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An observer at rest near the source of the sound with f = 784 Hz. Another source of sound with 775 Hz is moving toward the observer at 2 m/s. If the v of the sound waves in air is 340 m/s, what is the beat f heard by the observer?

Assume that 𝛼 is increasing on [𝑎, 𝑏]. Note that if 𝑓 ∈ 𝑅(𝛼) on [𝑎, 𝑏], then 𝑓





A company manufactures two products X and Y. Each product has to be processed in three departments: welding, assembly and painting. Each unit of X spends 2 hours in the welding department, 3 hours in assembly and 1 hour in painting. The corresponding times for a unit of Y are 3, 2 and 1 respectively. The man-hours available in a month are 1500 for the welding department, 1500 in assembly and 550 in painting. The contribution to profits are $100 for product X and $120 for product Y.





Formulate the appropriate linear programming problem





Solve it graphically to obtain the optimal solution for the maximum contribution

The following statements apply to natural higher unsaturated fatty acids: (select one or more) 


a. they usually contain an even number of carbon atoms 

b. are cis-isomers  

c. some representatives cannot be synthesized in the human body 

d. are broken down into separate pathways that are not related to the β-oxidation of saturated fats 

e. contain conjugated double bonds 


The Michaelis-Menten hypothesis: (select one or more) 


a. postulates the formation of an enzyme-substrate complex 

b. shows that the reaction rate depends on the substrate concentration 

c. allows to determine the pl of the enzyme 

d. shows that the rate of the chemical reaction can be independent of the substrate concentration 


The enzyme through which the pentose phosphate pathway is linked to glycolysis is: (select one) 


a. glucanase

b. xylanase

c. acetalase

d. transcarbomylase

e. transketomylase

f. metallase 



Which of the following statements is valid for the enzyme complexes of electron transport chains? (select one or more) 


a. they are integral membrane proteins localized in the inner mitochondrial membrane 

b. they cannot be isolated from each other in a functional form 

c. have similar absorption spectra of visible light 

d. interact with each other via mobile electronic carriers 


The sequence of post-synthetic mRNA changes in eukaryotes is: (select one) 


a. 5-terminal cap formation, RNA splicing, 3-terminal polyadenylation, core export 

b. RNA splicing, core export, 5-terminal cap formation, 3-terminal polyadenylation 

c. 5-terminal cap formation, 3-terminal polyadenylation, RNA splicing, core export 

d. 5-terminal cap formation, core export, 3-terminal polyadenylation, RNA splicing 

e. RNA splicing, 5-terminal cap formation, 3-terminal polyadenylation, core export 


What do glycogen breakdown and synthesis have in common? (select one or more) 


a. both processes require uridine diphosphate glucose 

b. both processes produce pyrophosphate 

c. both processes involve glucose 1-phosphate 

d. both are performed in the cytoplasmic glycogen granules 

e. the same enzyme is used to introduce branches into the chain and to remove the branches 


Which of the following reactions is unique to gluconeogenesis (select one) 

a. lactate-pyruvate 

b. oxaloacetate-phosphoenolpyruvate 

c. phosphoenolpyruvate-2-phosphoglycerate 

d. glucose-6-phosphate-fructose-6-phosphate 

e. phosphoenolpyruvate 


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