4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1. (a) [BB] n³ + 2n is divisible by 3. (b) n³ + (n + 1)³ + (n + 2)3 is divisible by 9. (c) [BB] 5" - 1 is divisible by 4. (d) 8"-3" is divisible by 5. (e) 52n - 25n is divisible by 7. [BB] 10+1 + 10 + 1 is divisible by 3. (g) n³ +5n is divisible by 6. (h) on I 2n 5n is divisible by 6

Q: w + 4 w + 10 6. 8.

A:

Q: Find the Rank of B 2. 2 B= 24 2

A: According to question,Given matrix,B = 212243212

Q: 3 A C 3 9 D X B

A:

Q: 4x e 3x

A: I = ∫4x e−3x dx

Q: -7.4v+2.4(-7.1v+-10)+6.7

A: simplified value is -24.44 v - 17.3

Q: e-4x

A:

Q: A- 3 D B 9

A: In the given figure we have to determine the value of y.

Q: Answer g

A:

Q: w + (-7), when w = - 1

A: The expression is given by w+(-7) To evaluate: The value of the expression when w=-1.

Q: 1 2e10 - 3 da e5z

A:

Q: 5x+9 e

A: We need to evaluate the following integral I = ∫e5x+9dx                           ........1 Formula…

Q: k-2=10

A: Given equation is k-2=10 We have to find the value of k. Add both sides 2 and further simplify it…

Q: Which of the following is the graph of the placewise function f(x) for x≤0 for x>0

A: Sol:- Some information about above function :- Domain of  -e-x:x≤ 0, x2+x-6x2+2x-3:x>0 :…

Q: stock b 1.3,   -3.5,   -5.4 ,   6.3,  -7.6,  9.2 find IQR

A: 1.3,   -3.5,   -5.4 ,   6.3,  -7.6,  9.2Sample of size(n)=6

Q: 4j - 8 = 12 + 9j

A: