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Verify that the following equations are integrable and find their primitives: 1. 2(x) dx + (z-y ² + (a-x) ²]dy-y dz = 0

Verify that the following equations are integrable and find their primitives: 1. 2(x) dx + (z-y² + (a-x)²]dy-y dz = 0


Use the tetrahedron that has corner coordinates A=(1,-1,0), B=(6,1,3), C= (–3,2,0) and D=(0,6,5) and check that its centroid will be at (1,2,2).


a)A tetrahedron has 4 corners, 4 faces, 6 edges, and 12 corner angles. How many of our tetrahedron’s 12 corner angles are right angles, and which one(s)?


(b) Determine the projection of the tetrahedron onto the viewing screen when the eye is at (–6,2,2). Colour the side or sides that the viewer can see from this position.


_________ regulated the imposition and collection and distribution of levies for training purposes

Select one:

a. Employment Equity Act

b. Basic condition of employment Act

c. The Skills Development Levies Act

d. Affirmative Action


Write the following compound statements in symbols. Use the appropriate symbols and indicate the type of statement.

1. The square root of sixteen is positive four or it is negative four.

2. Two is the smallest even number and it is the only even number which is a prime

number.

3. If the ratio of two consecutive Fibonacci numbers is equal to 1.618, then the ratio

of the two consecutive Fibonacci numbers is a golden ratio.

4. A number is an even number if and only if it is divisible by two.

5. The longest distance between two points is a line and it is also considered as a

geometric figure.



Identify the following statements either simple or compound

1. The book was prepared to help administrators and teachers in implementation. 

2. If Jayson will grab the offer then, it will give him a great opportunity to grow 

professionally. 

3. The movie was great or it was fantastic. 

4. Cebu is the oldest and finest city in the Philippines. 

5. There are separate topics for Logic to be tackled on the following semesters. 



Let The National- Income Model Be: Y = C + I0 + G) C= A+B +B(Y- T0) (A ˃ 0, 0 ˂ B ˂ 1) G = Gy (0 ˂ G ˂ 1) (A) Identify The Endogenous Variables. (B) Give The Economic Meaning Of The Parameter G. (C) Find The Equilibrium National Income. (D) What Restriction On The


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5. Let the national- income model be:

Y = C + I0 + G)

C= a+b +b(Y- T0) (a ˃ 0, 0 ˂ b ˂ 1)

G = gy (0 ˂ g ˂ 1)

(a) Identify the endogenous variables.

(b) Give the economic meaning of the parameter g.

(c) Find the equilibrium national income.

(d) What restriction on the parameters is needed for a solution to exits?



In a group of 120 students, 72 of them play football, 65 play table tennis and 53 play hockey. If 35 of the students play both football and table tennis, 30 play both football and hockey, 21 play table tennis and hockey and each of them plays at least one of the three games,


a) draw a Venn diagram to illustrate this information


b) how many of the students play:


i) all the three games


ii) exactly two of the three games iii) exactly one of the three games iv) football alone


The force R is the resultant of the forces P1, P2, and P3 acting on the rectangular plate. Find P1 and P2 if 𝑅 = 40 kN and 𝑃3 = 20 kN.


this refer to the case or element which will make the statement fasle


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