Math Answers

Find the general integral of the linear p.d.e

1) Px(x+y) =qy(x+y) - (x-y) (2x+2y+z)

2) x(x^2+3y^2) p - y(3x^2+y^2) q=2z(y^2-x^2)

3) (y+zx) p - (x+yz) q=x^2-y^2

Based on a​ poll, 60​% of adults believe in reincarnation. Assume that 6 adults are randomly​ selected, and find the indicated probability. What is the probability that all of the selected adults believe in​ reincarnation?

Find by double integration the area of the region in 𝑥𝑦 plane bounded by the curves 𝑦 = 𝑥

2 and

𝑦 = 4𝑥 − 𝑥

2

.

Find the average value of 𝑓(𝑥, 𝑦) = 𝑥

2𝑦 over the region 𝑅 which is a rectangle with vertices

(−1, 0), (−1, 5), (1, 5), (1, 0).

∬(𝑦 + 𝑥𝑦

−2)𝑑𝐴

𝑅

, 𝑅 = {(𝑥, 𝑦)|0 ≤ 𝑥 ≤ 2, 1 ≤ 𝑦 ≤ 2}

Given A = {x | x ∈ Z- ∧ 3x > -10}. Determine elements of A.

Let A, B and C denotes the subset of a set, S and let 𝐶̅denotes the complement of C in set S.

If (A ∩ C) = (B ∩ C) and (A ∩ 𝐶̅) = (B ∩ 𝐶̅), then prove that (A = B).

Determine the domain of each of the following functions: 1. f(x) = x + 10 6. A(x) = x2 -2 2. F(x) = 2 3 𝑥 + 5 7. H(x) = √𝑥 − 2 3. g(x) = 5 – 3x 8. K(x) = √𝑥 2 − 2 4. g(x) = 1 (𝑥+5)(𝑥−1) 9. C(x) = 2x3 + 4x2 - 2x + 1 5. b(x) = 𝑥−1 𝑥 2+5𝑥+6 10. √𝑥+1 𝑥−2 

B. Exercises: Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h 

Let f(x) = x – 3 , g(x) = 2x + 1 and h(x) = x2 – 5. Find the following 1. f ₒ g 2. f ₒ h 3. h ₒ g 4. g ₒ f 5. g ₒ h