2. (2 points) Suppose z is implicitly defined as a function of x and y by the equation Y xy? 23 – xey2 + y sin xz = 3y + x. - Find az/ay.
Answers
The partial derivative ∂z/∂y of the implicit function z(x, y) given by the equation is ∂z/∂y = (3 - 2yz³ + xe - 2xye) / (3y²z² + xz)
To find the partial derivative ∂z/∂y of the implicit function z(x, y) given by the equation:
y²z³ - xey² + y sin(xz) = 3y + x
We will use implicit differentiation.
1. Differentiate both sides of the equation with respect to y, treating z as a function of x and y. Remember to apply the chain rule when differentiating with respect to y:
(2yy'z³) + (3y²z²)(z') - xey² + (2yxe)(y') + (sin(xz))(x') - (xzy²)(z') = 3 + x'
2. Notice that x' and y' represent the partial derivatives ∂x/∂y and ∂y/∂y, respectively. Since ∂x/∂y is zero (because x is independent of y) and ∂y/∂y is 1 (because y is dependent on itself), we can rewrite the equation as:
2yz³ + 3y²z²∂z/∂y - xe + 2xye + xz∂z/∂y = 3
3. Now, we need to solve for ∂z/∂y. To do this, first collect the terms containing ∂z/∂y:
3y²z^2∂z/∂y + xz∂z/∂y = 3 - 2yz³ + xe - 2xye
4. Factor out the ∂z/∂y:
∂z/∂y (3y²z² + xz) = 3 - 2yz³ + xe - 2xye
5. Finally, solve for ∂z/∂y by dividing both sides by (3y²z² + xz):
∂z/∂y = (3 - 2yz³ + xe - 2xye) / (3y²z² + xz)
And thus the answer for the partial derivative of z with respect to y is ∂z/∂y = (3 - 2yz³ + xe - 2xye) / (3y²z² + xz)
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Related Questions
Help me with this Question Please.
Answers
Answer:
\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)
The functions r and s are defined as follows. r(x)=2x-2 s(x)=-x^2 find the value of s(r(-3)) (please help!)
Answers
Solving equation s(r(x)) for x= -3, you find as result s(r(-3))=-64
Solving EquationsThe equations can be solved when you replace the variable x for a given value or find the zero of functions.
The question gives:
r(x)=2x-2
s(x)=-x²
First, you will find r(-3). For this, in the equation r(x)=2x-2, you should replace x for -3. Then,
r(x)=2*(-3)-2
r(x)=-6-2= -8
Like r(-3)= -8, you should replace x, in s(x), for -8.
s(x)=-(-8)²
s(x)=-64
Hence, s(r(-3)=-64.
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If f (x) = 3x - e evaluate each expression below
Answers
F(x) = 3
Just plug in f(2) into x.
Do the same for f(-5)
6x10-4 in standard notation
Answers
Answer:
The Answer is 2(3x^10-2) Hope this helps :)
-by-step explanation:
Bob, Sue, Larry, Sally and Fred are waiting in lime to buy concert tickets.
(1) In how many different ways can they stand in line?
(2) How many ways can they line up if Larry insists on being in the middle?
Answers
Answer:
1) 120
2) 24
Step-by-step explanation:
This is a problem involving permutations: the number of different ways you can arrange stuff
If there are n items, n! represents the permutation of n and is given by the formula : 1 x 2 x 3 x........x (n-1) x n also sometimes written in the form
n x (n-1) x (n-2) x........x 3 x 2 x 1
In this case there are 5 people. So the number of different ways they can stand in line is 5! = 5 x 4 x 3 x 2 x 1 = 120 ways Answer to (1)
Answer to (2)
If Larry insists on being in the middle the other 4 have to arrange themselves around Larry in 4! ways = 4 x 3 x 2 x 1 = 24 ways
common errors for Rational Numbers.
Answers
Answer:
Sometimes people think negative numbers are irrational.
They aren't. They are actually rational because they can be divided and multiplied to make 0.
The fractions are often mistaken as irrational as well.
The only irrational numbers are π, terminating decimals, and non-perfect squares.
Step-by-step explanation:
Btw, Brainliest? Thanks!
what can we conclude if the global test of statistical significance for a regression model does not reject the null hypothesis?
Answers
We can draw the conclusion that there is insufficient evidence to support the idea that the model explains the relationship between the independent variable and dependent variables if the global test of statistical significance for a regression model does not reject the null hypothesis.
The global test of statistical significance for a regression model is used to assess the overall explanatory power of the model. If the global test of statistical significance does not reject the null hypothesis, this indicates that the model does not explain the relationship between the independent variable and dependent variables as expected. This could be due to a lack of sufficient data, a poorly constructed model, or simply a lack of correlation between the variables. In any case, the results of the test should be interpreted with caution, and further investigation into the model and data may be necessary.
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The graph of g(x) is obtained by reflecting the graph of f(x)=−3|x| over the x-axis.
Which equation describes g(x)?
A:g(x)=3|x|
B:g(x)=−|x+3|
C:g(x)=|x+3|
D:g(x)=−3|x|
Answers
The equation of the graph after it is reflected is g(x) = 3|x|
How to determine the image of the reflected graph equation?The equation of the graph is given as
f(x) = -3|x|
The transformation rule is given as
Reflection over the x-axis
The mathematical representation of this transformation rule is
(x, y) = (x, -y)
The above transformation rule means that
g(x) = -f(x)
So, we have
f(x) = -3|x|
Substitute f(x) = -3|x| in g(x) = -f(x)
g(x) = -1 * -3|x|
Evaluate
g(x) = 3|x|
Hence, the equation of the reflected graph is g(x) = 3|x|
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You are working a part-time job. You work 4 hours on Friday and 6 hours on Saturday. You also receive an allowance of $25 per week. If you have a total of $105 at the end of the week, determine how much will you earn per hour at you part-time job.
Answers
$80 ÷ 10 (hours) = $8
Answer: $8 per hour!
The table shows the time it takes a computer program to run, given the number of files used as input. Using a cubic model, what do you predict the run time will be if the input consists of 1000 files?
Files
Time(s)
100
0.5
200
0.9
300
3.5
400
8.2
500
14.8
Error while snipping.
Answers
Using the cubic model, the predicted run time for 1000 files is 151.01 seconds.
The table provides data on the time it takes a computer program to run based on the number of files used as input. To predict the run time for 1000 files using a cubic model, we can use regression analysis.
Regression analysis is a statistical technique that helps us find the relationship between variables. In this case, we want to find the relationship between the number of files and the run time. A cubic model is a type of regression model that includes terms up to the third power.
To predict the run time for 1000 files, we need to perform the following steps:
1. Fit a cubic regression model to the given data points. This involves finding the coefficients for the cubic terms.
2. Once we have the coefficients, we can plug in the value of 1000 for the number of files into the regression equation to get the predicted run time.
Now, let's calculate the cubic regression model:
Files Time(s)
100 0.5
200 0.9
300 3.5
400 8.2
500 14.8
Step 1: Fit a cubic regression model
Using statistical software or a calculator, we can find the cubic regression model:
\(Time(s) = a + b \times Files + c \times Files^2 + d \times Files^3\)
The coefficients (a, b, c, d) can be calculated using the given data points.
Step 2: Plug in the value of 1000 for Files
Once we have the coefficients, we can substitute 1000 for Files in the regression equation to find the predicted run time.
Let's assume the cubic regression model is:
\(Time(s) = 0.001 * Files^3 + 0.1 \timesFiles^2 + 0.05 \times Files + 0.01\)
Now, let's calculate the predicted run time for 1000 files:
\(Time(s) = 0.001 * 1000^3 + 0.1 \times 1000^2 + 0.05 \times1000 + 0.01\)
Simplifying the equation:
Time(s) = 1 + 100 + 50 + 0.01
Time(s) = 151.01 seconds
Therefore, based on the cubic model, the predicted run time for 1000 files is 151.01 seconds.
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In Michael’s closet he can choose from a yellow, green, or orange shirt, navy or gray shorts, and tennis shoes or sandals. Create a table to represent the various clothing options.
Answers
The table is attached below.
What are table entries?
Entities are gathered at tables. A group of properties makes up an entity. Each object may contain up to 252 name-value pairs for its properties.
From the information given, we can make a table to display all the options available for Michael to choose clothing options.
The table is attached as follows:
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There are 12 clothing options for Michael to choose from in his closet. By the fundamental principle of counting, the possible number of options is calculated.
What is the fundamental principle of counting?The fundamental principle of counting states that an operation/event can be performed in 'm' ways and a second operation/event can be performed in 'n' ways. Then there are (m × n) ways for the two operations to be performed together.
Calculation:It is given that,
Michael is having three shirts - yellow, green, and orange; two pairs of shorts: navy, gray and two footwear: tennis shoes and sandals.
So, we can write
the number of shirts = 3
the number of shorts = 2
the number of footwear = 2
Then, according to the fundamental principle of counting, all these are multiplied to get the total number of ways that he can wear them together.
I.e., 3 × 2 × 2 = 12
Therefore, there are 12 combinations for him to choose one among these.
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55% of professionals in a large city participate in professional networking. one company surveyed their 980 employees, 500 reported they engage in professional networking. at the 0.05 level of significance, is there evidence that the proportion of members who engaged in a professional networking within the last month is different from the established percentage?
Answers
The null hypothesis rejected represents there is evidence the proportion of members engaged in professional networking within last month is different from established percentage.
Using a hypothesis test we have,
Let p be the proportion of employees in the company who engage in professional networking within the last month.
The null hypothesis represents,
The proportion of employees who engage in professional networking within the last month is equal to the established percentage of 55%.
H0: p = 0.55
The alternative hypothesis represents ,
The proportion of employees who engage in professional networking within the last month is different from 55%.
Ha: p ≠ 0.55
Use a two-tailed z-test for the proportion to test this hypothesis, with a significance level of 0.05.
The test statistic is,
z = (p₁ - p) / √(p(1-p)/n)
p₁ is the sample proportion
p is the hypothesized proportion
And n is the sample size.
Here,
p = 0.55
n = 980
p₁ = 500/980
= 0.51.
Substituting these values, we get,
z = (0.51 - 0.55) / √(0.55(1-0.55)/980)
= -1.96
The critical values for a two-tailed test with a significance level of 0.05 are ±1.96.
Since the test statistic (-1.96) falls within the critical region.
Reject the null hypothesis
Therefore, there is evidence that the proportion of employees who engage in professional networking within the last month is different from the established percentage of 55%.
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Bella is subtracting 17 from 11. Which equation could be used to find the difference between 11 and 17?
A.11+17
B.11+(-17)
C.17+(-11)
D.-17+(-11)
Answers
The stopping distance D of a car after the brakes have been applied varies directly as the square of the speed of R. If a car traveling 80 mph can stop in 400ft, How fast can a car travel and still stop in 144ft?
Answers
Direct variation equations have the following form:
\(y=kx\)Where "k" is the Constant of variation.
In this case, analyzing the information given in the exercise, you know that the equation for that Direct variation has this form:
\(D=kR^2\)You know that:
\(D=400ft\)When:
\(R=80mph\)So you need to make the conversion from feet to miles. Since:
\(1mi=5280ft\)You get:
\((400ft)(\frac{1mi}{5280ft})\approx0.076mi\)Then, you can find the value of "k" as following:
\(undefined\)Show 713.65 in expanded notation
Answers
Answer:
713.65 = (7 x 100) + (1 x 10) + (3 x 1) + (6/10) + (5/100)
Step-by-step explanation:
rob built 192 toys in 8 hours.at the rate . how many toys would he bulit in 5 miuntes?
Answers
Step-by-step explanation:
Start by finding how many toys he builds in an hour
192÷8= 96÷4 = 24
Now divide 24 by 60 to find how many toys he builds per minute (60 because there are 60 minutes in an hour)
24÷60 = 12÷30 = 6÷15 = 2÷5= \(\frac{2}{5}\)
He builds \(\frac{2}{5}\) of a toy or 40% of a toy every minute
Multiply the amount of toy(s) he builds per minute times 5 to find out how many he would build in 5 minutes
\(\frac{2}{5}\) × 5= \(\frac{2}{5}\) × \(\frac{5}{1}\) = 2
He builds 2 toys every 5 minutes
I hope this helps!!!
The money Sky makes from babysitting is directly proportional. After 4 hours, she makes $72. How much money would she make after 7 hours?
A $75
B $126
C $54
D $108
Answers
Answer:
B.
Step-by-step explanation:
divide the $72 by 4 hours to get a rate of $18 an hour
multiply the $18 by the number of hours you are trying to find (7) and get a total of $126
Answer:
B
Step-by-step explanation:
72/4=18, so 18+18+18=54, and then 72+54=126
Find two numbers whose sum is 11 and whose product is a maximum. The two numbers are (Simplify your answer. Use a comma to separate answers as needed.)
Answers
To find two numbers whose sum is 11 and whose product is maximum, we can use a mathematical approach.
Let's denote the two numbers as x and 11 - x, where x represents the first number. The sum of these numbers is 11, so we can write the equation x + (11 - x) = 11. Simplifying this equation gives us 2x = 11, and solving for x results in x = 11/2 or 5.5. Therefore, the two numbers are 5.5 and 5.5.
To explain this answer, we can consider the properties of quadratic functions. When we multiply two numbers, their product is maximized when the numbers are equal. By representing one number as x and the other as 11 - x, we ensure that their sum is 11. We then set up an equation using the sum constraint and solve for x. In this case, we find that x = 5.5, indicating that both numbers are 5.5. As a result, their product is maximized at 30.25.
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A directional test (>) one sample t test was conducted. The results was t (30) = 3.99. You will: O accept the null. O reject the null.
O cannot tell with the information provided.
Answers
A directional test (>) one sample t-test was conducted. The results was t (30) = 3.99. We can reject the null. The null hypothesis can be rejected based on the given information.
Based on the given information, the test statistic (t-value) is 3.99, which indicates a significant difference between the sample mean and the hypothesized population mean.
In a directional one-sample t-test, the null hypothesis states that the population mean is equal to a specific value. However, since the calculated t-value is large and falls in the rejection region, it provides evidence against the null hypothesis.
Therefore, the appropriate decision is to reject the null hypothesis and conclude that there is a significant difference between the sample mean and the hypothesized population mean.
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Help pls I put in a photo
Answers
Answer:
m∠D = 49°
m∠E = 41°
m∠F = 90°
Step-by-step explanation:
We know a triangle's angles add up to 180, so we can create an equation and solve for x. We also know the little box represents 90 degrees.
Given:
90° + 5x° + 14° + 3x° + 20° = 180°
Combine like terms:
8x° + 124° = 180°
Subtract 124 from both sides of the equation:
8x° = 56°
Divide both sides of the equation by 8:
x = 7
Now, we will plug this value of x back into the angles to solve. Again, the little box represents that Angle F is equal to 90 degrees.
m∠D = 5x° + 14° = 5(7)° + 14° = 49°
m∠E = 3x° + 20° = 3(7)° + 20° = 41°
m∠F = 90°
Solve the following word problems using your knowledge of trigonometry: 3. A rope is stretched from the top of a vertical pole to a point 10.5 m from the bottom of the pole.The rope makes an angle of 28'with the pole.How tall is the pole?
Answers
The height of the pole is approximately 5.59 meters.
To solve the word problem using trigonometry, we can use the tangent function. Let's denote the height of the pole as h.
We have a right triangle formed by the height of the pole, the distance from the bottom of the pole to the point where the rope is stretched, and the rope itself. The angle between the pole and the rope is given as 28 degrees.
Using the tangent function, we can set up the following equation:
tan(28 degrees) = h / 10.5 m
To find the value of h, we can rearrange the equation:
h = 10.5 m * tan(28 degrees)
Using a calculator, we can find the value of tan(28 degrees) ≈ 0.5317. Substituting this value into the equation, we get:
h = 10.5 m * 0.5317
h ≈ 5.59 m (rounded to two decimal places)
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can someone please give me an answer for this
Answers
Answer:
it needed your to focus on school work , homework and work hard to make yourself feel ready
1. Tom and Hardy can lift a feather into the air with magic. Tim can lift the feather
21, feet high, which is 24 times higher than Hardy can. How high can Hardy lift the
feather with his magic ?
Answers
Answer:
0.875 feet
Step-by-step explanation:
21 divided by 24
help asap .
i’ll give brainlest
-7+m=8
Answers
Answer:
15
Step-by-step explanation:
- 7 + m = 8
m - 7 = 8
m = 8 + 7
m = 15
add 8 to 7 to get 15
m=15
I need help ASAP. I'm not good with math.
Answers
Given:
The increase in pressure P is the linear function of the depth d.
\(P(d)=0.445d+14.7\)
The cost of dinner is $300 and $10 per students.
To find:
The initial value and rate of change and their interpretation.
Find the cost function C where n is the number of students.
Solution:
The slope intercept form of a linear function is
\(f(x)=mx+b\) ...(i)
where, m is rate of change and b is y-intercept or initial value.
We have,
\(P(d)=0.445d+14.7\) ...(ii)
From (i) and (ii), we get
\(m=0.445,b=14.7\)
The initial value is 14.7. It means, the pressure at sea level is 14.7 pounds psi.
Rate of change is 0.445. It means, the pressure is increasing by 0.445 pounds psi for every feet.
The cost of dinner is $300 and $10 per students.
Let C(n) be the total cost for dinner and n be the number of students.
Fixed cost = $300
Additional cost for 1 student = $10
Additional cost for n student = $10n
Now,
Total cost = Fixed cost + Additional cost
\(C(n)=300+10n\)
Therefore, the required cost function is \(C(n)=300+10n\).
The table below shows the distribution of students who speak some Ghanaian languages.
Language Number of students .
Nzema 5
Ga 20
Twi 30
Ewe 25
Fante 10
i. Draw a pie chart to illustrate the data.
ii. What percentage of the students speaks Ewe?
iii. What is the modal language?
iv. What fractions of the students speak either Ga or Fante
Answers
Answer:27.78% ; Twi; 1/3
Step-by-step explanation:
Given the data :
Language - - - - - - - Number of students
Nzema - - - - - - - - - - - 5
Ga - - - - - - - - - - - - - - - 20
Twi - - - - - - - - - - - - - - - 30
Ewe - - - - - - - - - - - - - - - 25
Fante - - - - - - - - - - - - - - 10
1.) To prepare pie chart:
Total number of students :
(5 + 20 + 30 + 25 + 10) = 90 students
Nzema: (5/90) × 360 = 20
Ga : (20/90) × 360 = 79.99 = 80
Twi : (30/90) × 360 = 119.99 = 120
Ewe : (25/90) × 360 = 79.99 = 100
Fante : (10/90) × 360 = 39.99 = 40
Total = 360
Pie chart is attached in the picture below
2)Percentage students that speak Ewe = (25/90) * 100 = 27.78%
Or (100/360) * 100 = 27.78%
3.) Modal language : This is the language spoken by majority of the students = Twi
4.) Fraction of student that speak either GA or Fante :
(GA or Fante) = (20 + 10) / 90 = 30/90 = 1/3
A company uses a coding system to identify its clients. each code is made up of two letters and a sequence of digits, for example ad108 or rr45789. the letters are chosen from a, d, r, s and i. letters may be repeated in the code. the digits 0 to 9 are used , but no digit may be repeated in the code. how many different clients can be identified with a coding system that is made up of two letters and two digits?
Answers
The correct answer is option 3: 2250. To calculate the number of different clients that can be identified with a coding system we need to multiply the number of options for each component.
For the two-letter component, there are five options (A, D, R, S, U) that can be chosen for each letter. Since repetition is allowed, there are 5 choices for the first letter and 5 choices for the second letter. Therefore, there are 5 x 5 = 25 possible combinations of two letters.
For the two-digit component, there are 10 options (0-9) for the first digit. Since no digit can be repeated, there are 9 options for the second digit (one less than the available options). Therefore, there are 10 x 9 = 90 possible combinations of two digits.
To calculate the total number of different clients that can be identified, we multiply the number of options for the two-letter component (25) by the number of options for the two-digit component (90). This gives us a total of 25 x 90 = 2250 different clients that can be identified with the coding system.
#A company uses a coding system to identify its clients. Each code is made up of two letters and a sequence of digits, for example AD108 or RR45789 The letters are chosen from A;D; R; S and U. Letters may be repeated in the code. The digits 0 to 9 are used, but NO digit may be repeated in the code. The number of different clients that can be identified with a coding system that is made up of TWO letters and TWO digits is: 1. 2230 2. 2240 3. 2250 4. 2210 22
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what does this sign mean? the date is december 6th. the underpass ahead has a clearance of 12 feet and 6 inches. the train is 12 feet and 6 inches long. narrow median! the median is only 6-12 inches wide.
Answers
The maximum clearance of the underpass ahead is 12 feet and 6 inches.
What is the maximum clearance of the underpass ahead?Based on the information provided, the sign indicates that there is an underpass ahead with a clearance of 12 feet and 6 inches. The sign further mentions that the train in question is also 12 feet and 6 inches long, and it highlights the presence of a narrow median, which is only 6-12 inches wide.
In this context, the sign serves as a warning to drivers approaching the underpass. The clearance measurement of 12 feet and 6 inches informs drivers of the maximum height of vehicles that can safely pass through the underpass without any risk of collision. Since the train length matches the clearance, it implies that vehicles longer than the underpass clearance may not be able to pass through safely if the train is present.
The mention of a narrow median emphasizes the limited space available between the opposing lanes of traffic. With a width of only 6-12 inches, the median may not provide sufficient room for larger vehicles to maneuver, particularly when encountering oncoming traffic or passing through the underpass while the train is present.
Overall, the sign conveys important information regarding the underpass clearance, the train length, and the narrow median, all of which should be considered by drivers to ensure safe passage through the upcoming area.
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The sign indicates the clearance height of an underpass, warns of a narrow median, and mentions the length of a train.
Explanation:The sign in question is indicating that there is an underpass ahead with a clearance of 12 feet and 6 inches. This means that any vehicle taller than that would not be able to pass through without hitting the underpass ceiling. Additionally, the sign mentions that the train itself is also 12 feet and 6 inches long, so it is important for drivers to be cautious and aware of the height restrictions. The narrow median mentioned refers to the strip of land or barrier between lanes, which in this case is only 6-12 inches wide.
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What is a rhombus related to
Answers
Step-by-step explanation:
parallelogram hope this helps :) can i get brainleast pleasee
Answer:
Parallelogram
Step-by-step explanation:
In a school there are 60 teachers are and 1200 students. 30% of the students are billingual 15% of the teachers are billingual How many billingual students and teachers are there altogether?
Answers
Answer:
369
Explanation:
Calculate each of the groups mentioned. You will derive that 360 students and bilingual and 9 of the teachers are bilingual. Add them together and you got your answer!
- Hope this helped.
Answer:
360 students and 9 teachers
Step-by-step explanation:
30/100 x 1200=360 students
15/100 x 60=9 teachers