Answer:
Option c. 11,488.21 cm3
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
we know that
The volume of the sphere is equal to
we have
---> the radius is half the diameter
substitute
Answer:
The answer is F: 108
Step-by-step explanation:
144 - 108 = 36
108 ÷ 3 = 36
The slope is -3/4
Step-by-step explanation:
You figure this out by using the Rise/Run method.
The rise is how many units up (+) or how many units down (-) the points are away from each other, and rise is how many units to the left or right the points are away from each other.
Since the line is going at a downward angle, we can tell that the slope will be a negative slope. We can see that the 2nd point is 3 units down from the first, and the 2nd point is 4 units to the right of the first one. With this information, we can figure out that the slope is -3/4
It looks like the vector field is
<em>F</em><em>(x, y)</em> = 3<em>x</em> ^(2/3) <em>i</em> + <em>e</em> ^(<em>y</em>/5) <em>j</em>
<em></em>
Find a scalar function <em>f</em> such that grad <em>f</em> = <em>F</em> :
∂<em>f</em>/∂<em>x</em> = 3<em>x</em> ^(2/3) => <em>f(x, y)</em> = 9/5 <em>x</em> ^(5/3) + <em>g(y)</em>
=> ∂<em>f</em>/∂<em>y</em> = <em>e</em> ^(<em>y</em>/5) = d<em>g</em>/d<em>y</em> => <em>g(y)</em> = 5<em>e</em> ^(<em>y</em>/5) + <em>K</em>
=> <em>f(x, y)</em> = 9/5 <em>x</em> ^(5/3) + 5<em>e</em> ^(<em>y</em>/5) + <em>K</em>
(where <em>K</em> is an arbitrary constant)
By the fundamental theorem, the integral of <em>F</em> over the given path is
∫<em>c</em> <em>F</em> • d<em>r</em> = <em>f</em> (0, 1) - <em>f</em> (1, 0) = 5<em>e</em> ^(1/5) - 34/5
Always believe in yourself and don’t doubt yourself