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4. The area S enclosed by a circle of radius a in spherical geometry (see Ex. 1) is given by the formula s-2m(1-cosa) COS where r is the radius of the sphere. Deduce from this the formula for the...
Find the average surface area of a spherical balloon when the radius changes from r =...
Find the average surface area of a spherical balloon when the radius changes from r = 4 to r = 4.05 cm. The surface area formula for a sphere with radius r is A = 4πr^2 . Round to two decimal places.
Do not use I=delta/S!!! Use law of cosines Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, wha...
Do not use I=delta/S!!! Use law of cosines
Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r? Note in spherical geometry the angles sum is>180 Using below picture (this is what we are given), we should know angle b and the angle at the perpendicular. If we find the length on...
Can someone explain if this is right and where we get 2pi/15??? Let ABCDE be a regular pentagon on the unit sphere S with each side equal to s and each angle equal to (4 π)/15. Find an exact value...
Can someone explain if this is right and where we get
2pi/15???
Let ABCDE be a regular pentagon on the unit sphere S with each side equal to s and each angle equal to (4 π)/15. Find an exact value for cos(s). Note that as in Euclidean geometry, a regular pentagon on a sphere can be inscribed in a spherical circle) Let 0 be Centre of unttệpheve Aonbe) L ABCDE be hauue ) g": l+1-2(4) (1) cos ( 요ㅠ IS...
1. Let ABCDE be a regular pentagon on the unit sphere S with each side equal to s and each angle equal to 4pi/5. Find the exact value of cos a. Noticed that as in Euclidean geometry a regular pe...
1.
Let ABCDE be a regular pentagon on the unit sphere S with each side
equal to s and each angle equal to 4pi/5. Find the exact value of
cos a. Noticed that as in Euclidean geometry a regular pentagon
called a spear can be inscribed in a spherical circle
The only ideas that can be used include: area ABC-RA2(A+B+C-Ipi), the Pythagorean theorem: Cos c-cos a cos b. Vectors-dot product cross product, sin A-sin a/sin c; coS A-COs a sin...
1. (20 marks) (a) (4 marks) Derive a formula for the surface area of an object that is created by rotating a function f(x) around: 1. the r-axis with y20 2. the y-axis with 20 You will need to clearl...
1. (20 marks) (a) (4 marks) Derive a formula for the surface area of an object that is created by rotating a function f(x) around: 1. the r-axis with y20 2. the y-axis with 20 You will need to clearly show how you have chosen to break the surface up into tiny pieces and what high school geometry is needed to find the area of these tiny pieces (b) (6 marks) Confirm that your formula provides the expected surface areas...
he polar function Find a formula for the derivative r =1-cos(O), 05021. (4 points) Set up,...
he polar function Find a formula for the derivative r =1-cos(O), 05021. (4 points) Set up, but do not solve, an integral to find the arclength of the curve r = 1-cos(), 030 s2r. (4 points) 9) Set up, but do not solve, an integral to find the area enclosed by r=1-cos(o), Oses2r. (4 points)
1. Image charges in sphere We have two charges of magnitude +Q seperated by a distance of 2d, see drawing. a) Find a grounded conducting sphere (potential set to zero) with radius R, where R is the m...
1. Image charges in sphere We have two charges of magnitude +Q seperated by a distance of 2d, see drawing. a) Find a grounded conducting sphere (potential set to zero) with radius R, where R is the minimum radius needed to neutralize the repulsion from the two charges on each other. Hint: Try to reverse engineer the idea of image charges for a sphere which was discussed in the lectures. Place image charges and find an expression for the force....
Consider a hemi-spherical tank with radius R = 16 see figure that is initially entirely filled...
Consider a hemi-spherical tank with radius R = 16 see figure that is initially entirely filled with a fluid. At time t=0, the fluid begins to drain through an opening in the bottom of the tank see figure] until the tank is completely empty at t = tend- t= 0 te (0, tend) (a) At any time t, consider the maximum depth of fluid in the tank, h = h(t), and the corresponding radius of the surface of the fluid,...
1. The lateral surface area S of a cone excluding its base is given by where r is the radius of t...
1. The lateral surface area S of a cone excluding its base is given by where r is the radius of the base and h is the height. Determine the radius of a cone which has a lateral surface area 1200 m2 and a height of 20 m, by using the fixed point iteration with Start withr 17, and perform calculations in Matlab until two consec utive iterates do not differ by more than 10-8. What do you observe re...
See Figure 1. A solid, conducting sphere of radius a has total charge (-)2Q uniformly distributed along its surface, where Q is positive
2. Gauss' Law See Figure 1. A solid, conducting sphere of radius a has total charge (-)2Q uniformly distributed along its surface, where Q is positive. Concentric with this sphere is a charged, conducting spherical shell whose inner and outer radii are b and c, respectively. The total charge on the conducting shell is (-)8Q. Find the electric potential for r < a. Take the potential out at infinity to be 0.
Do not use I=delta/S!!! Use law of cosines
Here is the question: Let r be the radius of the incircle of triangle ABC on the unit sphere S. If all the angles in triangle ABC are right angles, what is the exact value of cos r? Note in spherical geometry the angles sum is>180 Using below picture (this is what we are given), we should know angle b and the angle at the perpendicular. If we find the length on...
Can someone explain if this is right and where we get
2pi/15???
Let ABCDE be a regular pentagon on the unit sphere S with each side equal to s and each angle equal to (4 π)/15. Find an exact value for cos(s). Note that as in Euclidean geometry, a regular pentagon on a sphere can be inscribed in a spherical circle) Let 0 be Centre of unttệpheve Aonbe) L ABCDE be hauue ) g": l+1-2(4) (1) cos ( 요ㅠ IS...
1.
Let ABCDE be a regular pentagon on the unit sphere S with each side
equal to s and each angle equal to 4pi/5. Find the exact value of
cos a. Noticed that as in Euclidean geometry a regular pentagon
called a spear can be inscribed in a spherical circle
The only ideas that can be used include: area ABC-RA2(A+B+C-Ipi), the Pythagorean theorem: Cos c-cos a cos b. Vectors-dot product cross product, sin A-sin a/sin c; coS A-COs a sin...
1. (20 marks) (a) (4 marks) Derive a formula for the surface area of an object that is created by rotating a function f(x) around: 1. the r-axis with y20 2. the y-axis with 20 You will need to clearly show how you have chosen to break the surface up into tiny pieces and what high school geometry is needed to find the area of these tiny pieces (b) (6 marks) Confirm that your formula provides the expected surface areas...
he polar function Find a formula for the derivative r =1-cos(O), 05021. (4 points) Set up, but do not solve, an integral to find the arclength of the curve r = 1-cos(), 030 s2r. (4 points) 9) Set up, but do not solve, an integral to find the area enclosed by r=1-cos(o), Oses2r. (4 points)
1. Image charges in sphere We have two charges of magnitude +Q seperated by a distance of 2d, see drawing. a) Find a grounded conducting sphere (potential set to zero) with radius R, where R is the minimum radius needed to neutralize the repulsion from the two charges on each other. Hint: Try to reverse engineer the idea of image charges for a sphere which was discussed in the lectures. Place image charges and find an expression for the force....
Consider a hemi-spherical tank with radius R = 16 see figure that is initially entirely filled with a fluid. At time t=0, the fluid begins to drain through an opening in the bottom of the tank see figure] until the tank is completely empty at t = tend- t= 0 te (0, tend) (a) At any time t, consider the maximum depth of fluid in the tank, h = h(t), and the corresponding radius of the surface of the fluid,...
1. The lateral surface area S of a cone excluding its base is given by where r is the radius of the base and h is the height. Determine the radius of a cone which has a lateral surface area 1200 m2 and a height of 20 m, by using the fixed point iteration with Start withr 17, and perform calculations in Matlab until two consec utive iterates do not differ by more than 10-8. What do you observe re...
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