1 In AABC, AB = xcm, BC=(4- x)cm, ZBAC=y and ZBCA = 30°. Given that siny show that =D4(v2-1) (5 marks) x

Q: that Find flz)= r°cos20 + ir?sin po Such %3D is analytic-

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Q: Let ŕ ). ) - (0**) k (4 Sin 2+) + (4 cos 2 t, be the Position oF Perticle space in at time. Finc the…

A: The velocity is dr/dt and the acceleration is d2r/dt2

Q: The value of 6 dz,where C:|z|= counterclockwise, is sinh(z+2) 7-4 O a. O b. 27isinh(3) sinh(3) O d.…

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Q: Find the length of the astroid x = cos3 t, y = sin3 t, 0 ≤ t ≤ 2π.

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Q: Two waves travelling in the same directio are given by: y1 = 0.2 sin(2ttx-20t+0) and

A: Given,  two waves travilling in the direction are                     y1=0.2sin(2πx-20t+φ)…

Q: find area Inside the oval limaçon r = 4 + 2 cos 0 Inside the cardioid r Inside one leaf of the…

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Q: Obtain the following Laplace ti 1) L{cos3t + 5e-t} 2) L{e¬3t (2t² – 5t + 1)} 3) L{sin7t – cosh3t} -

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Q: 2. Find the point on the curve r(t) = (12 sin t, -12 cos t, 5t) at a distance 137 units along the…

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Q: Find the coordinates at t = 0, π/4 , π of a particle moving along the path c(t) = (cos 2t,sin2 t).

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Q: 25. Find x, y, e R from 2coshy - 7sinhx = 3 and coshy – 3 sinh? = 2 %3D %3D

A: Find x and y.

Q: 1₁ -1.2 - St 0 √x sin ex dx

A: Given :   I1=∫01.2xsinex3dx

Q: -똥, V5 with s in quadrant Il and let sin(t) 4 8) Let cos(s) = -, with t in quadrant III. Determine…

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Q: 31. If an electrostatic field E acts on a liquid or a gaseous polar dielectric, the net dipole…

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Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

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Q: ди k > 0 at Ans. u = e'(A,eka! cosh ax + Bjekai sinh œx) u = e¯'(A2e' u = e"(Azx + B3) k ¯kai 'cos…

A: The given problem is to find the solution for the given partial differential equation in different…

Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

Q: 4 .Using n=8 approximate the value of cos(1+Vx )dx using 0. (a) the Midpoint Rule, (b) the Trapezoid…

A: Formula used: Midpoint rule- The interval [a,b] into n subintervals of equal width,…

Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: aw Q:3) Find ду if w 2u' v+ In(5v) , u=x+y & v=e"siny

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Q: S₁ + Sa cos²0 de 01/2000 sin ²0 de csc ³0 de + Sc 01/se sec ³0 de The integral dx (x²+4)² can be…

A: We have to solve above integral

Q: 8.432 5) Setup and find the arclength of y=º from 6 15x54 using trapezoidal rule n=6. Give the final…

A: We have to find out the arc length

Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

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Q: Which of the following gives the arc length of the parabola 2y = x² - 13xS1 Hint: Use Trigonometric…

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Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

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Q: Evaluate. d [arctan a – In ¤] dæ 1 1+#? 1 sec2 x sec² ¤ 1-x²

A: As we know that: The sum rule: f±g'=f'±g' The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1…

Q: Find the length of the hypocycloid defined by the equations x = a cos° (0), y = a sin° (0), 0 < 0 <…

A: Here we have to find the length of the hypocycloid defined by the equation x=acos3(θ) , y=asin3(θ)

Q: Determine the speed (in meters per second) of a particle with a trajectory (3 sin (3t), 8 cos (3t)),…

A: We have to find dsdtt0=π4

Q: a. The velocity of a car in meters per seconds travelled from its origin is given by v(t) = In (t2 +…

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Q: (a) , f(r cos 0,r sin 0 )rdrde

A: Answer and explanation is given below

Q: Express the circular function cos+sin as a single cosine with a phase displacement T Rcos (+a) where…

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Q: 2. In 00, AE is tangent to OO at E, mZBCF =112 and mBE :mDE = 3:7. Find: (а) тBЕ (b) mZA E A В (c)…

A: Circle

Q: Sinex dx is a) Conv. to o 6) diverge b) cont. to 프 auou (P

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Q: d the area of the surface generated by revolving the curve x =cos (2t), y = 7+ sin ( 2° - xis. .....…

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Q: Show that the function e cosy ti Siny) is an andlytic Runction 2 W= Sin Z Q2. Determine whe ther…

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Q: 3. If y = w sin w, then what is dy/dw??

A: y=wsinwTo find d2ydw2

Q: 4.2. Calculate the arc length of the cardioid given by r = a(1 – cos 0) -

A: The cardioid is symmetrical in nature and ranges from θ=0 to θ=π as a half figure. We can also…

Q: a. Show that If z = x+ iy where y 1 b. Evaluate: cosh?(-z) – sinh²(z)

A: Given that z =x+iy For a part , y&lt;0 and we need to prove that | eiz | &gt;1 For b part, we need…

Q: Find the length of one arch of the cycloid = 5(t-sin(t)),y- 5(1-cos(t)).

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Q: Suppose r(t) = cos(nt) i + sin(at) j + 5tk represents the position of a particle on a helix, where z…

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Q: (b) If u =x cosy+ ye», where x=s+2 and y= st, prove that 2- ds du - (s - 21) (* siny-xye -e").

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: Find the motion of the mass-spring system in Fig. 72 with mass 0.125 kg, damping 0, spring constant…

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Q: 1. Use Green's Theorem to evaluate [(3ye* -7 sin (3x*))dx + (5x* +2x*y* +8e*-y* )dy, where C is the…

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Q: 22. Find the value of arcsine ( 2x + y ) given that TT sin-( 4x + 3y ) = 2 cos ( x + y ) = . TT and…

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Q: 2- Find the solution on the exterior of a sphere of radius a 1 or (r F) + Sin e 0 (sin 0) = 3u, u…

A: Given: ∂∂rr2∂u∂r+1sinθ∂∂θsinθ∂u∂θ=3u⇒r2∂2u∂r2+2r∂u∂r+1sinθsinθ∂2u∂θ2+cosθ∂u∂θ=3u…

Q: Find the area. a. Inside one leaf of the three-leaved rose = cos30 b. Shared by the circle r=2 and…

A: Given that a) r=cos(3theta) b) r=2 and r= 2 (1 +sin(theta)) c) r=-3cos and r=1-cos( theta) We have…

Q: (1) Find the area of the hypocycloid F (t) = (cos³ (t), sin® (t)), te [0, 27].

A: Given The given hypocycloid is r¯=cos3t,sin3t, t∈0,2π. Apply formula A=∫D∫dA=∫Cx dy+0 dx=∫Cx dy

Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

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