Other Math Answers

A 2kg box is pulled up by a force P which is acting parallel to the plane at a constant velocity of 3

m

s

. The length of the

plane is 4m and the top of the plane is 2m above the floor. Determine the pulling force P and the work done by

the same force. Use μk = 0.3

4. Which of the following biconditionals are equivalences?

a. She is his wife, if and only if he is her husband.

b. She is his mother, if and only if he is her son.

c. A is the mother of B, if and only if B is a son of A.

d. A is the father of B, if and only if B is a son of A.

e.A necessary and sufficient condition that the two triangles be similar, is that two angles of one be respectively congruent to two angles of the other.

f. A necessary and sufficient condition that two quadrilaterals be similar is that the four angles of one be respectively congruent to the four angles of the other.

1.Let a and b be real numbers and let p, q, and r denote the following sentences:

p = (a – x < b – x); q = (a < b); r = (a/x<b/x). Indicate whether each of the following compound sentences yields a true or false statement (A) when x = 2; (B) when x = -2.

a.p ↔ q

b. p ↔ r

c. r → p

d. p →r

e.q ↔ r

f. q → p

g. r → q

h. q →r

What can you say about each of the above expressions a – h when x = 0?

2. Which of the above sentences in No. 1 become implications and which of them become equivalences, if the admissible values for x are:

a. all positive real numbers?

b.All negative real numbers?

c.All real numbers?

3.Prove the following equivalences.

a.(p → q) <=> (~p V q)

b. ~(p ↔ q) <=> (p V q)

c.(p → q) <=> (~q → ~p)

d. [(q Λ r) V p] <=> [(p V q) Λ (p V r)]

write down the degree of fn =f↓n-1 +f↓n-2. f0 = 0, F1= 1

Hanna has taken an annuity of €140,000 to buy a new home, but she needs a loan. The term of the loan has been agreed for 12 years and the annual interest rate on the loan is set at 1,8 %. The loan is shortened monthly.

a) how big is the annuity of the loan?

b) how much of the loan is left after three years?

c) How Much Does Hanna pay in interest in total?

The recipe for mint chocolate ice cream requires 2&1/2 cups of cream for 10 people. You need ice cream for 16 people.how much cream will you need?

1. Help learners to solve the problem using diagrams to illustrate the above ratio.

2.discuss three possible challenges that learners may face when solving this problem.

3.how would you help learners overcome the challenges. Use drawings to illustrate your answer.

(PvQ)n~(PvQ)