Provide an appropriate response.
-x = 7u cos 10v, y = 7u sin 10v, z = 3w
A) 2100u
B) 1470u
C) 2100v
D) 1470v

Question

Quizplus · Accepted Answer

The given equation represents a parametric equation for a 3D space curve. The parameter u represents the magnitude of the curve in the xy-plane and the parameter v represents the angle of inclination from the positive x-axis. The parameter w represents the magnitude of the curve in the z-direction. As there is no reference to w in the answer choices, we can only focus on u and v.

To find the magnitude of the curve in the xy-plane, we use the Pythagorean theorem:

magnitude in xy-plane = sqrt((x^2)+(y^2))
= sqrt((7u*cos(10v))^2 + (7u*sin(10v))^2)
= sqrt(49u^2) 
= 7u

Therefore, we need to find the value of 7u, which is only provided in choice B. Choice A is incorrect as it represents the product of u and z, which is not relevant in this context. Choices C and D are incorrect as they represent the product of v and 7u, which is also not relevant in this context.

Provide an Appropriate Response