Find the length of the curve r(t) = 4ti+1j+ b) O d) 632 15 1264 15 1264 5 2558 15 2528 15 + k from t = 1 to t = 5.

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: Evaluate F. dr along the line segment C from P to Q. F = -8xi+y j; P(-2,0), Q(7,0) F• dr =

A:

Q: Q2/ Find the distance between the Line 2x - 2y + 1 = 0 & 3z + 2y = 4 to the Z-axis.

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Q: Find the length of the curve x = - (5 + 4t), y= 1- t, z= - (4+ 2t), for 3 <t < 5. length = (Think of…

A: Find the length of the given curve.

Q: Find the distance between two points (1, 2) and (3, −1).

A: We want to find the distance between the given two points. We use formula for finding the distance…

Q: Calculate the length of PQ where P = (-2,1,6) and Q = (-3,4, –1).

A: We will find the length of PQ→ in the following step

Q: Find the points on the graph of z = xy³ + 8y-¹ where the tangent plane is parallel to 8x + 5y + 8z =…

A: The given curvez=xy3+8y-1Let F(x,y,z)=xy3+8y-1-z∇F(x,y,z)=(y3,3xy2-8y2,-1)Hence, the gradient at…

Q: Describe the traces of the curve x2 + 9z2 = 9 in the vertical planes (those parallel to the…

A: The traces of a surface are the cross-sections created when the surface intersects a plane parallel…