In (R, t,), if A = { :n E N}, then 3+n I(А) —

Q: 10 of 17 If y(t)+(t-r)y(r)dr=t, then y(t)= Su-nyndr3Dt,

A: Convolution Theorem: The Laplace Transform of the convolution of f(t) and g(t) is:…

Q: 23. Given that 4sinh - 2coshx = Ae*+ Be* then A and B are respectively А. 1,-3 C. -1,-3 В. -1,3 D.…

A: Topic- trigonometry

Q: then 7(1 - а)М? + 6(1 - а) Мт %3D ВM?, 7(1 - а)т? + 6(1 — а)Мт %3D Вт?, Subtracting we obtain Y(1 –…

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Q: Show that for A symmetric inf. = Amin(A).

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Q: 11. If a = y2 and b = y, and -1sys3, then what is the largest possible difference between a and b?…

A: Please refer the attached image for complete solution.

Q: 2. Using OLS or any other suitable method, Prove that E(ß1) = B1 E(ßo) = Bo

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Q: If =x+3y-z,=4xyz, w=22 -xy evabuate d(u, v,w)/ (, 2). at (1-,0).

A: We have to first find all partial derivatives.

Q: - (m'n') m²n_> 14. (2xy)²(-3x²)(4) 15. (2ryz?)°(x²z}*, 21 im2, n (m35 m2).(nein (2)(x3(35 (2 243…

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Q: D. Show that if a, = 3n³ - 17n² + 2n - 6, then an O(n³).

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Q: 2 Evaluate: :S,vte-t² dt.

A: Detailed explanation mentioned below

Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

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Q: 28x+4y+kz -10 -5x-8y-4z = -2 e must have, k +|

A: The given system of equation is: - 6x + 4y + 7z = 3 28x + 4y  + kz = -10 - 5x - 8y - 4z = -2

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: In GL(2, Z,3), det 4. O 35 11

A: Third option is correct.

Q: {2, 3} CA implies that 2 E A and 3 e A. Select one: O True False

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Q: R(z) = In(6z +e²)

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Q: Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same as

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Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

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Q: It x~N(μ,σ"), then ²~. Option 2 ption 1 *** *** *** N(0, 1) G(1⁄2,2) x² (2)

A: Given, if x~Nμ,σ2 Then x-μσ2

Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: 4. ( Give a case in which |(x, y) |xlly|l.

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Q: 5. Show that b, is always positive, by establishing the equation (Qn-1,Qn-1) (Qn-2,Qn-2) b,

A: We will apply the properties of inner-product to prove the given statement.

Q: Suppose X,~ Uniform(0, 2) and X, ~ Uniform(0, X,). Find E[2X,+X,].

A: Given,X1 ~U(0,2)X2 ~U(0,X1)E(X1)=2+02=1E(X2)=X1+02=X12

Q: 1 Evaluate [ (x² + --- e2x +c 2 a) + In x+ b) 3 +C 3 e2x .3 c) + In x- d) + In x - 3 +c +c 2 2

A: We know  (1) integration of Xn dx =  Xn+1 / (n+1)  + C  (2) integration of emx dx = emx / m + C  (3)…

Q: Qa. If Fes) = T , fined fcts %3D -2)-५) -৪)

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Q: 2. alak S 6sin"xcox dx

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Q: D. Show that if an 3n3 - 17n2 + 2n - 6, then a, = O(n³).

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Q: Show that 1/3  Tn +  2/3 Mn  = S 2n

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Q: Then, we assume that Wn+1 - H Wn - l kn+1 kin 1 2 E Wn-p Wn-p p=0 p=1 (6) n+1 - € Zn - € Vn+1 = 1 Vn…

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Q: 3-Evaluate S Fdr where 2X Cisgiven by rT) = C 3+U-3t)jrék

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Q: in(Zg++s)indeyclic grauf2enerated by I, Z,3

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Q: 6. Show that =+ E-(-1)"(n+ 1) E)". when Iz – 2| < 2.

A: Seriese expansion

Q: 3. Consider A={m,a,t,h}; C={x:x=3n,1sns4,neN}; B={s,t,e,m} ; D={x:x=2n,15n S6,nEN} What is ANB?

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Q: 1, Y2, · · , Y9 and it is believed that Y; ~ N(u, 16). Find P(|Y – µl < 2). ...

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Q: 12)List the first five berms of Ehe regence a,=6, aan= 5a -4 as=3 a=? asz?

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Q: 3. fualende Zdv, where, E- (nyE):0くn<l,o<y<1-n,oくまく1-1-

A: We have to evaluate the triple integral ∭E z dV where E is the region containing the set of points…

Q: (8) If w = 5x² + 2y², x= -3s+t, and y = s – 4t. Find and Əw as

A: The objective is to find the partial derivatives .

Q: 3sin4t dt 2. 5(1- 3cos21)

A: We have to find integral

Q: solve jhe Bemoulli diffarantil by let hing V= ; 3.

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Q: In(2 + x – 2y2 – 3z), 7 =, then If f(x, y, z) Duf (2,-1, 1) = - A) 11

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Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

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Q: mTQ mOR U 44 mTS T. 25 S. MSOR MRQT %3D

A: Topic:- geometry

Q: Suppose X~N(113,18), and Z~N(0,1). Then x = 94, is equivalent to z = ______.

A: Given that, Suppose X~N(113,18), and Z~N(0,1). Here, mean μ=113 and standard deviation σ=18

Q: What is the best substitution to make to evaluate S O u = 3x Ou = e³x u=1+e³x Ou = e-3x e³x 1+e³x dx…

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Q: Find y' in y = (x³ 3x²(x²+e) x³ +3 A. y' = B. y' = C. y' = +3)(x²+e) +7x6 In (2³ + 3) +7x6 (x³ + 3)…

A: Understanding of derivative when function is there in power of any function.

Q: Then, we assume that Wn+1 - H Wn - u kin+1 kn 1 2 E Wn-p E Wn-p p=0 p=1 (6) Zn+1 - € Zn - E Vn+1 Vn…

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Q: When u × v = 0 and u ∙ v = 0, what can you conclude about u and v?

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Q: . Prove that, e²i = e²1=22. ez2

A: Let,z1=x1+iy1z2=x2+iy2z1-z2=x1+iy1-x2+iy2=x1+iy1-x2-iy2z1-z2=x1-x2+iy1-y2…

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.