(b) Find the area of the parallelogram with adjacent sides, a = i-j+k and b = 2j - 3k (c): Find the domain and range of: 1) y • 2) y -2 - V

Q: Find the shortest distance, d, from the point (11, 0, –6) to the plane x + y + z = 6. = p

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Q: The equation of the area of the plane region bounded by y = x^3 and the lines x = 1 and y =0 is…

A: Detail solution written below

Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

Q: The coordinate axes divide the xy-plane into four sectionscalled________?

A: The coordinate plane looks as below:

Q: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

A:

Q: Find the area bounded by the parabola y² = 8x, the line y = x + 2, and the x-axis. A 3.33 square…

A: as per company guidelines we can solve only first question when multiple question being posted

Q: Find the midpoint M of CD M = (, ) X1+X2 Y1 %3D 21 C = (-2,-10) D = (-6,0) M = ([ ? ], [ ]) Enter…

A: Explanation of the answer is as follows

Q: 8. , (2x – y) dA, where R is the region in the first quadrant enclosed by the circle x? + y² = 4 and…

A: Dear bartleby student ,According to bartleby rule Answer the first question, unless the student has…

Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and бх — Зу — 32 -13 — 0. %3D

A:

Q: Find the point on the plane 5x+3y+: =11 that is nearest the origin. What are the values of x, y, and…

A: Given: The equation of plane 5x+3y+z=11, To determine: The point on the plane that is nearest the…

Q: a) Show that the distance between the parallel planes Ax + By + Cz = D1 and Ax + By + Cz = D2 is |D1…

A: (a) To show that the distance between two parallel planes Ax+By+Cz=D1 and Ax+By+Cz=D2 is…

Q: The smaller angle (in degrees) between the planes x + y + z =1 and 2x - y + 2z = 0 is

A: Introduction :

Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: @/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for…

A: Given equations of planes are x+y+z=1 and x-2y+3z=1 Here, a1=1,b1=1,c1=1 & a2=1,b2=-2,c2=3…

Q: What is the shortest distance from the surface xy + 15x + z2 = 204 to the origin? distance =

A:

Q: Find the distance between the parallel planes – 2x + y + z = 0 and 6х — Зу — 3г — 22 — 0. - NOTE:…

A: Find the distance between the parallel planes.

Q: ` What is the shortest distance from the surface xy + 9x + z² = 76 to the origin? distance =

A: z2+9x+xy=76z2=76-9x-xy   ---- Eq 1Let P(x,y,z) be a point on the given surface. We know that…

Q: Find the acute angle (in degrees) between the planes – 4x – 5y + 5z = 0 and 2x – 3y + 3z = - 7.

A: As per the company's guidelines we are supposed to answer only one question.Kindly repost the other…

Q: The shape of the cable in a suspension bridge is parabolic when it is suspended between two towers…

A:

Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

A:

Q: A sphere of constant radius r passes through the origin O, and cuts the axes in A, B, C. Prove that…

A: Given: Equation of the sphere with origin at O x2+y2+z2-ax-by-cz=0→1The radius of the sphere is…

Q: Find formulas for the distances between (0, 0) and (a, a2 ), a > 0, along the line between these…

A: Derivative of a function is determined as the change of variable with respect to change in another…

Q: 16)- Consider the quadrature formula 6 | f(x)dx = Af (-6) + Bf(6) -6 If the degree of precession is…

A:

Q: Find the value of c>0c>0 such that the area of the region enclosed by the parabolas y=x^2−c^2 and…

A:

Q: Find the distance between the planes – 3x + 5y = 32 and – 3x + 5y = 27.

A: Simply use the formula for the distance between two planes.

Q: Show that D = |d1-d2l Vaz+b2+c2 P+1 represnts the distance between the parallel planes ax + by + cz…

A: Please refer the attached image for complete solution.THANK YOU.

Q: Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0).

A:

Q: Find the distance from the x-axis to the plane z = 3.

A: Given equation of plane - z = 3z-3 = 0       ................(1)General equation of plane is given…

Q: Find the angle between the planes x+ y=1 and 2x+у-2z32?

A:

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: How close does the semicircle y = V16 – x² come to the point (1, v5)? |

A:

Q: Find the distance between the following parallel planes: (a) 3x – 4y +z=1 and 6x – 8y + 2z =3 (b) –…

A: Solve the above questions.

Q: Find the distance from Po = (3, 9, 6) to the plane 3x + 4y – 5 = 0.

A: The given equation of plane is 3x+4y-5=0 and the point is P0=3, 9, 6. The distance between a point…

Q: . (a) Show that as (x, y)→ (0, 0) along any straight line y = mx, or along any parabola y = kx², the…

A: Given : f(x) = x³y/(2x^6+y²)  To find : To prove that limit exist along parabola

Q: 4. Evaluate where C is a circle of radius 2, parallel to the r - z plane and around the y-axis with…

A: Using the parametric equation of the curve C.

Q: Find the points on the cone 2 = r² + y? that are closest to the point (4, 2, 0). (Hint: You can…

A: Here we use the distance formula  D=(x2-x1)2+(y2-y1)2+(z2-z1)2 where D is the distance between the…

Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

A:

Q: Find the shortest distance, d, from the point (10, 0, –6) to the plane x + y + z = 6. d =

A:

Q: Find the distance between the two parallel planes 2x + 4y + 12z=7 and x + 2y + 6z= 10.

A: We have to find

Q: Evaluate f.y ds where C is the upper half of circle x? +y² = 9, traversed in the counterclockwise…

A:

Q: (a) What is the formula for finding the distance between the points (x, yı) and (x2, y2)? (b) What…

A: Given: (a) Points (x1, y1) and (x2, y2) (b) Points (x1, y1) and (x2, y2)

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

A:

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: (A) Find the unique point P on the y-axis which is on both planes. (–, ,

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Find a formula for the distance from the point P(x, y, z) to the xz-plane

A: The distance between two points x1,y1z1 and x2,y2z2: d=x2-x12+y2-y12+z2-z12 The distance from the…

Q: Graph the first-octant portion of each plane.y + z = 5

A: y+z=5 We need to graph the first octant portion

Q: Find the point on the plane 2x + 5y + z =9 that is nearest to (2,0,1). Vhat are the values of x, y,…

A: