Domains of functions of three or more variables Find the domain of the following functions. If possible, give a description of the domains ( for example, all points outside a sphere of radius 1 centered at the origin ) . 50. Q ( x , y , z ) = 10 1 + x 2 + y 2 + 4 z 2
Domains of functions of three or more variables Find the domain of the following functions. If possible, give a description of the domains ( for example, all points outside a sphere of radius 1 centered at the origin ) . 50. Q ( x , y , z ) = 10 1 + x 2 + y 2 + 4 z 2
Solution Summary: The author explains that every polynomial function is defined for all values of R3.
Domains of functions of three or more variablesFind the domain of the following functions. If possible, give a description of the domains (for example, all points outside a sphere of radius 1 centered at the origin).
Consider an axisymmetric feeding bowl as shown on the left below. Its cross-section is shown on the right with the axis of symmetry aligned along the y-axis.
The top curve of the cross-section is given by the function
b. What is the capacity of this bowl?
Capacity=
cm³
c. Find the volume of water inside the bowl if the water level is 3.3 cm measured from the bottom.
Volume of water =
1
961
y =
C
961
The horizontal base joins the endpoints of the top curve. Both x and y are in cm.
You may need to use a computer algebra system to solve some of the following problems. Round all your answers to at least 3 significant figures.
a. Assume that the bowl is solid and is made with plastic. Find the amount of plastic (as a volume) required to make this bowl.
Amount of plastic =
cm³
cm3
-x4 (9-x)
1 4
-x¹ (9 + x)
y
0≤x≤9.1
-9.1 < x < 0
X
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY