Question 01: Find the equation of the sphere which passes through the points (1, 0, 0), (0, 1, 0) and (0, 0, 1) and has its radius as small as possible.

Q: The surface of equation = 1 is: 16 A cone A circular cylinder A sphere An ellipsoid O O

A:

Q: 19-22 Show that the equation represents a sphere, and find its center and radius. 20. x² + y² + z² =…

A:

Q: In some designs of eyeglasses, the surface is "aspheric," meaning that the contour varies slightly…

A:

Q: The surface of equation= ++ = 1 is: - 4 16 An ellipsoid A circular cylinder A cone A sphere

A: Equation of ellipsoid

Q: Question 2 Given the equation -4x² + 40x - 4y² - 32y - 4z² +24z = -200 ] Show that the given…

A: We find center and radius of the following sphere.…

Q: 4. An elliptical track has a major axis that is 80 yards long and a minor axis that is 72 yards…

A:

Q: Question 20 Given the equation -4x² + 8x - 4y² – 56y - 4z² + 32z = -312 - a) Show that the given…

A:

Q: Problem 3. Suppose a robotic arm consists of two segments of lengths L, and L2 (sce Fig. 2). Let L1…

A: Given that: L1=5, L2=3θ1=θ2=θ According to parallelogram law: r→=L1sinθ1+L2sinθ2, L1cosθ1-L2cosθ2…

Q: Question 2 of 10 Typically, a point in a three-dimensional Cartesian coordinate system is…

A: Given : A point in a three dimensional Cartesian coordinate system is represented

Q: Let z be a complex variable  z=x+iy question attached in pic

A: (a) To evaluate the given integral around the circle |z - 2| = 3.Parametrise the equation of the…

Q: Question 2 Given the equation −4x² + 8x − 4y² − 56y − 4z² + 32z = -312 a) Show that the given…

A: I am attaching image so that you understand each and every step.

Q: Question 2 [ Given the equation -5x² + 30x - 5y² - 10y - 5z² - 90z = 21 a) Show that the given…

A:

Q: Question 4 The equation ( x - 2) 2 + (y2 + 5) 2 + (z - 1) 2 = 16 represents a: O parabolic cylinder…

A: As we know that equation of sphere is (x-h)2+(y-k)2+(z-g)2=r2  centered at the point (h,k,g) As per…

Q: 1Q Find the equations for the spheres whose centers and radii is given Center (0, -1, 5) (-1, 1/2,…

A:

Q: Question 2 Given the equation -5x² + 10x - 5y² - 80y5z² + 60z = −340 a) [1.. Show that the given…

A: This question is based on standard equation of sphere.

Q: Question 20 Given the equation -4x² + 8x - 4y² - 56y - 4z² + 32z = -312 a) Show that the given…

A:

Q: The length of the longest axis for the ellipsoid, * + = lis in which this axis is along the axis.…

A: We Know the general equation of ellipsoid is  x2a2+y2b2+z2c2=1 Where, a=Length of semi axis along…

Q: The surface of equation + = 1 is: A cone O An ellipsoid O A sphere O A circular cylinder

A: The given equation is, x24+y29+z216=1

Q: My question was denied, but my class is pre-calculus. Question 19, A parabolic question considering…

A: Given that, the diameter of the mirror is 5 centimeter and the depth of the mirror is 2.5…

Q: QUESTION 4 What are the z-traces of the surface x2+ y? +z=5? O a. Circles. b. Ellipses. c.…

A:

Q: Question 10 1 pts What is the point on the parabola y = x? that is closest to the point (6,3), and…

A:

Q: Question 1 > Eliminate the parameter t to find a simplified Cartesian equation of the form Y S¤(t) =…

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

Q: Question 3 What is the equation of a parabola with a vertex at (4,8) and directrix at y 4 Ox+4)^2-16…

A:

Q: 3) The figure shows a lamp located three units to the right of the y-axis and a shadow created by…

A: According to our guidelines, we can answer only one question   at a time Kindly repost the another…

Q: In Problem,find the equation of a sphere with radius r and center Po r = 2; P0 =(1, 2, 2).

A: The sphere is a three dimensional round shaped solid. The radius of a sphere r is the distance from…

Q: 1. The Greek mathematician Menaechnus (350 B.C.) obtained a purely theoretical solu- tion to the…

A: To justify Manaechnus's geometric method to solve "dublication of cube" problem

Q: Problem 6. Consider the curve defined by the equation 8ry - x2 - y? - 5 = 0. %3D 16 (1) Find all of…

A:

Q: 4. State a parametric representation of the hyperbola whose equation is given that will satisfy the…

A: Equation of hyperbola = x29 - y24 =1

Q: Experiment #1: While bouncing the Infinity Ball, Nikki notices that the trajectory of the ball is in…

A: Given: Nikki notices that the trajectory of the ball is in the shape of parabola. She compares the…

Q: 1. Find the equation of the hyperbola satisfying the following conditions: Vertices 4. (+7,0) and e…

A:

Q: Homework 11 Parametric: Problem 2 Eliminate the parameter t to find a Cartesian equation for: and…

A:

Q: 10. Find the equation of the hyperbola thai has its center at the origin and satisfies the given…

A:

Q: Find the eccentricity of a hyperbola whose transverse axis and conjugate axis are equal in length O…

A:

Q: Question 10 The equation of the ellipse that has a center at (5, 1), a focus at (8, 1), and a vertex…

A: Detailed solution is given below.

Q: Question 1 of 12 -/5 (a) Find an equation of the sphere that is inscribed in the cube that is…

A: We know that , Equation of the sphere , ( x - x0 )2 + ( y - y0 ) 2 + ( z - z0 ) 2 = r 2  here ( x0 ,…

Q: A. Problems Involving Cc 1. Find the standard equ directrix of the parabola as one of its foci, and…

A:

Q: the problem. 4) A bridge is built in the shape of a semielliptical arch. It has a span of 106 feet.…

A:

Q: The surface of equation + + = = 1 is: 16 A cone An ellipsoid A circular cylinder OA sphere

A: The explanation of the solution as follows:

Q: 5 - 5 = 1 49 = 1 15 49 D- =1 64 49 = 1 14 16

A:

Q: Question 2 Given the equation -5x² + 30x - 5y2 - 10y - 5z2 - 90z – 5z² 90z = 210 a) Show that the…

A:

Q: 18/2 12- ww ww w -9 -6 -12 -18 x2 y? 1. Identify a and b for the hyperbola with equation 3.

A:

Q: Question 2 Given the equation −4x² + 8x − 4y² − 56y - 4z² + 32z = -312 a) Show that the given…

A:

Q: Question 6 In the zy-plane, what is the r-coordinate of the vertex of the parabola whose equation is…

A: To find the x-coordinate of vertex

Q: Question 25 Determine the length of the latus rectum of the following conic section: = 32x 0 8 O 16…

A:

Q: Question 1 Find the equation of a parabola that has a vertex of (-5, -3) and contains the Standard…

A:

Q: Question 10 The equation of the hyperbola that has a center at (10, 6), a focus at (15, 6), and a…

A:

Q: Find the equation of the parabola which has a directrix y = 1, axis x = 2, and passes through the…

A:

Q: Question 6. Write the cartesian equation of the sphere centered at (0, 3, –1) of radius 5. Write a…

A: General cartesian equation of a sphere whose centre is point h,k,l with radius as r units is given…

Q: Problem 2 A surface in R3 is defined by the equation z2 +1 = x² + y?. Sketch the intersection…

A: Given, z2+1=x2+y2.   XY trace: Put z=0, we get x2+y2=1. It is a circle with a unit radius and…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.