Calculate the compound interest.
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The value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)
<h3>What is integration?</h3>It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.
The parametric equations for the line segment from (0, 0, 0) to (2, 3, 4)
x(t) = (1-t)0 + t×2 = 2t
y(t) = (1-t)0 + t×3 = 3t
z(t) = (1-t)0 + t×4 = 4t
Finding its derivative;
x'(t) = 2
y'(t) = 3
z'(t) = 4
The line integral is given by:
After solving the integration over the limit 0 to 1, we will get;
or
= 73037.99 ≈ 73038
Thus, the value of line integral is, 73038 if the c is the given curve. C xeyz ds, c is the line segment from (0, 0, 0) to (2, 3, 4)
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Answer:
.
Step-by-step explanation:
Since repetition isn't allowed, there would be choices for the first donut,
choices for the second donut, and
choices for the third donut. If the order in which donuts are placed in the bag matters, there would be
unique ways to choose a bag of these donuts.
In practice, donuts in the bag are mixed, and the ordering of donuts doesn't matter. The same way of counting would then count every possible mix of three donuts type times.
For example, if a bag includes donut of type ,
, and
, the count
would include the following
arrangements:
.
.
.
.
.
.
Thus, when the order of donuts in the bag doesn't matter, it would be necessary to divide the count by
to find the actual number of donut combinations:
.
Using combinatorics notations, the answer to this question is the same as the number of ways to choose an unordered set of objects from a set of
distinct objects:
.