Write as a product: x2+y2+2xy

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]

$w(s,t)=f(u(s,t),v(s,t))$

From the given set of conditions, it's likely that you are asked to find the values of $\dfrac{\partial w}{\partial s}$ and $\dfrac{\partial w}{\partial t}$ at the point $(s,t)=(1,0)$ .

By the chain rule, the partial derivative with respect to $s$ is

$\dfrac{\partial w}{\partial s}=\dfrac{\partial f}{\partial u}\dfrac{\partial u}{\partial s}+\dfrac{\partial f}{\partial v}\dfrac{\partial v}{\partial s}$

and so at the point $(1,0)$ , we have

$\dfrac{\partial w}{\partial s}\bigg|_{(s,t)=(1,0)}=\dfrac{\partial f}{\partial 
u}\bigg|_{(u,v)=(-6,-8)}\dfrac{\partial u}{\partial s}\bigg|_{(s,t)=(1,0)}+\dfrac{\partial f}{\partial 
v}\bigg|_{(u,v)=(-6,-8)}\dfrac{\partial v}{\partial s}\bigg|_{(s,t)=(1,0)}$
$\dfrac{\partial w}{\partial s}\bigg|_{(s,t)=(1,0)}=(-1)(5)+(2)(-8)=-21$

Similarly, the partial derivative with respect to $t$ would be found via

$\dfrac{\partial w}{\partial t}\bigg|_{(s,t)=(1,0)}=\dfrac{\partial f}{\partial 
u}\bigg|_{(u,v)=(-6,-8)}\dfrac{\partial u}{\partial t}\bigg|_{(s,t)=(1,0)}+\dfrac{\partial f}{\partial 
v}\bigg|_{(u,v)=(-6,-8)}\dfrac{\partial v}{\partial t}\bigg|_{(s,t)=(1,0)}$
$\dfrac{\partial w}{\partial t}\bigg|_{(s,t)=(1,0)}=(-1)(7)+(2)(6)=5$

6 0

4 years ago

What is my GPA if I have 2 b’s and 3 a’s??

alexandr402 [8]

Step-by-step explanation:

3.60

8 0

3 years ago

Read 2 more answers

Describe the general properties of rotations. Include a discussion of the properties of rigid transformations, and line segments

liraira [26]

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.

3 0

4 years ago

Read 2 more answers

A Internet provider has implemented a new process for handling customer complaints. Based on a review of customer complaint data

sergey [27]

Answer:

a) 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.

b) 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.

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± $\frac{z*s}{\sqrt{N} }$ 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± $\frac{1.96*4.42}{\sqrt{50} }$ ≈ 26.22±1.225 i.e. between 25 and 27.45

b. 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 25.0 min. and 27.5 min. with 95% confidence. 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.

5 0

3 years ago

Given the number x=78 and y=-13 which statement is true

rjkz [21]

|x| = |78| = 78

so x = 78

and

|y| = |-13| = 13

so y = 13

Answer is C. |x| = 78 and |y| = 13

4 0

4 years ago

Read 2 more answers

Write as a product: x2+y2+2xy –1