7 = (–9,6, –1) ≤ R³

Q: Q4. Use Pascal's triangle to expand (3 + x)°.

A:

Q: Let x be a real number. Which of the following is the same as P(Z x) c) P(Z ≤ -x) d. none of the…

A:

Q: Consider 2x° – 3y? = 8 -

A: SolutionStep I :  2x3 - 3y2 = 8Now, 2x3-3y2=8⇒2x3-8 = 3y2ddx2x3-8 = ddx3y26x2 =…

Q: Show that Sn is solvable when n ≤ 4.

A: We see that S1  is the trivial group {e} and it is solvable.   We see that , |S2| = 2 so it is…

Q: How many individual simple functions make up the following composite input? 2 1 5 6 A) 4 в) 5 c) 6…

A:

Q: Show that Sn is solvable when n ≤ 4.

A: Given: Sn. We have to show that Sn is solvable when n≤4.

Q: Ex(30) and fYx show that of - Ix Exlz0)& Lekf:Xy be fIxYbe be it is

A: Introduction: The function f(g(x)) or (f ∘g) represents the combination of functions f(x) and g(x),…

Q: . Let a, b € Z so that 4a + 5b is a multiple of 13. Prove that 13 divides 9a + 8b.

A: We have to show that 13 divides 9a+8b To prove this we using 4a+5b divisible by 13

Q: Ex. Show that [b, c) ~ [a, o), where a, b, c ER and b< c. [H7-9]

A:

Q: Suppose s and t are distinct natural numbers. Show that lcm(s, t) + lcm(s+1, t+1) > 2st/(sqr(|s −…

A: Given: s and t are distinct natural numbersTo prove: lcm(s, t)+lcm(s+1, t+1)&gt;2sts-t

Q: need to find the formula

A:

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

A:

Q: R² = gen gen

A: see below the reason

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: To show that the group &lt;a, b | a^5 = b^2 = e, ba = a^2b&gt; is isomorphic to Z2, we need to…

Q: Show that is isomorphic to Z2.

A:

Q: Suppose the multiplication cx is defined to produce (cx1, 0) instead of (cx1, cx2 ). With the usual…

A: The multiplication cx where x∈ℝ2 is defined as cx=cx1, 0 because x=x1, x2 where x1 and x2 belong to…

Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

A:

Q: = (-10,6, –4) be in R and a be in R. Then , 36 , Let x ат — ).

A:

Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: 9. Which of the following is one of the possible answers when you integrate the expression 2csc² x?…

A:

Q: Find the length of (3et − 3, 4et + 7) for 0 ≤ t ≤ 1

A: To find the length

Q: 8. A (5+, 10-) where A-Z 9. Ax [5+, 10-] where A = Z' 10. Ax=(1, 10) where A = (0,1)

A: These are the problems from the Set Theory.

Q: Deduce from Q2 that if an integer N can be written as N = x² + ny² , and if a prime number q | N can…

A: We will use standard division algorithms to deduce the given statement.

Q: リ ー上 5, Use the inverse imatirice s tofind and (24) 22 3 ミ 3. 3. 3 -2

A:

Q: Find the 11th pair of x and y where x<0 and y<0 in 53x-81y=-126

A:

Q: Find the product of x and y if x, 3/2, 6/7, y  are in G.P

A:

Q: Show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

A: We have to show that &lt;a, b | a5 = b2 = e, ba = a2b&gt; is isomorphic to Z2.

Q: For -3-3: (a) Find the modulus and argument of z. (b) Express + in the form of a+ib where a,beR.

A: This is a problem related to complex number. Based on the general concept and formula used for…

Q: Which of the following are difference sets? (ii) {0, 1, 3, 5} in Z13,

A:

Q: Let Z, = {0,1,2,3,4, 5,6} where each x € Z, is a least residue when an integer is divided by 7. %3D…

A:

Q: -5² + 3(¯5)² 50 O -50 O 49 O -49

A:

Q: l, tet that 17/2n+3m e integed, prouve iff, 17/9n +5 m and m be

A: Properties used: Property 1. If x divides y, then x divides ky and vice versa. x|y⇔x|ky Property 2.…