Find your question
and Get expert's answers*
Homework Help
*Click here to submit
Refer a Friend
Discount up to 15%*
Prepared References
Save up to 50%*
Homework Help >> Mathematics
  Trace of sphere in the coordinate planes  

Question: 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: 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?

Ask an Expert for Solution

Ask an Expert for Answer Trace of sphere in the coordinate planes

Request for Solution Files

Expected delivery within 24 Hours

Course: Mathematics

Ref. No:- TGS064

Like US:-
Assignment Help

Ask an Expert & Get Answer

  • Quality work delivery
  • 100% Plagiarism free
  • Time on delivery
  • Privacy of work
Order Now
More Mathematics Questions

The 8kg mass is dropped off the bridge with the initial velocity of 50 cm/sec downward. If air resistance on object is given by 6v and the bridge is
Assume that the stock pays dividends continuously at rate q>0 and the dividends are reinvested in the stock. Supposing that interest is compounde
Determine present worth (at 8%) of the inheritance which starts at $8000 per year next year and then falls by $500 per year over its 16-year life?
North Slope Realty Co. pays weekly salaries of $7,900 on Friday for the 5-day week ending on that day. Determine adjustment at the end of accounting
A sterile solution of potassium chloride haves 2 mEq/mL. If a 20 mL ampul of the solution is diluted to 1 liter, what is the percentages strength of
Suppose that resistance it encounters while coasting is proportional to square velocity. How far will boat coast in first minute after its motor qui
Find differential equation for population P(t) of country when individuals are permitted to emigrate from country at the constant rate ?
Therefore, every individual reproduces j times where j is lifetime of individual. For which values of q, {pn} do we have ultimate extinction with pr
Present value of perpetuity is equal to present value of perpetuity-immediate paying 36.444 each year. Compute k suppose effective annual interest rat
Consider set A = {6,7,9} and set B = {3,6,2,6,3,5}. Determin the value of |D x F|? What three properties should the binary relation on the set B have