

Q: 21. Find the standard form of the equation. 100x + 600x+16y² +160y – 300 = 0 (x+5)* , (v+3)² [A] = 1…

A:

Q: Find the point on the line 2x + y = 7 that is closest to the point (−4, 2).

A: We use second derivative test to find out point where distance minimum

Q: Find the point on the line 3x + y = 5 that is closest to the point (−2, 1).

A: To Find the point on the line 3x + y = 5 that is closest to the point (−2, 1).

Q: Complete the following... a) Solve the quadratic function −3(x−1) 2+12 = 0  There are two solutions…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…