What is the angle between the unit vector answer to question 3 and the x-axis. Give your answer to the nearest integer degree. 125 120 150 O 130

Q: Compute the work done by the force 7 = (sin(x + y), xy, x²z) in moving an object along the…

A: Given force The object is moving along the straight line and from

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where…

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Q: Find the tangent plane to the equation z = z = 3x² + y² + 4y at the point (1, 0, 3)

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Q: Without finding T and N, write the acceleration of the motion a(t) to the position vector r(t) =…

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Q: A) Link between plane and line in the differentiation. 7) Find the aquations of alono pocinh the…

A: Link between line and plane.

Q: i If (a,ß), a<0 is the unit vector that is parallel to the tangent line to the curve y=-1x²-x at the…

A: The equation of the given curve is            y = -x2 - x        =&gt; dy/dx = -2x - 1 So, slope of…

Q: 8) Find a unit vector in the direction that f(x, y, z)=2x² +6xz²-yz³ increases most rapidly at the…

A: Given: A function fx , y , z=2x2+6xz2-yz3. To Find: Unit vector in the direction of the given…

Q: Sketch the direction field of the DE y'=2x+y.  (Plot 9 or more points) Then sketch approximate…

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Q: Find one normal vector of the tangent plane to f(x, y) = cos(x² +y²) at point P(1,1, cos 2).

A: As we know the expression of the normal vector to the tangent plane at a point on the curve can be…

Q: 2² Find wheref=x² + In(x²). dx² (*) Ⓒ*) O (*+)

A: As per the guidelines we are supposed to answer only one question at a time. If you want answers of…

Q: What are the coordinates of V'

A: For Triangle ∆TUV, the coordinates at point T is (-7,-6) at point U is (-8,3)  and at point V is…

Q: Find the second derivative of the vector-valued function r(t) = (7t + 5 sin(t))i + (4t + 5 cos(t))j…

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Q: 5. What are the coordinates of the JNBS if J'(-2, 4), N'(3, 5), B'(2, 3), and S'(0, 2) after R(90".…

A: Given: J'(-2,4) , N'(3,5), B'(2,3) and S'(0,2)

Q: Find the unit vectors that are parallel to the tangent of the polynomial y= x^3 +2x + 1 at the point…

A: Consider the given function and differentiate to get the slope of the tangent.

Q: (3) This problem will walk you through the steps of finding a directional derivative through the…

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Q: You will find the directional derivative of z(x, y) = 5 sin (4 x y), in the direction (3,-3) at the…

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Q: Find unit vector tangent and normals to the are y=1/2 X3+1/2. Point(1,1)

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Q: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,

Q: Let x' = (1, 1, 3) and y' = (-2, 0, -2). calculate the angle between x and y

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Q: In R', evaluate the alternating 2-form 5 = -3 · dx ^ dy on the pair of vectors (a, b) If %3D a = (4,…

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Q: Eveluake F.dv wlere flaiy,z) where the segnent on Cis (-',2,0) to (3,0,1)

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Q: 2 ( y' V(4-y') (4-у?)3

A: To evaluate : I=∫02y34-y23dy I=∫02y24-y23ydy Let 4-y2 = t ⇒-2ydy =dt ⇒ydy =dt-2 Now for, y=0, t=4…

Q: Find all points on the curve r(t) = ti + t^2 j + t^3k where its tangent line is parallel to the…

A: The curve is represented by the vector function r(t)=ti+t2j+t3k .To find the points on the curve…

Q: What is E’ when this figure is rotated 180°? H. -1 ) (-4, –5) ) (4, –5) D (4, 5) О(6, -4)

A: topic- rotation