A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble is
Question:
A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble is then placed on the first one. This process is continued until n chambers, including the sphere, are formed. (The figure shows the case n = 4.) Use mathematical induction to prove that the maximum height of any bubble tower with n chambers is 1 + √n.
FIGURE FOR PROBLEM 26
Step by Step Answer:
By ignoring the bottom hemisphere of the initial spherical bubble we can rephrase the problem as fol...View the full answer
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
Use mathematical induction to prove that for n > 2, ..+ an-12"-1 +1") det(C, A1) = (-1)"(o + ajd + = (-1)" p(2)
-
Use mathematical induction to prove that if n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then...
-
Use mathematical induction to prove that 43 divides 6n+1 + 72n1 for every positive integer n.
-
Consider X[k] be the N-point DFT of an N-point sequence x[n]. (20 %) x [n] = {1, -2, 1, 3} x [n] = {0, 2, -1,0,0,4} (a) Determine the linear convolution x [n] * x [n] (5%) (b) Determine the...
-
In 2012, Fleming Chemicals used the following input combination to produce 55,000 gallons of an industrial solvent: Materials ...................... 33,000 lbs. Labor .............................
-
Nelson Industries manufactures a part for a type of aircraft engine that is becoming obsolete. The sales history for the last 10 years is as follows: Year Dec-08 Dec-09 Dec-10 Dec-11 Dec-12 Dec-13...
-
Define the gage factor of a strain gage.
-
The market for apple pies in the city of Ectenia is competitive and has the following demand schedule: Price Quantity Demanded $1.............. 1,200 pies 2.............. 1,100 3.............. 1,000...
-
At 1 January 2015 Sonalt Ltd, an Internet service provider, owned the following intangible assets: Description Additional information Internet domain name Acquired in a separate acquisition on 1...
-
Jaspers unadjusted trial balance reports Unearned Client Revenue of $3,200 and Client Revenue Earned of $29,000. An examination of client records reveals that $2,800 of previously unearned revenue...
-
Use Newtons method to find all the solutions of the equation correct to eight decimal places. Start by drawing a graph to find initial approximations. |cos(x? x) = x*
-
Find f.
-
Let an \(x^{\prime} y^{\prime} z^{\prime}\) coordinate system be defined using the three principal directions obtained from problem 8. Determine the transformed stress matrix...
-
4. 5. Determine the components of the force shown in the a and b directions. Also determine the a and b projections of the force. 1400 lb K 3000 N zo 30 b Using rectangular components determine the...
-
Assume that the plate is made of Carbon steel (1%) 2 cm thick and that 300 W is lost from the plate surface by radiation, calculate the inside plate temperature. k=43 W/m.*C Answer:
-
If you were to imagine a simple lump of coal about 6 cm in diameter, what volume of carbon dioxide do you think it would produce when burned? Enough to fill a disposable water bottle? To fill a...
-
5. A unidirectional fiberglass reinforced epoxy composite is provided with a Vf = 55% volume fraction [43.8 3.72 0 GPa. What stress must be applied to the of fibers. It has a stiffness tensor C =...
-
On a cold evening the night before her son's surprise birthday party, Mrs. Kowal blew up 20 balloons. She inflated them in the garage so that her son would not see them. Early in the morning, she...
-
What is traditionally more global, debt or equity?
-
Velshi Printers has contracts to complete weekly supplements required by fortysix customers. For the year 2018, manufacturing overhead cost estimates total $600,000 for an annual production capacity...
-
Find f' in terms of g'. f(x) = g(x 2 )
-
Find f' in terms of g'. f(x) = g(x 2 )
-
Find f' in terms of g'. f(x) = [g(x)] 2
-
Three not-for-profit organizations operate separately in Sunland City. The most established entity, Sunland Support, has been around for over 100 years and generates by far the largest amount of...
-
E. Chrissy's Vases is a boutique selling artisan vases. The boutique purchases several styles of vases from one source. The cost of the vases to the boutique is $10 each. All other costs for...
-
Hampton Muffins sells its muffins to restaurants and coffee houses for an average selling price of $26 per case. The following information relates to the budget for Hampton Muffins for this year (all...
Study smarter with the SolutionInn App