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Consider the helix with arc-length parametrization
r(s) = αcos(αs)i + αsin(αs)j + αbsk, α - (a2 + b2)-1/2.
Show that the unit binormal vector makes a constant angle with the axis of the cylinder on which the helix lies.
In the group S3, let r = (123),s = (12),e = (1). (a) Verify that {e, r, r2, s, rs, r2s} is a complete list of elements of S3.
in a study to compare language development in hearing-impaired hi and hearing-normal hn children a researcher obtained
At a sand and gravel plant, sand is falling off a conveyor belt and onto a conical pile at the rate of 10 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude
A 52 foot building casts a shadow that is 48 feet long. At the same time, the shadow cast by a nearby statue is 18 feet long. How tall is the statue?
A tennis tournament is arranged on a straight knockout basis for 2 n players, and for each round, except the final, opponents for those still in the competition are drawn at random. The quality of the field is so even that in any match it is equal..
Find the derivative of, then do a sign graph of the first derivative, and classify the nature of any critical points... f(x)=xe^-4^x
z = x + iy f(z) = u(z) + iv(z) Given Re(f) = u A) use laplacian to find out if f can be made an analytic function, with suitable choice for v B) if the answer to A is yes, find v and f' If the answer to A is no, assume v = 0 and find where (if anywhe..
this fall the sports team were trying to raise some money for their new uniforms.they decide to sell day lillies.
If $34,000 is borrowed for 9 years at 6.75% interest, compounded annually, and then paid in full at the end of that period, how much must be paid back at that time?
Write in the language of the predicate logic with proper quanti?ers and parentheses the statement: "Some cats chase any dog
1. At what interest rate will it take $3000 to grow to $24,000 in an account that earns interest compounded monthly for 20 years? 2. Alice invests $10,000 in an account that earns 8% simple interest annually. What is the value of the account after..
Which of the following would be a valid tensor equation? You should indicate if the equation is valid; and if it is not valid, you should state why.
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