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
Answer:
14.40 dollars
Step-by-step explanation:
72 divided in 5
Answer:
8 units If the area of the squares are 32 units^2, we have that: Area = Side * Side Side^2 = 32 Side = sqrt(32) = 5.657 units So as the squares are adjacent to two sides of the triangle, we have that the triangle has two sides of 5.657 units As it is a right triangle, we can use the Pythagoras' theorem: c^2 = a^2 + b^2 c^2 = 5.657^2 + 5.657^2 c^2 = 64 c = 8 units
Step-by-step explanation:
Answer:
Step-by-step explanation:
The given figure is parallelogram becasue their opposite sides are equal.
68+45+30+x=180 degree (sum of adjacent sides of a parallelogram are equal)
143 +x=180
x=180-143
x=37 degree
y=45 degree
Answer:
6
Step-by-step explanation:
so 6 times 10 equals 60, 60 times 6 is 360 so there you go
