42. Whatever the value of p > 0 in the equation y = x²/(4p), the y-coordinate of the centroid of the parabolic segment shown here is ỹ = (3/5)a. a y х ||

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A: Is it sen y =x

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

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Q: Find the midpoint of CD. M = (, X1+X2 _Yi+Y2 2 %3D C= (10,-1) and D = (-6,3) ([ ? ],[ ])

A: We can find the mid point of CD as below

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Q: (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from…

A:

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Q: Evaluate f (3x²y — y²)dx + (x³ - 2xy)dy, where C' is the parabola y = x²/4 from the origin to (2,1).

A: The given problem is to evaluate the given line integral of vector field over the given path C is…

Q: (IV). (10') Let u : 3 Find the coordinates of x with and x = respect to uj and u2.

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Q: Find the equation of the following function. Make sure to show your work. (Hint: try using a point…

A: Equation of the given function is in two parts. They are as given below: -∞<x≤-1 and -1≤x<∞

Q: Given y2 - 2xy = 1 a) Find y' b) Find y" and make sure your answer y" is in terms of x and y only.

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Q: Evaluate  ∫C (3y + exsinx) dx + (8x - ln(y3+2)) dy, where C is the circle x2 + y2 = 9  with positive…

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Q: Let (t) , a) Find the domain of F(t) b) Find " (t)

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Q: b) Evaluate the value of I = S(eºy − 3x) dx + (6xey + y)dy, where C' is the parabola y = C (0, 0) to…

A: The integrand is given here as         (e6y - 3x)dx + (6xe6y + y)dy        = (e6ydx + 6xe6ydy) -…