Simplify each expression.
1 answer:
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Answer:
<h2>Diana uses 5/8 square yard of fabric for both pillows.</h2><h2>There remains 3/8 square yard of fabric.</h2>Step-by-step explanation:
Givens
- The total amount of fabric is 1 square yard.
- One pillow requires 3/8 square yard of fabric.
- A second pillow requires 2/8 square yard of fabric.
To find the total amount of fabric Diana used, we must sum those fractions
Diana uses 5/8 square yard of fabric for both pillows.
Now, we subtract to find the remaining amount of fabric
Therefore, there remains 3/8 square yard of fabric.
Answer:
0
Step-by-step explanation:
We want to compute the curve integral (or line integral)
where the force field F is defined by
F(x,y) = (y, -x)
and C is the path consisting of the line segment from (1, 5) to (0, 0) followed by the line segment from (0, 0) to (0, 9).
We can write
C =
where
= line segment from (1, 5) to (0, 0)
= line segment from (0, 0) to (0, 9)
so,
Given 2 points P, Q in the plane, we can parameterize the line segment joining P and Q with
<em>r(t) = tQ + (1-t)P for 0 ≤ t ≤ 1 </em>
Hence can be parameterized as
for 0 ≤ t ≤ 1
and can be parameterized as
for 0 ≤ t ≤ 1
The derivatives are
and
In consequence,
