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Let f be a smooth function. Calculate the curvature and the torsion of the curve that is the intersection of x = y and z = f(x).
Calculate T ; N; B; "\\kappa" ; "\\tau" of the curve x(t) = (t; t 2 ; t 4) at the point (1; 1; 1).
3.10 If U, V are ideals of R, let U + V = {u + v | u ∈ U, v ∈ V }.
Prove that U + V is also an ideal.
3.9 Show that the commutative ring D is an integral domain if
and only if for a, b, c ∈ D with a #= 0 the relation ab = ac implies that
b = c.
3.8 D is an integral domain and D is of finite characteristic,
prove that the characteristic of D is a prime number.
3.7 If D is an integral domain and if na = 0 for some a #= 0 in
D and some integer n #= 0, prove that D is of finite characteristic.
3.6 If F is a field, prove that its only ideals are (0) and F itself.
3.5 If U is an ideal of R and 1 ∈ U, prove that U = R.
Prompt the user to enter the number of employee wages to be calculated. The program will end when the data for all the employees has been entered.
For each employee, indicate if the employee is salaried or paid hourly
- If the employee is salaried, enter the annual salary. The gross for that employee will be determined by dividing the annual salary by 24. Add the result to the total salaried wage.
-If the employee is paid hourly, enter hours worked (40 ≥ hours ≥ 0) and rate per hour. The gross for that employee is determined by multiplying hours worked by rate per hour. Add the result to the total hourly wages.
-After performing the calculations for each employee, display the total wages for salaried employees, total wages for hourly employees, and total gross wages.
A lot consists of 10 good articles, 4 with minor defects and 2 with major defects. i. One article is chosen at random. Find the probability that (a) It has no defects, (b) It has no major defects, (c) It is either good or has major defects. ii. Two articles are chosen (without replacement), Find the probability that (a) Both are good (b) Both have major defects (c) At least one is good (d) at most one is good (e) Exactly one is good (f) Neither has major defects
#340153 on Dec 2023