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Select the component form of the vector shown.

Posted in Mathematics

Answer:

Step-by-step explanation:

Given is a line segment BC in the graph

The coordinates of C is (4,1) and coordinates of B (-2,-2)

In vector form C = 4i+j

                        B = -2i-2j

Hence vector BC = OC-OB

= 4i+j-(-2i-2j)\= 4i+j+2i+2j\=6i+3j


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Posted in Mathematics

Perform the indicated operation. (-6)(4) 10 -10 24 -24

Answer:

-24

Step-by-step explanation:

(-6)(4)

To perform the indicated operation we multiply

When we multiply a positive number by positive number then answer is positive

negative times negative is positive

positive times negative is negative

negative times positive is negative

(-6)(4)

we multiply negative number by positive number so its negative

-6 times 4 is -24

(-6)(4)=-24

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Posted in Mathematics

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx k S is the part of the paraboloid z = 2 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has upward orientation

 Let r(x,y) = (x, y, 9 – x^2 – y^2) 

So, dr/dx x dr/dy = (2x, 2y, 1) 

So, integral(S) F * dS 
= integral(x in [0,1], y in [0,1]) (xy, y(9 – x^2 – y^2), x(9 – x^2 – y^2)) * (2x, 2y, 1) dy dx 
= integral(x in [0,1], y in [0,1]) (2x^2y + 18y^2 – 2x^2y^2 – 2y^4 + 9x – x^3 – xy^2) dy dx 
= integral(x in [0,1]) (x^2 + 6 – 2x^2/3 – 2/5 + 9x – x^3 – x/3) dx 
= integral(x in [0,1]) (28/5 + x^2/3 + 26x/3 – x^3) dx 
= 28/5 + 40/9 – 1/4 
= 1763/180 

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