Question

Suppose the centres of two unit spheres are located 1 unit apart. (a) Express the volume...

Suppose the centres of two unit spheres are located 1 unit apart.

(a) Express the volume of the intersection of the two spheres as an integral in any one of rectangular, cylindrical, or spherical coordinate system (you only have to pick one).

(b) Calculate the volume of the intersection of the two spheres.

Math   Calculus   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let D be the smaller cap cut from a solid ball of radius 2 units by...
Let D be the smaller cap cut from a solid ball of radius 2 units by a plane 1 unit from the center of the sphere. Express the volume of D as an interated triple integral in (a) spherical and (b) cylindrical coordinates. I was able to calculate the rectangular coordinates, however I do not understand how I should converse those to spherical and cylindrical coordinates.
Let S1: x^2+y^2=4 and S2: z=−√(x^2+y^2) be two surfaces in space. (a) [2] Graph these two...
Let S1: x^2+y^2=4 and S2: z=−√(x^2+y^2) be two surfaces in space. (a) [2] Graph these two surfaces. (b) [4] Find equations of S1 and S2 in spherical coordinate system . (c) [4] Find the intersection of S1 and S2 in this (spherical) coordinate system. (d) [5] SET UP but DO NOT EVALUATE the triple integral in spherical coordinate system to evaluate the volume which is above the xy -plane, outside of S1 and inside of S2 . (Bonus) [2] Can...
Two spheres carrying the charge Q1=+Q,Q2=−Q uniformly distributed across the surface have radii R1 and R2,...
Two spheres carrying the charge Q1=+Q,Q2=−Q uniformly distributed across the surface have radii R1 and R2, and their centers are a distance dapart. We assume that d>>R1,R2. (a) Why is this assumption necessary? (b) Choose a coordinate axis along the direction that connects the centers of the two spheres.Choosethe origin at the center of sphere 1. This defines the radial direction. In unit vector notation, what is the net electric field at some point P between the surfaces of the...
1. Three objects have the same volume, one spherical, one rectangular, and the other cylindrical. If...
1. Three objects have the same volume, one spherical, one rectangular, and the other cylindrical. If you put these 3 objects under water, how do their buoyant upward forces compare? A. According to Archimedes’ Principle, they are all subject to the same amount of buoyant forces because they have the same volume B. The cylindrical object gets the most buoyant force because it has a longer shape C. The rectangular object gets the most buoyant force because of its flat...
5. Suppose that there are two pizzerias located at either end of a one mile long...
5. Suppose that there are two pizzerias located at either end of a one mile long Main Street. Along Main Street there is potential market of 4000 customers, uniformly spread out on the street. Each consumer is willing to pay a maximum of $21 for a pizza at their door step. To travel a distance d from the consumer’s location the consumer incurs a cost of $2 per mile. To go to a pizzeria the consumer incurs the cost traveling...
Suppose that in a linear city, there is only one restaurant, located at the center of...
Suppose that in a linear city, there is only one restaurant, located at the center of Main Street (which has a length of one kilometer). Consumers are distributed uniformly on this street. Let the street be denoted by the interval [0,1] where at each point on the interval lives one consumer. Assume that the costs of production are zero. However, transport costs are positive. Suppose that transportation costs are c=$1 for each unit of distance. Let utility be U=B-c-p, where...
1)Two plane plate capacitors have the same capacitance.If the distance among the plates of the first...
1)Two plane plate capacitors have the same capacitance.If the distance among the plates of the first capacitor is the double of the one of the second capacitor,how is the relationship among the area of the plates ? 2)You have two equal and opposite charged located at a distance d from one another. a)calculate the potentialin every point of the space(set the origin of the coordinate system in the mid point of the segment connecting the charges) b)calculate the value of...
Two parallel wires with a distance of 10 centimeters apart from each other carry a 20...
Two parallel wires with a distance of 10 centimeters apart from each other carry a 20 ampere current. While observing, the wires repel. 1. Execute a drawing of the system, include all the arrows that indicate the flow of the current, and for each wire, the magnetic field. 2. Elaborate how you can calculate the value of the magnetic field II of one wire over the other and the force per unit length (F/I) for which they repel. 3. Calculatre...
2. Suppose you have two small pith balls that are 6.5 cm apart and have equal...
2. Suppose you have two small pith balls that are 6.5 cm apart and have equal charges of -27 nC? What is the magnitude of the repulsive force, in newtons, between the two pith balls? 3. Suppose you have two point charges each of 72 NC. How many millimeters apart must the two charges be to have a force of 1.05 N between them? 4. A free electron is suspended in an electric field near the surface of the Earth....
Darcy's law gives us the volume flow rate-volume per time (for example, cubic meters per day,...
Darcy's law gives us the volume flow rate-volume per time (for example, cubic meters per day, m^3/day). Another way to express volume is on a per-unit-area basis. For example, if we have a 1-m^3 cube, we know its base is 1 m^2 the cross-sectional area of the cube-and its height is 1m. If we fill the cube with water, we can say we have 1m of water per unit area. Darcy's law can be rearranged to calculate the volume flow...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT