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I'm confused as to how to go about answering #2 and #3, and I'm not confident in my approach to #1. Help!
Let G be the set of the fifth roots of unity.
1. Use de Moivre's formula to verify that the fifth roots of unity form a group under complex multiplication, showing all work.
2. Prove that G is isomorphic to Z5 Let F be a field. Let S and T be subfields of F.
3. Use the definitions of a field and a subfield to prove that S ∩ T is a field, showing all work.
The natural length of a spring is 10 cm. A force of 25 N stretches it to a length of 20cm. How much work, in units of N-cm, is done in stretching it from a length of 10cm to a length of 15cm?
A company's records indicate that on any given day, 1% of their day shift employees and 2% of the night shift employees will miss work. Sixty percent of the employees work the day shift.
Construct a diagram to plot the positions and directions of both runners. Use trigonometry to find coordinates of points where buddy changes his direction.
a hundred squash balls are tested by dropping from a height of 100 inches and measuring the height of the bounce. a
A cylinder is inscribed in a right circular cone of height 3.5 and radius (at the base) equal to 2.5. What are the dimensions of such a cylinder which has maximum volume?
find the 90%coinfidence interval for the variance and standard deviation for the time it takes an inspector to check a bus for the safety if a sample of 27 buses ha standard deviation of 6.8 minutes. Assume the variable is nornmally distributed.
the length and width of the base of a rectangular prism are 5.5 cm and 3 cm. The height of the prism is 6.75 cm. Find the exact value of the surface area of the prism, in square centimeters.
The car can be ordered in any one of seven exterior colors. How many different cars can be ordered?
In a mass production of bolts it is found that 5% are defective. Bolts are selected at random and put into packet of 10.
question points b and c are on a circle with radius 5 and lines ab and ac are tangent to the circle. let d be a point
Demostrate that your result gives the obviously correct answer for the limiting case.
how to find volume of a cone in cubic units when the radius is 5 and height is 11
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