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Solve the following exercises using the law of cosines and the law of sines In a triangle we have the lengths a)80 and b)50 and the angle C)50. What is the length of c and the angle of the resulting vector?

Question 1 (10 points) Develop the following practical case, applying the General Business Accounting Plan: Make accounting entries at the three-digit level: Case 1 01/02 Merchandise is purchased for 50,000 soles plus VAT, the merchandise is entered and paid in cash.

Describe how you would prepare 1.0 L of a 0.10 M solution of acetic acid from 2.0 M solution of acetic acid

x : 15 = 30 : 9

A public transport bus leaves the terminal with 2/7 of its seats empty. When it reaches the first stop, 3/5 of the bus's capacity gets on and 1/4 gets off. At the next stop, 1/3 of the bus' total seating capacity gets off. Finally, at the third stop, 3/6 get on and 1/8 get off. Are there any seats left on the bus? What fraction of the passengers must travel standing?

Derive the functions: f(x)= (3x^1/2 + 7x)^4/5

3grams of solute in 100mL of solvent equals what percent (w/v)

given the vectors u = (-1,10,6) and v = (11,-4,3) calculate -2u+4v

It is estimated that 0.60% of households in a neighborhood in the capital are in favor of installing new surveillance for greater security. If 25 households are randomly selected and asked for their opinion, What is the probability that at least 10 are in favor of the new surveillance service, given that the problem fits a normal approximation to the binomial? Round the mean and deviation to two digits. Write your final answer using 4 decimal places.

If the line D: x = 1 is the directrix of the parabola p: y raised to the power of 2 - kx + 8 = 0, then one of the values of k can be: