Let w(s,t)=f(u(s,t),v(s,t)) where u(1,0)=−6,∂u∂s(1,0)=5,∂u∂1(1,0)=7 v(1,0)=−8,∂v∂s(1,0)=−8,∂v∂t(1,0)=6 ∂f∂u(−6,−8)=−1,∂f∂v(−6,−8
Blababa [14]

From the given set of conditions, it's likely that you are asked to find the values of

and

at the point

.
By the chain rule, the partial derivative with respect to

is

and so at the point

, we have


Similarly, the partial derivative with respect to

would be found via

Step-by-step explanation:
3.60
A rotation is a rigid transformation, sometimes called an isometric transformation, that moves every point of the pre-image through an angle of rotation about the center of rotation to create an image. Rotations preserve size, rotations of 360 map a figure to itself, and lines connecting the center of rotation to the pre-image and the corresponding point on the image have equal length.
Answer:
<em>a)</em><em> The mean time for handling a customer complaint under the new process using 95% confidence level is between 25.0 min. and 27.5 min. </em>
<em>b) </em><em>there is no substantial evidence</em><em> </em><em>(in 95% confidence level) that the new process has reduced the mean time to handle a customer complaint.</em>
<em>c) </em><em>The population about which inferences from these data can be made is the people following the new implemented plan when handling customer complaints.</em>
Step-by-step explanation:
the random sample of the response times of 50 customers who had complaints has
size=50
mean≈26.218
standard deviation ≈4.42
a. Confidence interval can be estimated using the formula:
M±
where
- M is the sample mean (26.22)
- z is the corresponding z-score for the 95% confidence interval (1.96)
- s is the sample standard deviation (4.42)
- N is the sample size (50)
When we put the numbers in the formula, mean time for handling a customer complain under the new process using 95% confidence interval is:
26.22±
≈ 26.22±1.225 i.e. between 25 and 27.45
b<em>. </em>According to the customer complaint data for the past 2 years, the mean time for handling a customer complaint was 27 minutes. After the plan, estimated mean time for handling customer complaint is between <em>25.0 min. and 27.5 min. with 95% confidence. </em>Since 27 min. is within this interval, we can conclude that there is no substantial evidence (in 95% confidence level) that the new process has reduced the mean time to handle a customer complaint.
c. The population about which inferences from these data can be made is the people following the new implemented plan when handling customer complaints.
|x| = |78| = 78
so x = 78
and
|y| = |-13| = 13
so y = 13
Answer is C. |x| = 78 and |y| = 13