On a water ride at the amusement park, a rotating valve sprays water for 15 ft in all directions. What its the area of the circu
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You're correct, the answer is C.
Given any function of the form
, then the derivative of y with respect to x (
) is written as:
In which
is any constant, this is called the power rule for differentiation.
For this example we have
, first lets get rid of the quotient and write the expression in the form :
Now we can directly apply the rule stated at the beginning (in which
):
Note that whenever we differentiate a function, we simply "ignore" the constants (we take them out of the derivative).
Given any function of the form
In which
For this example we have
Now we can directly apply the rule stated at the beginning (in which
Note that whenever we differentiate a function, we simply "ignore" the constants (we take them out of the derivative).
We know that
<span>Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.
</span>Then
a²<span> will go with the </span>y<span> part of the equation
</span>Also, since the focus is 8 <span>units below the center, then </span><span>c = 8
</span>since the vertex is 17<span> units above, then </span><span>a = 17
</span>The equation b²<span> = a</span>²<span> – c</span>²<span> gives me
</span>b²=17²-8²-----> b²=225
the equation is
y²/a²+x²/b²=1------> y²/289+x²/225=1
the answer is
y²/289+x²/225=1
see the attached figure
<span>Since the focus and vertex are above and below each other, rather than side by side, I know that this ellipse must be taller than it is wide.
</span>Then
a²<span> will go with the </span>y<span> part of the equation
</span>Also, since the focus is 8 <span>units below the center, then </span><span>c = 8
</span>since the vertex is 17<span> units above, then </span><span>a = 17
</span>The equation b²<span> = a</span>²<span> – c</span>²<span> gives me
</span>b²=17²-8²-----> b²=225
the equation is
y²/a²+x²/b²=1------> y²/289+x²/225=1
the answer is
y²/289+x²/225=1
see the attached figure