47. Find the area of the surface. The part of the plane r(u, v) = (5u + 4v + 6)i + (3u + 3v + 8)j + (2u + 3v + 6)k; 0 ≤u≤ 6, 0≤vs4 a. 24√67 b. √√22 c.√√34 d. √√38

Q: 4. What general shape are the level cuves of z = √x² + y² - 4?

A: The objective is to tell the general shape .

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

A:

Q: Q2 |The points A(1,0), B(2,0), C(4,2), and C(xy) are the verticies of a parallelogram. Find x and y,…

A: We will find the fourth vertex (x,y) of the parallelogram .olso we will find perimeter and area of…

Q: 3 If A B 224 and D(3cos 0, 2sin ) are four points, then find the maximum area of quadrilateral ABCD,…

A: The diagonal divides the quadrilateral into two equal parts. Area of triangle is obtained as area of…

Q: xux-yuy+y2u=y2x find the general solution

A:

Q: Find the point on the sphere x? + y² + z² = 3 farthest from the point (-6, 6, –6). Farthest point is

A: Given equation of the sphere, Given point is (-6, 6, -6). Distance of the point (-6, 6, -6) from…

Q: What is the distance between the given pla P₁: z=x+2y + 1 P2: 3x + 6y-3z = 4 O 0.95 O 1.50 O 0.14

A:

Q: Tind he latance from the pomt (-2, 4) to tu plane 37+2y4 6E5

A: Given a point (1, -2, 4) and a plane 3x + 2y + 6z = 5

Q: What is the distance between the given planes? P1: z= x + 2y + 1 P2: 3x + 6y - 3z = 4

A: To solve the given problem:

Q: Find the distance from the point Q= (2,2,2) to the line of intersection of the planes x+y+z=1 and…

A: Distance from the point Q(2,2,2) to the line of intersection of planes x + y + z = 1 and x + y = 2

Q: What is the distance between the origin and the plane 3x-2y + 5z +7=0? O 7 7√√30 30 7√√√38 38 0

A:

Q: Find the point on the sphere x+y²+z²=625 that is farthest from the point (-23,14,-13). 23 625 V1200…

A:

Q: 3. Find the area of the rhombus. dl (2x +2) cm d2 (6x + 8) cm

A: As we know that the area for a rhombus when the p and q are the diagonal is:- A=pq2

Q: Given P (8, 0) and Q (0, -6). The perpendicular bisector of PQ meets the axis of the axis at A and…

A: The points are P(8,0) and Q(0,-6)

Q: Find the point on the sphere x² + (y + 2)² + (z+ 9)² = 4 nearest to a. the xy-plane. b. the point…

A:

Q: Use calculus to show that the maximum possible area of a triangle with one vertex at (0, 0) and the…

A:

Q: j √(6y 7 + 9z 7 + 6xk) · d7 where C is the boundary of the triangle with vertices (3, 0, 0), (0, 5,…

A: First parametrize the boundaries of the triangle. (3,0,0) to…

Q: Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the cone z = √√x² +…

A:

Q: S is the lower portion of the sphere x2 + y2 + z2 = 25 cut by the cone z = √√√x² +

A:

Q: To identify how much heat is required to bring a kettle of water to its boiling point, you are…

A: Here,