5 [In this question i and jare horizontal unit vectors due east and due north respectively] A particle of mass 1.75 kg is at rest when it is acted on by three forces, F₁, F₂ and F3, where F₁ = (7i - 2j) N, F₂ = (mi+j) N and F3 = (3i+2mj) N and m is a constant. The particle begins to move on a bearing of 135º. (a) Find the value of m. (b) Show that the magnitude of the acceleration of the particle is 4√2 ms².

Q: Use the union rule to answer. If n(A) = 6, n(B) = 11 and n(An B) = 5, what is n(A U B)? n(A U B) =

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Q: | (1– 2r)dr

A: Given:∫01(1-2x)dx = ∫011dx- ∫012xdx                     ∫fx±gxdx=∫fxdx±∫gxdx…

Q: Lind Domin ond Ronge ? FlxJ=5+X り= メー9

A: f(x) = 5+x/ x2-9 Set the denominator in 5+x/ x2-9 equal to 0 to find where the expression is…

Q: (2c) Prove or disprove the following statement: “ A UBCANB for any A and B "

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Q: Let A = {1}, B = {2}, and C = {3}. (a) Explain why A x B B x A. (b) Explain why (A x B) × C # A × (B…

A: Cartesian product: The cartesian product of the sets A and B is defined as the set of all the…

Q: If n(A ∪ B) = 96 and n(A) = n(B) = 67, find n(A ∩ B).

A:

Q: Show that if a < c< b, then fave (a, b) = () fave l(a, c) + C - a | favg [c, b]

A: Solution...

Q: Show that

A: Our Aim is to Prove that:-111abca2b2c2=a-bb-cc-a   -(i)

Q: Prove: If a|b and b|c, then a|c. Hint: Use the definition of divisibility.

A: Prove: If a|b and b|c, then a|c.

Q: danx fonthebougast Awiwnitean quakin yo bomx+ fthe Camve Le Secx 19-

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Q: p(a)= 0.7 p(b)=0.2 and A and B are mutually exclusive, find p(A and B)

A: Given that  p(A)=0.7 , p(B)=0.2

Q: THE EVALUATE メLt X11 e 3.

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Q: If n(A) = 106, n(A ∪ B) = 141, and n(A ∩ B) = 46, find n(B).

A:

Q: Is that a < or a c?

A: It is a less than symbol "&lt;" . Kindly find the clear solution of that problem here.

Q: Prove: If = ¿ (where a, b, c, and d are nonzero), b then d*

A: Given:               ab=cd  (where a,b,c  and d are non zero.)

Q: Prove or disprove: if a, b, c e N, then a2 - 6 + 4c + 2.

A: a2-b2≠4c+2 we have to prove this relation in three cases like a&lt;b,a&gt;b and a=b

Q: 1 (b) (r² + m)²

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Q: Find, if possible, (a) AB and (b) BA.

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Q: If n(A) = 40, n(B) = 22, and n(A ∩ B) = 4, find n(A ∪ B).

A: topic - sets

Q: If n(A) = 41, n(B) = 15, and n(A ∩ B) = 2, find n(A ∪ B).

A: We will use the following n(A U B) = n(A) + n(B) - n(A ∩ B)

Q: Suppose P(E) = 0.74, P(F) = 0.4, and P(E´∩F) = 0.49. Find P(E´∪F). Note the complement symbols.…

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Q: If n(A) = 44, n(B) = 23, and n(A ∩ B) = 8, find n(A ∪ B).

A: Explanation of the solution is given below...

Q: If n(A ∪ B) = 99 and n(A) = n(B) = 69, find n(A ∩ B).

A: Given, n(A ∪ B) = 99 and n(A) = n(B) = 69   The objective is to find  n(A ∩ B).

Q: (21)8=... Select one: (10010)2 a. b. (1001)2 (10001)2 C.

A: Here convert the number (21)8, into base 2 number.

Q: If A={1,2} and B={a,b,c}, find: I. A*B II. P(B) III. n(P(A))

A: A={1,2} B={a,b,c} A*B={(1,a),(1,b),(1,c),(2,a),(2,b),(2,c)}     2)P(B)={…

Q: If n(A) = 46, n(B) = 19, and n(A ∩ B) = 5, find n(A ∪ B).

A: Using , n(A u B) = n(A) + n(B) - n(A intersection B),

Q: If n(A) = 45, n(B) = 18, and n(A ∩ B) = 7, find n(A ∪ B).

A: Given that  n(A) = 45, n(B) = 18, and n(A ∩ B) = 7. We find n(A ∪ B).

Q: Determine: 1 (1 -1 2] [2 3] +0 1

A: given  1-124-1023+1001-1-1 solution we will use property of matrix multiplication and addition to…

Q: Evaluate |5(z – 4)Vz2 – 8z dz

A: Here I am attaching image so that you understand each and every step.

Q: a. |15| b. |15| +4 c. 3- | 17| d. |12|+|12|

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Q: If a|b, then a|(bc). Direct proof.

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Q: "x is in A"  and "x is in B"

A: " x is in A intersection B" is same as " x is in A" and " x is in B".  For "x is in A union B" is…

Q: Show khat the glosp brjections frem f5 faom f5 whan f rafiell iisomaphi- with

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Q: Q.4) Evaluate 10! с. 8p5 а. 6!- 3! b. 4!(10–4 )! d. 9с7 С1

A: There are several powerful methods for counting objects and sets of objects without actually having…

Q: If A n CCB n C and AnCcBnC, then show that ASB.

A: Introduction :

Q: Let R = {(a, b), (b, a), (a, c), (c, d), (d, a)} a. Is (a, c) E R³? b. Is (a, a) E R²? c. Is (c, c)…

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Q: n

A: