b) Heron's Formula states Area = √5(5-a)(s-b)(s-c), where s = 1/(a+b+c) prove using the following steps.

Q: b) Compute Re fli) when: $(2) = √2-₁² and f(0) = -i

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Q: 2.4 Solve for x: a) In(x + 1) = 9 b) 3e - 1 =

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Q: i) (i x j).k = 2.

A:

Q: Use De Moivre's Theorem to find (-2-2√3 i)². Put your answer in standard form.

A: Step 1Complex number has two basic forms, one is rectangular form and other is polar…

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

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Q: test by using integral Solve it 2n 3n2+4 n=1

A: In this problem, we need to solve the given series by using integral test.

Q: Find w = a + bi = √z where a and b are real numbers. 13+84i W = ‚ w =

A: Step 1:Step 2:

Q: Q. : Find the squae roots of (a) 3 (b) z = 4 + 4i

A: Square root of complex number

Q: Oues: Solve:- min flx,,) = (x, - 1)*+ Cn3- 1)? Subrected to n, +22=4 X,ー-2 き6 Hint : Convert to…

A: Given that,minx1, x2fx1, x2=x1-12+x2-12Subjected tox1+x2=4x1-x2-2≥0The minimum of the given function…

Q: Please answer in typing format for like

A: Given : For two events A,B∈Ω,(i) P(B|Ac)= 0.1 (ii)P(Bc|A)= 0.8(iii)P(A)= 0.4Where Ω is the set of…

Q: Find all of the 5-th roots of the number z Show all of your working! -√3+i. ==

A: We have to find all of the 5-th roots of the numberz = -  + iWe know that, Polar Form of a Complex…

Q: 11 - d 18t7 dt dx 1 a) O 12x5 b) c) O 18x7/2 4 e) O 9x3

A: The correct option is (e).

Q: Let a and b be positive real numbers satisfying a+b=22. Find the largest possible value of…

A:

Q: 1 S dx = 3x+2 0-²(3x + 2) + C O 2√3x +2+c 3 O²(3x + 2)² + C A O√3x + 2 + c

A: The given integral is: I=∫13x+2dx  ...1   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: b? – a? x dx 9. - Proof Prove that 2 a

A: This can be proved using Fundamental theorem of calculus. The second part of the theorem is used.…

Q: gcd(a,b) = (a+b, lcm(a,b))

A:

Q: Approximate Vsin²(x) + 3dx using n=4 with each of the following: a) Right endpoints b) Left…

A: Given that f(x)=∫15sin2(x)+3dx with n =4 a) The right  Riemann sum uses the right endpoints of a…

Q: 13 14 15 17 0 6 (x + 7)²dx = 618 1107 10

A: Given query is to find statement is correct or not.

Q: (8) To evaluate f √√x²-49 x -.dx we substitute x = A)7 sec8 B) 7sine C) 7tane D) 7cose

A: We need to fin the substitution for 'x' to evaluate the integral: ∫x2-49xdx

Q: Evaluate: ₁²-du So -3 (x² y²)²7 x+y du dt

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

A: We will solve  the integration.

Q: Given that D/d = √f + p/f – p, express p in terms of f, d and D

A:

Q: Find modulus and argument of: a. (5-7i)(8+5i) b.  (√3 +i)/(√3 -i)

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Q: Show that Q(√5, √7) = {a+b√5 +c√7 + d√√35 | a, b, c, d € Q} = Q(√5 + √7).

A:

Q: 11. Prove (AUB) × C = (A x C) U (B × C)

A: 11 prove (A U B)*C = (A X C) U (B X C) here this is the property of distributive  so this is direct…

Q: 3) Find all the roots of the following equations z = √1-i 14 b) c) Z - i z = z = 964

A: a)

Q: f (3x² − 2) dx using the definition of the definite

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Q: Q/ Solve the DEs: 1-a+ykdx+(1+x*)dy = 0

A: 1-(1+y2)dx+(1+x2)dy=0

Q: If Po(xo, yo) is such that P₁Po/PoP2 = 7/6 where P₁(2,5) and P2(5,-1), find xo.

A: If P0x0, y0 is such that P1P0P0P2=76, where P1=2, 5, and, P2=5, -1.To find x0.

Q: Q: Using De Movier's Theorem find all roots of of (−√3 + i)¹/²

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Q: (3) I= √(1-x²) ³² 203 x dx

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Q: Use the formula d = √² +²2-2r₁ r₂ cos (0₂-0₁) to find the distance 3π between 4, 4 and 8, T

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Q: b. Find the roots of √√√64 e¹.4i

A: