Question

Suppose vector F= (3x^2y) i unit + (5xy - 3z^2) j unit + (4x^2y) k unit .Evaluate
integration (dell cross vector F)* n unit vector differentiate S ,
whew S is the surface of the sphere (x^2 + y^2 + z^2 =7) ,above xy-axis plane.

Suppose vector F=(y^2 cos x+ z^3) unit i - (4- 2ysinx ) j unit + (2+ 3xz^2 ) k unit. Find the scalar potential and also determine the work done in moving an object in this field from (1,2,3 ) to (5,10,9 )

Suppose x= (2t+1)/(t-1) ,y= (t^2)/(t-1) , z=(t+2). Determine the unit tangent ,the principal normal, curvature , radius of curvature, the binormal , torsion , radius of torsion

Answer 1

Answer:

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Step-by-step explanation:

(i) If x = 2 is one root of the equation (k – 3)x2 –

kx – 8 = 0, find the value of k. Also, find the

other root of the equation.

(ii) If x = 4 is one root of (k + 2)x2 – (5k + 2)x – 4

= 0, find the value of k. Also, find the other

root of the equation.

Find value of k.

2x

2

+kx−5=0 & x

2

−3x−4=0

→x

2

−3x−4=0

x

2

−4x+x−4=0

x(x−4)+1(x−4)=0

(x+1)(x−4)=0

x=−1 and x=4

→ one root is common

∴2(−1)

2

+k(−1)−5=0

∴2−k−5=0

∴k=−3

Or

2(4)

2

+k(4)−5=0

∴32+4k−5=0

∴k=

4

−27