Let w = (x + 2y + 3z) dx A dy + (cos(x) + sin(y) + e²)dy ^ dz. (a) Write dw as f(x, y, z) dx A dy A dz in rectangular coordinates. (b) Write dw as h(p, 6,0) dp ^ do A do in spherical coordinates.

Q: 3. Solve the initial value problem for a 2 x 2 system of linear ODEs for r(t) and y(t): (3 = Use the…

A: In this question we will solve the given equation by using elimination method.

Q: Which indicates the derivatives of parametric equations? *

A: Solution: Option D Derivatives of a Parametric function:  x = g(t) and y = f(t)  dxdt= g'(t), dydt=…

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A:

Q: Find torsion of the motion r(t) = . Leave your answer correct to two decimal places.

A:

Q: Find dy/dx and d^2y/dx^2.

A: Given

Q: osen y

A: Is it sen y =x

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A: Recall: Equation of line: y-y1=mx-x1 ; where m=dydx or  y2-y1x2-x1 Length of the curve…

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A:

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A: To find the sum of the coordinates Y+X of a point D. Given that    Y(m) X(m) N11 2004.32…

Q: What is the formula for the derivative for dy/dx for a polar curve r=f(theta)?

A: Given that

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A:

Q: dy (ii) Find dx? for the parametric equations x = t+ sin t, y= 1+cost

A: • This problem can be solved by using Chain rule as explained in step 2.

Q: Let Uj and U2 be vector subspaces of a vector space V over the real numbers. Suppose that V1, V2, V3…

A: We shall answer first question only as you’ve asked more than one question. For others kindly post…