A Direction Field Is Given Below $\frac { d y } { d x } = \sin x$

question 12

Multiple Choice

A direction field is given below. Which of the following represents its differential equation?

• A) \(\frac { d y } { d x } = \sin x\)
• B) \(\frac { d y } { d x } = - y\)
• C) \(\frac { d y } { d x } = y - \frac { 1 } { 2 } y ^ { 2 }\)
• D) \(\frac { d y } { d x } = x + y\)
• E) \(\frac { d y } { d x } = x ^ { 2 }\)
• F) \(\frac { d y } { d x } = 1\)
• G) \(\frac { d y } { d x } = y ^ { 2 }\)
• H) \(\frac { d y } { d x } = x ^ { 2 } + y ^ { 2 }\)

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Definitions:

Sampling Error

The difference between the characteristics of a sample and those of the population from which it was drawn, arising purely by chance.

Directional Research Hypothesis

A hypothesis that specifies the direction of the expected difference or relationship between variables, predicting how one variable will affect another.

Nondirectional Research Hypothesis

A hypothesis that predicts a relationship between variables without specifying the direction of the relationship.