Answer:
L and M - None of these
L and N - Skew
M and N - Perpendicular
Step-by-step explanation:
Get the derivative:
<em>y</em> = (9 - <em>x</em>²)¹ʹ³
d<em>y</em>/d<em>x</em> = 1/3 (9 - <em>x</em>²)⁻²ʹ³ d/d<em>x</em> [9 - <em>x</em>²]
d<em>y</em>/d<em>x</em> = 1/3 (9 - <em>x</em>²)⁻²ʹ³ (-2<em>x</em>)
d<em>y</em>/d<em>x</em> = -2/3 <em>x</em> (9 - <em>x</em>²)⁻²ʹ³
Evaluate it at <em>x</em> = 1 :
d<em>y</em>/d<em>x</em> (1) = -2/3 • 8⁻²ʹ³
Since 8 = 2³, we have
8⁻²ʹ³ = 1 / 8²ʹ³ = 1 / (2³)²ʹ³ = 1 / 2² = 1/4
Then the tangent line has equation
<em>y</em> - 2 = 1/4 (<em>x</em> - 1) → <em>y</em> = 1/4 <em>x</em> + 7/4
When a scatter plot shows a positive association means that there is a linear correlation with a positive slope between the two variables. This correlation can be weaker or stronger (depending on the value of the correlation).
If there is a linear correlation between the two variables, the relation is then a direct proportionality (with slope positive or negative).
Hence, it is always true that <span>a scatter plot that shows a positive association suggests that the relationship is proportional.</span>
<h3>
Answers: </h3><h3>
A) satellites</h3><h3>D) Weather balloons</h3><h3>E) Automated weather stations</h3>
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Explanation:
Satellites are used to measure things like the formation of storms and predicting where they will go. They provide a big picture of the climate as a whole, and they're useful for studying climate patterns.
Weather balloons are used to measure humidity, wind speed, temperature and pressure in the atmosphere. They are useful because they are very inexpensive compared to satellites, and can be made quicker.
Automated weather stations are locations where much of the same things are measured with weather balloons, though on the ground rather high in the air. In addition, weather stations will likely have a rain gauge to measure how much rain has fallen in a certain area.
