Find an equation for the sphere

Assignment Help Mathematics
Reference no: EM131367

Question 1) A sphere is trapped inside the box whose walls are the following six planes:

x = 2 ; x = 8 ; y = 0 ; y = 10 ; z = 3 ; z = 13

(a) Find an equation for the sphere, in the form of a level surface of a 3-variable function:

                                          g(x; y; z) = C.

(b) Find a function z = f(x; y) whose graph is the bottom half of the sphere.

(c) Describe the trace of the sphere in each of the coordinate planes (possibly the empty set).

(d) Find the point(s) of intersection of the sphere with the line defined by {y = 1, z = 2x + 8}

Question 2) The temperature T (in °C) at any point in the region -10 ≤ x ≤ 10, -10 ≤ y ≤ 10 is given by the function

                                      T(x, y) = 100 - x² - y²

(a) Provide f(x, y) and the equation g (x, y, z) = c.

(b) Sketch isothermal curves (curves of constant temperature) for T = 100°C, T = 75°C, T = 50°C, T = 25°C, and T = 0°C.

(c) A heat-seeking bug is put down at a point on the xy-plane. In which direction should it move to increase its temperature fastest? How is that direction related to the level curve through that point?

Reference no: EM131367

Previous Q& A

  Develop a basic temperature class

You have to develop a basic temperature class

  Catfish creek canoe company

Report on Catfish Creek Canoe Company

  Case study (southwestern university) - forecasting problem

Case Study (Southwestern University) - Forecasting Problem

  Relative positioning and interactive positioning

Relative Positioning and Interactive Positioning by Dragging and Clicking and some Simple Animation

  Commercial law to open a meditation studio

Commercial Law open a meditation studio and looks around the inner city suburb of Paddington for suitable premises

  Capabilities of solidworks motion manager

Prepare a power point presentation and a short report relating to the capabilities of Solidworks Motion Manager.

  Mark the equilibrium price and quantity

The demand schedule for computer chips.

  Implications of the future of fabrication for international

Implications of the future of fabrication for international trade, transportation, and logistics

  Define consumer surplus, and gi en good

Define the term Consumer surplus, Gi en good and Income elasticity of demand using graph and equation.

  Cost-volume-profit model

Explain these objections to the accountant's convention cost-volume-profit model


Write a Review


Similar Q& A

  Finding the probability of cards

This assignment has questions related to probabiltiy.

  Evaluate the sequence generated by generating functions

Evaluate the sequence generated by generating functions

  Logistic map

This assignment has two question related to maths. Questions are related to bifurcation cascade and logistic map.

  System of equations

Evaluate which equations are under-identified, just-identified, and over-identified.

  Mathematics in computing

Questions related on mathematics in computing.

  Build an equation for a hyperboloid of two sheets

A function y = f(x) whose graph in the xy-plane, when rotated around the x-axis

  Linear programming problem

Linear programming problem consisting of only two constraints with one objective function.

  Derive the boolean expression

Derive the Boolean Expression and construct the switching circuit for the truth table stated

  Evaluate the matrix of transformation

Evaluate the matrix of transformation

  Evaluate the integral

Evaluate the integral

  Find the natural domain

Find the natural domain of the given functions.

  Find relative maxima and minima

The first or second derivative test to show that the critical value is a relative maxima or minima.

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd