Answer:i think maybe big but I actually don’t know because i don’t know who that is
Step-by-step explanation:
You can parameterize the curve
and compute the integral along each component curve, or you can use the fact that
is the continuous gradient of a function
and observe that the line integral is path independent.
In other words, there is a function
such that
, so the integral along any curve
from the points
to
is simply
You have
, and so
while
where
is an arbitrary constant. So we've found that
which means the line integral has a value of
The lowest number is 3.
3 x 588 = 1,764
1,764 = (42) squared
I don't know an easy way to do it. I just slogged through it one-by-one ...
I tried 2 , then I tried 3 and I didn't have to go any farther.
You could have done the same thing. The difference between us is that
I'm willing to work on it just for fun, whereas you're not willing to work on it
even for homework. That's why I became good in math and you might not.
<h3>Given:</h3>
<h3>Volume of the hemisphere:</h3>
<h3>Volume of the cylinder:</h3>
<h3>Total volume:</h3>
<u>Hence</u><u>,</u><u> </u><u>the</u><u> </u><u>volume</u><u> </u><u>of</u><u> </u><u>the</u><u> </u><u>given</u><u> </u><u>compound</u><u> </u><u>shape</u><u> </u><u>is</u><u> </u><u>35.34</u><u> </u><u>cubic</u><u> </u><u>centimeters</u><u>.</u>
The parametric equations for x and y describe a circle of radius 10 m, so the length of the base of the fence is the length of the circumference of a circle of radius 10 m. The formula for that circumference (C) is ...
... C = 2πr
... C = 2π·(10 m) = 20π m
The height as a function of angle (t) is found by substituting for x and y.
... h(t) = h(x(t), y(t)) = 4 + 0.01·((10cos(t))²-)10sin(t))²) = 4+cos(2t)
The average value of this over the range 0 ≤ t ≤ 2π is 4, since the cosine function has two full cycles in that range, and its average value over a cycle is zero.
Thus, the area of one side of the fence is that of a rectangle 20π m long and 4 m wide. That will be
... (20π m)·(4 m) = 80π m²
The amount of paint required to cover both sides of the fence is
... 2×(80π m²)×(1 L)/(10 m²) = 16π L ≈ 50.3 L
_____
You can work out the integral for area as a function of t. When you do, you will find it gives this same result.