Answer:
A) The graph of g(x) is shrunk vertically by a factor of 1/9
Step-by-step explanation:
The given graph g(x) = 1/9√x
f(x) = √x
The altitude of g(x) = 1/9
The altitude of f(X) = 1
When comparing the graph of g(x) with f(x), the graph of g(x) shrunk by 1/9 because of the altitude.
Here with I have attached the graph.
Therefore, answer: A) The graph of g(x) is shrunk vertically by a factor of 1/9
Thank you.
Answer: 3312q^2 - 9093q + 5914
Step-by-step-explanation:
The formula for volume of the cone is pi times r square time h/3
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
3/20 = 1.5/10 = 15/100
Hope this helps!
