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List several characteristics that eubacteria and archaea have in common and that distinguish them from eukaryotes. 


Let F be the R²-R function defined by f(x,y)=(x-y)³.


1.determine the rate of increase in f at the point (2,1) in the direction of the vector(1,-1).then use theorem.


2.what is the rate of increase in f at (2,1) in the direction of the negative x-axis?


3.determine the maximum rate of increase in f at (2,1). In which direction is the maximum rate of increase? (read corollaries).

QUESTION 4 Find the quadratic form q(X) that corresponds to the symmetric matrix

𝐴 = [ 1 2 3 2 − 1 2 3 2 − 1] ( is 3by3 matrix)

4. a. Name a product that has a price that adjusted very frequently in the last year. Explain why.                 

b. What is the difference between monopolistic competition and oligopoly? Explain with local   examples. 




1. Write inside the first plate an example of food rich in carbohydrates that you have eaten a while ago and tell us what you feel after eating it. What did you feel after eating the food rich in carbohydrates?

2. Write inside the second plate an example of food rich in lipids that you have eaten a while ago. What did you feel after eating the food rich in lipids?

3. Write inside the third plate an example of food rich in protein that you have eaten a while ago and tell us what you feel about what you have eaten. What did you feel after eating the protein - rich food?

4. Write inside the glass the function of nucleic acids


Let F be the R²-R function defined by f(x,y)=Inxy and let r be the R-R² function defined by r(t)=(e^t;t).


1.determine the composite function F o r: (simplify your answer).


2.determine gradf (x,y) and r'(t).


3.determine the derivative function (f o r)' by


3.1.differentiating the expression obtained in (1).


3.2.using the chain rule (theorem ) compare your answer.


A researcher is interested in estimating the average monthly salary of bank managers in NCR. He wants to be 90% confident that his estimate is correct. If the standard deviation is ₱8,500, how large a sample is needed to get the desired information and to be accurate within ₱1,150?


Calculate the equation for the plane containing the lines L1 and L2,where L1 is given by the parametric equation (x,y,z)=(1,0,-1)+t(1,1,1),t€R and L2 is given by the parametric equation (x,y,z)=(2,1,0)+t(1,-1,0),t€R.

Create a program using python programming language that determines the data type of a user input variables. Declare at least 3 user input variables then print out their data types.

6.


A multiple-choice test contains 10 questions. There are four possible answers for each question. b) In


how many ways can a student answer the questions on the test if the student can leave answers


blank?

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