if fis a differentiable function of rand g(x,y) = f(xy), show that
Answers
g(x, y) = f(xy) is a differentiable function.
We'll show that g(x, y) = f(xy) is a differentiable function by finding its partial derivatives with respect to x and y.
Given that f is a differentiable function of r, we know that f'(r) exists for all values of r. Now, let's find the partial derivatives of g(x, y) with respect to x and y:
1. ∂g/∂x:
Using the chain rule, we get ∂g/∂x = (∂f/∂r) * (∂r/∂x). Since r = xy, ∂r/∂x = y. Thus, ∂g/∂x = f'(xy) * y.
2. ∂g/∂y:
Similarly, we get ∂g/∂y = (∂f/∂r) * (∂r/∂y). Since r = xy, ∂r/∂y = x. Thus, ∂g/∂y = f'(xy) * x.
Since both partial derivatives ∂g/∂x and ∂g/∂y exist, we can conclude that g(x, y) = f(xy) is a differentiable function.
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Related Questions
What is the mode how do you find the mode
Answers
In statics the mode is the data/value that occurs most often.
Now, we have the next set of data:
-7 -6 -6 -6 -7
The number -6 occurs 3 times and the number -7 occurs twice.
Therefore, the mode is given by the number -6.
Answer: -6
Mode: The most frequent number
Step-by-step explanation:
-6 is the most frequently used number
Solve |y-2|<10
please
Answers
Y=(-8, 12)
Wouldnt the answer be anything above 12? Because if Y is unknown, and you're taking 2 away from it, and it still has to be greater than 10, then it should be anything above 12. Unless it's saying that the number is greater than 10, and you are just taking away 2 from a number and it doesn't have to be greater than 10.
in a certain town, 40% of the eligible voters prefer candidate a, 10% prefer candidate b, and the remaining 50% have no preference. you randomly sample 10 eligible voters. what is the probability that 4 will prefer candidate a, 1 will prefer candidate b, and the remaining 5 will have no preference?
Answers
The probability that 4 prefers A, 1 prefer B and 5 will have no preference = 0.0024
Here, in a certain town, 40% of the eligible voters prefer candidate a,
⇒ P(A) = 40%
⇒ P(A) = 0.4
10% prefer candidate b,
⇒ P(B) = 10%
⇒ P(B) = 0.1
and the remaining 50% have no preference.
⇒ P(T) = 50%
⇒ P(T) = 0.5
Also, the sample size = 10
So, the probability that 4 prefers A, 1 prefer B and 5 will have no preference would be:
P = ⁵C₄ (0.4)⁴ × ⁶C₁ (0.1) × (0.5)⁵
P = 0.0024
Therefore, the required probability is 0.0024
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Please solve fast for thumbs up.
2. Analyze the given process \[ G_{p}(s)=\frac{5 e^{-3 s}}{8 s+1} \] Construct Simulink model in MALAB for PID controller tuning using IMC tuning rule. Show the output of this model for Ramp input. (S
Answers
To construct a Simulink model in MATLAB for PID controller tuning using the IMC (Internal Model Control) tuning rule, we can follow these steps:
1. Open MATLAB and launch the Simulink environment.
2. Create a new Simulink model.
3. Add the following blocks to the model:
- Ramp Input block: This block generates a ramp signal as the input to the system.
- Transfer Function block: This block represents the process transfer function \(G_p(s)\). Set the numerator to \(5e^{-3s}\) and the denominator to \(8s+1\).
- PID Controller block: This block represents the PID controller. Connect its input to the output of the Transfer Function block.
- Scope block: This block is used to visualize the output of the model.
4. Connect the blocks as follows:
- Connect the output of the Ramp Input block to the input of the Transfer Function block.
- Connect the output of the Transfer Function block to the input of the PID Controller block.
- Connect the output of the PID Controller block to the input of the Scope block.
5. Configure the parameters of the PID Controller block using the IMC tuning rule:
- Set the Proportional Gain (\(K_p\)) based on the desired closed-loop response.
- Calculate the Integrator Time Constant (\(T_i\)) and set it accordingly.
- Calculate the Derivative Time Constant (\(T_d\)) and set it accordingly.
6. Run the simulation and observe the output response on the Scope block.
The output of the model will show the system's response to the ramp input, indicating how well the controller is able to track the desired ramp signal.
The IMC tuning rule provides a systematic approach to determine these parameters, taking into account the process dynamics and desired closed-loop response.
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find the area of the region enclosed by one loop of the curve. r = sin(4θ)
Answers
π/16 is the area enclosed by the curve r= sin(4θ)
The given curve is polar curve and hence the area of the polar curve is given by:
Let A be the area of the curve so,
A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\)
where a and b is the boundary at which r=0
so after equation r=0
sin(4θ) =0
=> sin(4θ) =0
=> 4θ = 0,π
=> θ = 0, π/4
so a=0 , b= π/4
now
A = \(\int\limits^b_a {\frac{1}{2}r^2 } \, d\theta\) ------(i)
so \(r^2\) = (sin(4θ))^2
=> \(sin^2\)( 4θ )
ans we know that
cos(2α) = 1 - \(2sin^2\)2 α
so \(sin^2\)= (1- cos(8θ) )/2
putting the value of r in the equation (i) we get :-
A = \(\int\limits^b_a {\frac{1}{4} *(1-cos8\theta) } \, d\theta\)
=> 1/4* \(\int\limits^b_a {(1-cos8\theta) } \, d\theta\)
here a=0 and b=π/4
after putting the value and solving the integral
A = π/16
so A is the area enclosed by r=sin(4θ) is π/16
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Sally has 10 pounds she wants to buy 28 cans of soda which cost 28p each does she have enough money
Answers
Answer:
Yes, Sally has enough money to buy 28 cans of soda.
Step-by-step explanation:
Yes, because £10 = 1000p
1000p / 28p = 35 cans
35 cans < 28 cans
So Sally has enough money for 28 cans.
Look at image for the question:
Answers
Answer: 2/7
Step-by-step explanation: 8 people with a dog/28 total people
8/28=4/14=2/7
I need help.................
Answers
Answer:
-33 and -21
Step-by-step explanation:
-36, -33, -30, -27, -24, -21, -18
-36
-36 + 3 = -33
-33 + 3 = -30
-30 + 3 = -27
-27 + 3 = -24
-24 + 3 = -21
-21 + 3 = -18
f(4) =
If g(x) = 2, x =
Answers
Sososos
Step-by-step explanation:
for security purposes a jewelry company prints a hidden watermark on the logo of its official documents. the watermark is a chord located 0.7 centimeter from the center of a circular ring that has a radius measuring 2.5 centimeters. what is the length of the chord?
Answers
The chord length is approximately 1.397 centimeters where 0.7 centimeters is the separation from the center of the circle to the chord.
We can use the properties of circles to find the angle formed by the chord at the center of the circle to evaluate the length of the chord.
0.7 centimeters is the separation from the center of the circle to the chord. This remove is additionally the stature of the isosceles triangle shaped by the chord and the two radii of the circle.
Let θ be the angle between the chord and the center of the circle. You can use trigonometry to find θ.
sin(θ/2) = 0.7/2.5
\(θ/2 = sin⁻¹(0.7/2.5)\)
θ/2 = 0.2793
θ=2×0.2793
θ ≈ 0.5586 radians
Now that we know θ, we can use the formula for the chord length of a circle.
chord length = 2 × radius × sin(θ/2)
Chord Length = 2 × 2.5 × sin(0.2793)
String length ≈ 1.397 cm
Therefore, the chord length is approximately 1.397 centimeters.
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in studies of gay men and women who have identical twins, researchers found that of the identical twins were also gay. a. 48 percent b. 22 percent c. 52 percent d. 11 percent
Answers
22Answer:
Step-by-step explanation:
Studies of gay men and women who have identical twins have found that approximately 48 percent of the identical twins were also gay. Option (a)
This statistic suggests that there is a strong genetic component to sexual orientation. However, it is important to note that sexual orientation is complex and influenced by a variety of factors beyond genetics, including environmental, social, and cultural factors.
Additionally, not all identical twins share the same sexual orientation, which suggests that genetic factors are not the only determinants of sexual orientation. Overall, research suggests that sexual orientation is a complex and multifaceted aspect of human behavior that is influenced by a range of factors.
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Vertical angles are always adjacent. True False
Answers
Answer:
False
Step-by-step explanation:
Vertical angles are not always adjacent, but they are always congruent.
Hope that helps!
Answer:
False
Step-by-step explanation:
Hope it will help you*
a researcher is conducting an experiment comparing how sleep affects student grades. three different groups are being compared, group 1 sleeps between 2-4 hrs per night, group 2 sleeps between 5-7 hrs per night and group 3 gets over 8 hrs of sleep per night. should the researcher conduct a series of t-tests comparing each group or should one anova be conducted to compare the groups? why?
Answers
One ANOVA must be used to compare the groups as there are more than 2 groups and each group has many data values.
The t test, analysis of variance (ANOVA), and covariance analyses are statistical methods used in the testing of the hypothesis for the comparison of means between the groups (ANCOVA).
The Person's t test is used to compare means between two groups, while an ANOVA is used to compare means among three or more groups. In an ANOVA, first is given a shared P value. For at least one pair where the average difference is statistically significant, the ANOVA test yields a significant P value. To identify the crucial pair, we do several comparisons . Two-way ANOVA employs two category independent variables, whereas one-way ANOVA uses simply one categorized independent variable. when there is at least one predictor variableSimilar to other tests, the null hypothesis and the alternative hypothesis are both categories of hypotheses. The alternative hypothesis suggests that there is a statistically significant difference between the means, in contrast to the null hypothesis, which asserts that there is no statistically significant difference in the means.To learn more about ANOVA visit:
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Csecond chance! Review your workings and see if you can correct your mistake.
A straight line passes through the points (2, 15) and (6, 39).
What is the y-intercept of the line?
Give your answer as an integer or as a fraction in its simplest form.
Watch video
Answer >
Answers
The y-intercept of the line is 3.
What is y-intercept?The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.The point where a graph contacts the y-axis is known as the y intercept. Any point on the y-axis has an x-coordinate of 0, as is known. Therefore, a y-x-coordinate intercept's is 0.\(slope(m) = \frac{y_{2} -y_{1} }{x_{2}- x_{1} } \\=\frac{39-15}{6-2} \\=\frac{24}{6} =6\)
\(point-slope form \\= y-y_{1} =m(x-x_{1} )\\\\\\y-15=6(x-2)\\y-15=6x-12\\y=6x-12+15\\y=6x+3\)
Therefore, The y-intercept of the line is 3.
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What is 2 divided by 3? Explain the steps pleas.
Answers
The value of 2 divided by 3 is 0.67
How to evaluate the quotient expression?From the question, we have the following parameters that can be used in our computation:
2 divided by 3
To start with, we need to represent the expression properly as a quotient
So, we have the following representation
2 divided by 3 = 2/3
Evaluate the quotient expression using a calculator
This gives
2 divided by 3 = 0.67
Hence, the solution to 2 divided by 3 is 0.67
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A car travels along the highway to Denver at a steady speed. When it begins, it is 300 miles from Denver. After 3 hours, it is 180 miles from Denver. Which function describes the car's distance from Denver?
Answers
Answer:
A, y = -40x+300
Step-by-step explanation:
y=180
x=3
180=-40(3)+300
180=300-120
A policy analyst would like to predict salary from a set of four predictor variables for a sample of 45 athletic trainers. A multiple linear regression analysis was conducted. Complete the following ANOVA summary table for the test of significance of the overall regression model. Except for the P-value, report all answers accurate to 3 decimal places; report the P-value accurate to 4 decimal places. Use a significance level of α=0.05.
Source SS df MS F P-value
Regression 20
Residual 400
TOTAL
What is your decision for the hypothesis test?
Reject the null hypothesis, H0:β1=β2=...=β4=0
Fail to reject H0
What is your final conclusion?
The evidence supports the claim that one or more of the regression coefficients is non-zero
The evidence supports the claim that all of the regression coefficients are zero
There is insufficient evidence to support the claim that at least one of the regression coefficients is non-zero
There is insufficient evidence to support the claim that all of the regression coefficients are equal to zero
Answers
To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.
From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.
Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.
Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:
df for regression = k - 1 = 4 - 1 = 3
df for residual = n - k = 45 - 4 = 41
Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.
MS for regression = SS for regression / df for regression = 20 / 3
MS for residual = SS for residual / df for residual = 400 / 41
Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.
F = (MS for regression) / (MS for residual)
Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.
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what number is lower -162 or 159
Answers
Answer:
-162
Step-by-step explanation:
Answer:
-162
Step-by-step explanation:
because -162 is negative
A report by Gallup Poll showed that the proportion of Americans that fear public speaking is.5000. A student believes that the proportion of students at her school that fear public speaking is less than.5000. She randomly surveys 400 schoolmates and finds that 125 fear public speaking. Conduct a hypothesis test at the 5% level to determine if the proportion at her school is less than.5000. What is the test statistic accurate to 2 decimal places? z = 7.50 O t = 7.50 O z = -7.50 O t = -7.50 None of the above
Answers
The significance level is 0.05.
There is evidence to suggest that the proportion of students at the school who fear public speaking is less than 0.5000.
Test statistic is -6.94 accurate to two decimal places.
What method is used to calculate significance level and test statistic?We can use a one-tailed hypothesis test with the following null and alternative hypotheses:
Null hypothesis: The proportion of students at the school who fear public speaking is equal to or greater than 0.5000.
Alternative hypothesis: The proportion of students at the school who fear public speaking is less than 0.5000.
The significance level is 0.05.
To conduct the test, we need to find the test statistic and compare it to the critical value.
First, we calculate the sample proportion of students who fear public speaking:
p⁻ = 125/400 = 0.3125
Next, we calculate the standard error of the sample proportion:
SE = sqrt[p⁻(1 - p⁻) / n] = sqrt[0.3125(1 - 0.3125) / 400] = 0.027
Then, we calculate the test statistic:
z = (p⁻ - p) / SE = (0.3125 - 0.5000) / 0.027 = -6.944
Since the alternative hypothesis is that the proportion of students who fear public speaking is less than 0.5000, we use a one-tailed test and look up the critical value for a 5% level of significance in the standard normal distribution table. The critical value is -1.645.
Since the calculated test statistic (-6.944) is less than the critical value (-1.645), we reject the null hypothesis.
Therefore, we can conclude that there is evidence to suggest that the proportion of students at the school who fear public speaking is less than 0.5000.
The test statistic is -6.94 accurate to two decimal places.
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Which side lengths form a right triangle?
Answers
Answer:
a is the answer
hope this will help you
Help plzz I will mark brainliestttt
Answers
Answer:
A
Step-by-step explanation:
Answer:
B. 8 in
Step-by-step explanation:
What value for x will make the equation −3x+1=2(4x−5)true?
Answers
Help me please , I’ll mark brainliest
Answers
Answer:
42 feet squared
Step-by-step explanation:
What is the value of x?
Answers
Answer:
the value of x=69 ft approx.
Answer:
\(\Large \boxed{\sf 69.02 \ ft}\)
Step-by-step explanation:
Solve for w using Pythagorean Theorem
\(\displaystyle w=\sqrt{77^2-22^2} =33\sqrt{5}\)
Solve for z using Pythagorean Theorem
\(\displaystyle z=\sqrt{(87.5)^2-(33\sqrt{5} )^2} = 47.02\)
Find value of x
\(x=VY+YK\)
\(22+47.02=69.02\)
Need help on this question asap pleasee
Answers
Answer:
15 cm
Step-by-step explanation:
\(\frac{12}{24}\) = \(\frac{x}{30}\)
cross multiply and solve for x
or just notice that the fraction reduces to 1/2 and 15 is half of 30
the answer is in the picture
You are given the following information about a population:
⢠There are two alleles: C and c.
⢠C codes for green hair and c codes for white hair.
⢠C is dominant over c.
⢠The frequency of the c allele is 0.3.
⢠The population is comprised of 100 individuals.
Assuming the population is in Hardy-Weinberg equilibrium, how many individuals have green hair?
A. 9% of the population will have green hair.
B. 91% of the population will have green hair.
C. 51% of the population will have green hair.
D. 49% of the population will have green hair.
Answers
Assuming the population is in Hardy-Weinberg equilibrium, the individuals have green hair are equal to 91% .
From the data present in problem,
Hardy and Weinberg proved mathematically that in a population all dominant and recessive alleles include all alleles for a given gene. Mathematically, denoted as p + q = 1.0
Where, p = frequency of dominant alleles (C)
q = frequency of recessive alleles (c) = 0.3
Number of population individua's = 100
Hardy and Weinberg described all the possible genotypes for a gene with two alleles. The binomial expansion representing this is,
p² + 2pq + q² = 1.0
Where, p² = proportion of homozygous dominant individuals (Green)
• q² = proportion of homozygous recessive individuals (White)
2pq = proportion of heterozygotes (Green)
Since, p+ q = 1.0
=>p = 1 - q = 1 - 0.3 = 0.7
=>p = 0.7
The genotypic frequencies are as follows:
CC (p²) = (0.7) = 0.49
Cc (2pq) = 2x(0.3)(0.7) = 0.42
cc (9²) = (0.3)² = 0.09
p² + 2pq + q² = (0.49) + (0.42)+(0.09)= 1.0
The expected number for each genotype are as follows: CC (p²) = (0.49×100) = 49
Cc (2pq) = (0.42×100)= 42
cc(q²) = (0.09×100) = 9
The number of individuals have green hair is as follows: (p²)+(2pq) = 49+42= 91
Thus, required individuals percentage is 91%.
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Find the work done by the force field F=x^3i+y^3j in moving an object from point p(1,0) to point q (2,2)
Answers
Is the question biased or fair?
Do you want to eat a juicy hamburger or the usual vegetable sandwich?
Answers
Answer:
biased
Step-by-step explanation:
To make 5 gallons of cleaning solution, 3 cups of bleach is mixed in with water.
Which table shows the relationship between the gallons of cleaning solution made and the cups of bleach used?
Answers
Answer:
Option B.
Step-by-step explanation:
Let 'g' represent the number of gallons of cleaning solutions.
Let 'c' represent the number of cups of bleach.
From the question given above, we were told that:
To make 5 gallons of cleaning solution, 3 cups of bleach is mixed in with water.
This implies that number of gallons (g) of the cleaning solution is directly proportional to the number of cups (c) of the bleach mixed with water i.e
g ∝ c
g = Kc
K is the constant of proportionality.
Next, we shall determine the relationship between g and c as follow
g = 5
c = 3
K =?
g = Kc
5 = K × 3
Divide both side by 3
K = 5/3
g = Kc
K = 5/3
g = 5/3 c
Thus, the relationship between g and c is:
g = 5c / 3
Next, we shall make c the subject of the formula. This is illustrated below:
g = 5c / 3
Cross multiply
3g = 5c
Divide both side by c
c = 3g/5
Next, we shall determine c when g = 10, 15, and 20.
This is illustrated below:
g = 10
c =?
c = 3g/5
c = (3 × 10)/5 = 30/5 = 6
g = 15
c =?
c = 3g/5
c = (3 × 15)/5 = 45/5 = 9
g = 20
c =?
c = 3g/5
c = (3 × 20)/5 = 60/5 = 12
Summary:
Num. of gallon (g) >> Num. of cup (c)
5 >>>>>>>>>>>>>>>> 3
10 >>>>>>>>>>>>>>> 6
15 >>>>>>>>>>>>>>> 9
20 >>>>>>>>>>>>>>> 12
Therefore, option B gives the correct table.
6) Reflection: Across the line x = 1
Answers
Answer:
The coordinates of the new triangle would be (2,2), (-1,0) and (-2,4)