1) a. XUxt Uyy=Xx- hyperbelic for x<0 B=O C=1 ム--4 Porobolic X=0 elliptic x70 b. xUxx -2xy Uy+ fuyy = eX A=x² Porobolic %3D B=2xy C- y2 D=0

Q: A natural cubic spline S on (0,2] is defined by Jsin - 1+2-r. S) = if Osr<l. |S,0) = 2+ b - 1) + cư…

A:

Q: 1.)A truck hauling cylindrical steel tank has to pass under an overhead parabolic arch bridge which…

A: Given:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: 2.10. If one rectangular solid with dimensions of 6 x 6 x10 millimeters is stacked of an identical…

A:

Q: An architetect wants to design a semicircular tunnel so that two average trucks measuring 8 feet…

A: Given: Dimension of the truck is 8 feet wide and 12 feet tall. Horizontal distance between two truck…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A:

Q: A cylindrical container with circular base is to hold 64 in^3. Find its dimensions so that the…

A:

Q: 3. What are the dimensions of the closed cylindrical can that has surface area 280 square…

A:

Q: What is the area of the conic (x + 3) + y 25

A:

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: First we consider the volume of small disk and integrate this across the given region to get the…

Q: Sketch the solid described by the given inequalities. 2 sps 3, 0s p s a/3, 0s0sa 1.5 1.0 0.5 0.0

A:

Q: A cylindrical can without a top must be constructed to contain V = 2500cm³ of liquid. Find the base…

A:

Q: A layer of equal spheres is in the form of a square. The spheres are arranged so that each sphere is…

A: The lines that trace the center of the spheres will form into square pyramid. See figure below.

Q: The surface z - - = 1 is a hyperboloid of one sheet. Select one: True False

A: The general form of the equation of hyperboloid of one sheet is: x2a2+y2b2-z2c2=1

Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Hex reasoned that a moving point traces out a line segment, and that a line segment moving parallel…

A:

Q: Determine the diameter of a hole that is drilled vertically through the center of the solid bounded…

A:

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A:

Q: 1. The solid bounded by the cylinder y = 9 – x² and the paraboloid y = 2x? + 3z².

A: In this question, we find the volume bounded by given surfaces. The surfaces: y=9-x2andy=2x2+3y2 The…

Q: Find the arclength of y = 2x /2 on 1 < ¤ < 3 2x3/2 uostion

A: given that y=2x3/2. we need to find the arc length in the interval [1,3] the arc length formulae is…

Q: Chapter 6, Section 6.2, Question 033 Find the volume of the solid generated when the region enclosed…

A:

Q: Draw a sketch of the cylinder z = -4 - y2.

A: A cartesian coordinate system contains two mutually perpendicular number lines named x-axis and…

Q: Find the points on the ellipse 2x +y = 1 where f(x,y) = xy has its extreme values.

A: Introduction: When a multivariable function is to be extremized under some constraints, we use the…

Q: Two children weighing 16 and 24 kilograms are sitting on opposite sides of a seesaw, both 2 meters…

A: Given,           Two children weighing 16 and 24 kilograms are sitting on opposite sides of a…

Q: If 2x^4 + x^2y^2 - y^8 = 3x^2 + 4,what is the value of dyldx at point (4,1)? %3D

A:

Q: 2.7 Describe cll soilutions of Asso where A is the Yow ta the matirix meg Vse Y S, and/or t as in…

A: Given  A=1-6-50-2-100100-200001-7000000 Here, we have to solve Ax=0

Q: 1. A supermarket employee wants to construct an open-top bax from a 14 by 30 in a piece four corners…

A:

Q: number 44 and it says use example 4 so i attached that as well

A:

Q: The space with lower border the parbolic 2: xy and upper border the level 2=4, must be divi ded into…

A:

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

A:

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: GIVEN: y = 9 x2 x = 0 x = 1 y = 0

Q: 9. In the ry-plane, a particle moves along the parabola y = x? – x with a constant speed of 2/10…

A: Given:-  In the xy-plane, a particle moves along the parabola y = r²r with a constant speed of 2√10…

Q: Exercise 10. A wire of length 28 m is to be cut into two pieces. One of the two pieces is to be made…

A: Concept: Maximum and minimum value: To find the maximum and minimum value of a function using first…

Q: 2. An LPG tank is to hold x cubic meter,. It is constructed of a cylinder capped on top by a…

A: The volume of the LPG tank is x cubic meter. It constructed with a hemisphere and a cylinder. Let's…

Q: 11. Show that the tangent to the hyperbola x-y = 1 at the point P(coshu, sinhu) except when vertical…

A:

Q: Find the points on the ellipse 2x +y 1 where f(x,y)= xy has its extreme values. %3D

A: Solution:- Here we have to find the extreme value of  f(x,y)=xy subject to constraint…

Q: 1. Draw a sketch of the cylinder z= ==V36 – 4y2.

A: Given: z=1336-4y2

Q: We wish to empty a hemispherical tank full of water out the top. Which should entail the larger…

A:

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A:

Q: Find the volume of the reqion bauoded the parabolalde2=4-x2-42 3 below the parabolaid aboue by

A: We need to find the volume of the region bounded above by the paraboloid above z = 4 - x2 - y2 and…

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What should…

A: Use application of derivative concept. volume of cylinder and total surface area of cylinder…

Q: 1. Find the dimensions of closed-top box with the largest volume if the total surface area must be…

A: It is known that perimeter of box is,  2(xy+xz+yz) Given that, 2(xy+xz+yz)=125 So, z=1252-xyx+y The…

Q: The volume of the closed cylindrical tank is 11.3 m³. If the total surface area is a minimum, what…

A: In this question, concept of volume and surface area of cylinder is used. Volume and Surface area of…

Q: In his work Nova stereometria doliorum vinariorum (New Solid Geometry of a Wine Barrel), published…

A:

Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

A: Given: The radius of the sphere is b. The radius of the hole is a. We have to show that the volume…

Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

A: Given: The region bounded by y=2x2, x=0, x=2 and y=0.

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,

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.