This is a hard question whaich found in UKMT question test online

This is a hard question whaich found in UKMT question test online

Evaluate the following integral using any Vector Calculus method The integral with bounds C; [(4+eyz)i+(xzeyz+2yz)j+(6z2+xyeyz+y2)k] dot dr, where C is the part of...

I need some help using vectors to find the area of this parallelogram. I use three points to create two vectors with the same initial points and use a 2x2 determinant to compute the cross...

The integral with bounds C (xyzi+y4j+(2y+z8)k) dot dr, where C is the intersection of the unit cube and the plane z=x/10+y/20+1/30; Specific which method you used.

The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis...

The vector from the point (1,2, -3) to the centre of the sphere x2+y2+z2-kx+3y-lz=1 is given by < 3, h, -2 > . Then the value of hkl is?

Let us assume that every vector in S_2 is a linear combination of vectors in S_1. Question: Does that mean that S_1 and S_2 are bases for the same subspace of V? I know that the...

Consider the solid body which lies above the upper half of the cone x^2 +y^2= 3z^2 and below the sphere x^2 + y^2 + z^2 = 4z. Assume this body is of constant density. Use...

∫∫ √(4v2 + 4u2 + 1) dvdu, with limits of integration 0≤v≤1 & 0≤u≤2 *Note: the entire expression is supposed to be under the square root symbol I have tried...

triple integrals

0∫2(0∫¶/2 xsin(y)dy)dx

A person's BMI is given by I(W,H) = W/H^2, where W is the person's weight in kilograms and H is height in meters. Suppose I am 1.65 meters tall and weigh 54.5 kilograms. After a month, I become 1...

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