10. Prove that w|+|2|="2² VWZ+ W+z +√WZ

Q: Find curl (3z i + 4x j + 9y k). curl (3z i + 4x j + 9y k) = ( i )i + ( i

A:

Q: if y = x+ v3+ 2x then prove that (3+2x2) + 2x 2y = 0 %3D dr

A:

Q: 6. Complete the square to get an equivalent expression: 7-6x – x² No integration necessary on this…

A: 6 Given expression is 7−6x−x2. We have to complete the square to get the equivalent expression…

Q: Let (x1, y1) = (7, 2) and (x2, y2) = (1, -1). Find √[(x2 - x1)2 + (y2 -y1)2]. Express the answer in…

A:

Q: Find an integer coefficient cubic that has x = 1 and x = 2+ /3 as zeros.

A: Given: The two zeros of a cubic polynomial are x=1 and x=2+3.

Q: 66. Let f(x) = ax? + bx + c (a + 0). By completing the square in x, show that 4aс - f(x) = a x + 2a…

A: Given,           Let fx=ax2+bx+c a≠0

Q: Define w := 1/2+√³,0 = -1/2 + √5, and 7 := " 1+5. Determine IQ[W,0,7](Q).

A:

Q: Show that V spans P² where V = {1 + 2t + 2t², t + t², 1 − t²}

A:

Q: 1 2 Let vị = V2 = 0 |, and w = 1 be vectors in R- 3 1 (a) Is w in {v1, V2}? (b) Is w in Span{v1,v2}?…

A:

Q: Show that Q(4 - i) = Q(1 + i), where i = √-1.

A: To show that ℚ4-i=ℚ1+i. That is we need to show that ℚ4-i⊆ℚ1+i and ℚ1+i⊆ℚ4-i. Here i=-1 that is…

Q: Suppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible…

A:

Q: 4. Solve for x : a) V5x +1 = æ + 1 b) a = V3x +7 – 3 c) V2x – 3 – Va – 2 = 1

A:

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

Q: Find d = gcd (270, 105) and hence find integers x , y such that d = 270x +105y .

A: GCD stands for greatest common divisor for two or more numbers.

Q: (x - 1) If 1 / ² ) = = √ Ada² + √ dx [ B (x − 3)(x + 7) - 3 - then A+B = Bdx x +7'

A:

Q: Prove BCスツ+)B[スかリック =B(X1y)

A:

Q: 12. Find m/R. (&x - 12) (3x + 5)

A:

Q: Find | |- •√√√√ V 5x ry sin(x² + y2) dedy

A: ∫02π3∫05π3xysinx2+y2dxdy

Q: 19 a) Edur 1+2r 1 b) (1 +25), | E dr

A: We will solve  the integration.

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: 18. Define I(a, b) = ª exp(-a²u²_b²u^²) du for a, b>0. Show that (a) 1(a, b) = a¹1(1, ab), (c) 1(a,…

A:

Q: 21. Let V1 = 1 0 -1 V2 H " V3 = 0 {V1, V2, V3} span R4? Why or why not? 1 0 0 . Does

A: