Answer:
(1) We have been given a function:
We can rewrite it using translation is:
It is the graph of translated 45 units left and 2 units down.
(2) Now,
So this is the graph of translated 5 units right and 2 units down.
(3)
So, this is the graph of translated 5 units left and 2 units down.
(4)
It is the graph of
translated 5 units left and 2 units down.
(5)
It is the graph of
translated 5 units left and 2 units down.
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,
Answer:
P = 0.018
Step-by-step explanation:
In this problem, the null and alterantive hypothesis are:
If the sample has a size of n = 40, the degrees of freedom are 40-1 = 39.
If the value of the test statistic is t = 2.463, we can look up in a t-table to find the p-value. In this test, because the mean can be bigger than 73 or smaller than 73, we have to do a two-tailed test.
For a two-tailed test for t = 2.463 and df = 39, the P-value is P = 0.018.
