Find dy/dx by implicit differentiation. /xy = 8 + xpy 13 2.2 dy/dx = 4x y y |() y
Answers
The required derivative is dy/dx = (13/2 - 4x y) / (x y - 2.2 x y²).
Given equation is xy = 8 + xpy.
To find: dy/dx by implicit differentiation.
To find the derivative of both sides, we can use implicit differentiation:
xy = 8 + xpy
Differentiate each side with respect to x:
⇒ d/dx (xy) = d/dx (8 + xpy)
⇒ y + x dy/dx = 0 + py + x dp/dx y + p dx/dy x dy/dx
Now rearrange the above equation to get dy/dx terms to one side:
⇒ dy/dx (xpy - y) = - py - p dx/dy x dy/dx - y
⇒ dy/dx = (- py - p dx/dy x dy/dx - y) / (xpy - y)
⇒ dy/dx (xpy - y) = - py - p dx/dy x dy/dx - y
⇒ dy/dx [(xpy - y) + y] = - py - p dx/dy x dy/dx
⇒ dy/dx = - py / (px - 1) [Divide throughout by (xpy - y)]
Now, substitute the values given in the question as follows:
xy = 8 + xpy Differentiating with respect to x, we get y + x dy/dx = 0 + py + x dp/dx y + p dx/dy x dy/dx
Thus,4x y + x dy/dx y = 0 + (13/2) + x (2.2) (1/y) x dy/dx
⇒ x dy/dx y - 2.2 x (y^2) dy/dx = 13/2 - 4x y
⇒ dy/dx (x y - 2.2 x y²) = 13/2 - 4x y
⇒ dy/dx = (13/2 - 4x y) / (x y - 2.2 x y²)
Thus, the required derivative is dy/dx = (13/2 - 4x y) / (x y - 2.2 x y²).
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Related Questions
Convert the measurement as indicated.
6 in to feet
6 in= ft (Type an integer or a decimal.)
Answers
6 in is equal to 0.5 feet.
What is inch?An inch is a unit of measurement that is commonly used in the United States, United Kingdom, and other countries that follow the Imperial system of measurement. It is defined as 1/12th of a foot or 2.54 centimeters. In other words, there are 12 inches in a foot. The inch is often used to measure the length or width of small objects or to express the size of computer screens, TVs, and other electronic displays.
given by the question,
the measurement as indicated.
6 into feet
6 in is equal to 0.5 feet.
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A
B
C
D
19.86 m
23.78 m
16.31 m
39.42 m
Answers
The measure of the side 'x' is 16.31 m. The correct option is C.
Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is a fundamental part of geometry that has many practical applications in fields such as physics, engineering, navigation, and surveying.
Given that in a right-angled triangle, the value of side RS is x, angle R is 25° and the side RT is 18 m.
The value of x will be calculated as,
sin65° = x / 18
x = 18 x sin65°
x = 16.31 m
Hence, the correct option is C.
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Please answer 10 points + brainlyest + 1 big thank u
Answers
Answer: -243
Step-by-step explanation:
Multiplying an odd term of negative terms makes the product negative.
First, you need the repeated multiplication in exponential form like this: -(3x3x3x3x3) or 3^5.
Finally, you need to evaluate the power, getting -243. Hope this helps!
Let T: R3 + R2 be the map TT (x, y, z) + (x2 + yz, ecyz) and w be the 2-form w = uvụ du 1 dv = Then calculate and simplify the following TW T*w Next, use this to calculate and simplify the following d(7*w) Do not use the fact that d(*W) = ** (dw). =
Answers
To calculate TW, substitute the coordinates (x, y, z) into T(x, y, z) = (x²+ yz, e^cyz). For Tˣw, substitute the coordinates (u, v) into Tˣw = u(x^2 + yz)dv. To calculate d(7ˣw), differentiate 7ˣw using exterior differentiation: d(7ˣw) = 7(du∧v + udv∧dv).
What is the calculation process for TW, Tˣw, and d(7ˣw) in the given scenario?The map T: R³ → R² is defined as T(x, y, z) = (x² + yz, e^cyz), and the 2-form w is given as w = uvdv.
To calculate TW, we substitute the coordinates (x, y, z) into the map T and obtain T(x, y, z) = (x² + yz, e^cyz).
Next, we calculate T³w by substituting the coordinates (u, v) into the 2-form w. Since w = uvdv, we have Tˣw = u(x² + yz)dv.
To calculate d(7ˣw), we differentiate the 2-form 7ˣw. Since w = uvdv, we have d(7ˣw) = d(7uvdv). Using the properties of exterior differentiation, we obtain d(7ˣw) = 7d(uv)∧dv = 7(du∧v + udv∧dv).
It's important to note that we are not using the fact that d(ˣw) = ˣˣ(dw) in this calculation.
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rite the composite function in the form f(g(x)). [identify the inner function u = g(x) and the outer function y = f(u).] y = 3 1 4x (g(x), f(u)) =
Answers
The composite function in the form f(g(x)) is f(g(x)) = 3(1 + 4x), with the inner function g(x) = 1 + 4x and the outer function f(u) = 3u.
Given the function y = 3(1 + 4x), we need to write it in the form f(g(x)) by identifying the inner function g(x) and the outer function f(u).
First, let's identify g(x), which is the inner function. In this case, g(x) = 1 + 4x.
Next, let's identify the outer function f(u). Since y = 3(1 + 4x), we can rewrite this expression as y = 3u, where u = 1 + 4x. So, f(u) = 3u.
Now, we can write the composite function in the form f(g(x)): f(g(x)) = f(1 + 4x) = 3(1 + 4x).
So, the composite function in the form f(g(x)) is f(g(x)) = 3(1 + 4x), with the inner function g(x) = 1 + 4x and the outer function f(u) = 3u.
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Help PLEASE ILL MARK BRAINLIEST!!!
Mario ran backwards 5 spaces then jumped up 3 spaces. How can we show this as an ordered pair?
Answers
explanation: going backwards represents subtraction on the x-axis so it would be -5 and jumping up represents increasing the y-axis so it would be +3
Evaluate the expression when x=−4/5 and y=1/3.
2x+6y
Answers
Answer:
2
--
5
Step-by-step explanation:
Start by multiplying 2 and -4/5 as fractions
2 -4 -8
------ x ------ = -------
1 5 5
Then multiply 6 and 1/3 as fractions
6 1 6 2
------ x ------ = ------- = -----
1 3 3 1
Lastly,add the two results after converting 2/1 to 10/5 to use the Greatest Common Factor so you can add.
-8 10 2
------- + ------ = -------
5 5 5
SUPER EASY DO FAST PLEASEE
Answers
is that a japanese symbol for beginner
what is the drag force on a 1.6 m wide, 1.4 m high car traveling at 10 m/s (≈ 22 mph)?
Answers
141.472 N of drag force is applied in 1.6m wide and 1.4m high car travelling at 10m/s
What is drag force?Drag force is the net force in the direction of flow experienced by any item moving through a fluid and is caused by pressure and shear stress forces acting on the surface of the object.
Formula of drag force is given by:
\(F_d = \frac{1}{2}C_dAPv^2\)
where
\(F_d\) = drag force (N)
\(C_d\) = drag coefficient (1.05 for moving car)
P = density of fluid (1.2 kg/m3 for air at NTP)
v = flow velocity (m/s)
A = characteristic frontal area of the body
A = height * width
=> 1.6*1.4
so A=2.24 \(m^2\)
and v=10 m/s
so \(F_d\) = 1/2* 1.05 * 2.24 *( 1.2 *10*10)
=> 0.5*1.05*2.24 *122
=> 143.472 N
so \(F_d\) = 143.472 N
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Penny reads 14 pages in 1/3 hour. What is the unit rate for pages per hour? For hours per page?
Answers
Answer: your
Pages per hour: 42
Hours per page: 1/42 of a hour
Step-by-step explanation:
14 x 3 = 42
1 hour divided by 42 pages = 1/42 of an hour per page
expand the following numbers 349056
Answers
Answer:
easyy
Step-by-step explanation:
It's B
John has 7 mice in his lab. He knows a mouse population doubles every month. When can he expect to have 2,625 mice? Please explain.
Answers
Answer:
31 years and 3 months or non
Step-by-step explanation:
the first thought that comes into my mind is
1 month=7 mice
n month= 7×n=2625 mice
n= 2625÷7=375
so it takes him to 375 months = 31 year and 3 months
but putting on a 2nd thought, I noticed that mice and mouse is different species. so there aren't exact answer
help is again wanted
Answers
Answer: 49°
Step-by-step explanation:
ABC = 41°
A complementary angle is when 2 or more angles sum to 90°
90-41
= 49°
Give a context-free grammar for each of the following languages. Please try to keep your grammars concise. a) L₁ = {w = {a, b}*w contains at least five as} b) L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k} c) Is your language for b) inherently ambiguous?
Answers
(a). The above context-free grammar (CFG) generates the language that has at least five "a's" and any combination of "b's".
(b). The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.
(c). it is ambiguous.
(a). Context-free grammar for L₁ = {w = {a, b}*w contains at least five as}:
S → aaaaaA | aaaaS | bS | aA | bA | ε
A → aA | bAb → bB | ε
B → bB | aB | ε
The above CFG generates the language that has at least five "a's" and any combination of "b's".
(b). Context-free grammar for L₂ = {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}:
S → AbC | AcB | BCa | CBa
A → aA | ε
B → bBb
B → bBbBbBb
C → cC | ε
C → cC | ε
The above CFG generates the language {a¹b³c¹|i, j, k ≥ 0 and i =jor i = k}.
(c). Yes, the language for b) is inherently ambiguous. It is because there are two variables A and B in the grammar, so the string can be generated in two ways. Thus, it is ambiguous.
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as you consider the various factors involved in starting a group, what is the most important factor you have to judge?
Answers
As you consider the various factors involved in starting a group, the most important factor you have to judge is the group's purpose or goal.
Step 1: Identify the group's purpose or goal - This is crucial because it will guide all other decisions, including membership criteria, communication methods, and meeting schedules.
Step 2: Assess the needs and resources of potential members - This will help you understand their motivations and ensure the group can support their needs while accomplishing its goal.
Step 3: Establish clear membership criteria and expectations - This will ensure that everyone in the group is on the same page and committed to the same goals.
Step 4: Choose an appropriate communication method - This will facilitate smooth and efficient communication among group members.
Step 5: Develop a meeting schedule that works for all members - Regular meetings help keep the group on track and provide opportunities for collaboration and feedback.
By focusing on the group's purpose or goal, you can create a solid foundation for a successful and productive group.
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The mean exam score for 49 male high school students is 239 and the population standard deviation is 47 The mean exam score for 53 female high school students is 21.1 and the population standard deviation is 4.3. At α=001, can you reject the claim that male and female high school students ha equal exam scores? Complete parts (a) through (e). Click here to view page 1 of the standard normal distribution table. Click here to view. page 2 of the standard normal distribution table. A. Male high school students have lower exam scores than female students B. Male and temale high school students have different exam scores. C. Male and female high school students have equal exam scores D. Male high school students have greater exam scores than female students
Answers
Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.
To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:
SE = sqrt((s1^2 / n1) + (s2^2 / n2))
Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:
SE = sqrt((47^2 / 49) + (4.3^2 / 53))
Next, we calculate the t-statistic using the formula:
t = (x1 - x2) / SE
Where x1 and x2 are the sample means. Plugging in the values, we have:
t = (239 - 21.1) / SE
We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.
In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.
Therefore, the correct answer is:
B. Male and female high school students have different exam scores.
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Consider the two rectangles shown.
A 2 cm B
6 cm
4 cm
C
S
4 cm
R 201
Complete the sentence to determine whether the rectangles are similar.
Rectangle ABCD
similar to rectangle PQRS because
rectangle ABCD
dilated to fit exactly over rectangle PQRS.
Answers
Rectangle ABCD is not similar to rectangle PRQS, because rectangle ABCD
as corresponding sides are not congruent.
What is congruency?We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.
The rectangle ABCD has dimensions 2×4 and the rectangle PQRS has dimensions 6×4.
If we dilate the with by 3 we'll have 6, but the height of PQRS will be 12.
So, The Rectangles is not similar.
Because their corresponding sides are not in the same ratio.
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Please help really need it
with the satellite directly overhead, how far above the surface of earth does the satellite need to be so it provides the maximum coverage of its signal?
Answers
Answer:
2,034.7 miles above the earth.
Step-by-step explanation:
Answer:
d=2034.7
Step-by-step explanation:
\(d=\sqrt{(4500)^{2}+(3958.8)^{2} } -3958.8\\d=2034.7\)
We calculate the point from the center of the earth to the satellite and because we have the radius we can subtract it getting the distance from the satellite to the earth.
Which of the following are solutions to the equation below? Check all that apply. X^2 - 8x + 16 = 5
Answers
Given equation is
\(\begin{gathered} x^2-8x+16=5 \\ x^2-8x+16-5=0 \\ x^2-8x+11=0 \end{gathered}\)The quadratic formula for the quadratic equation
\(ax^2+bx+c=0\)is
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)Here, a=1,b=-8,c=11.
\(\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4(1)(11)}}{2(1)} \\ =\frac{8\pm\sqrt[]{64-44}}{2} \\ =\frac{8\pm\sqrt[]{20}}{2} \\ =\frac{8\pm\sqrt[]{5\cdot4}}{2} \\ =\frac{8\pm2\sqrt[]{5}}{2} \\ =\frac{8}{2}\pm\frac{2\sqrt[]{5}}{2} \\ =4\pm\sqrt[]{5} \end{gathered}\)So, the solutions are
\(\sqrt[]{5}+4,-\sqrt[]{5}+4\)So, the correct options are C and E.
In ________, data miners develop a model prior to the analysis and apply statistical techniques to data to estimate parameters of the model.
Answers
In hypothesis testing, data miners develop a model prior to the analysis and apply statistical techniques to data to estimate the parameters of the model.
In hypothesis testing, data miners formulate a hypothesis or a model about a population parameter based on prior knowledge or assumptions. This model specifies the relationship between variables and the expected values of the parameters. The next step is to collect data and analyze it using statistical techniques to estimate the parameters of the model.
The estimation of parameters involves using the available data to make inferences about the unknown population parameters. This can be done using various statistical methods such as maximum likelihood estimation, least squares estimation, or Bayesian estimation. These techniques aim to find the best estimates of the parameters that are consistent with the observed data and the assumptions of the model.
Once the parameters are estimated, data miners can then evaluate the goodness of fit of the model and draw conclusions about the population based on the estimated parameters. This process allows for hypothesis testing and making inferences about the population based on the sample data and the estimated parameters of the model.
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You are the director of the customer service center in Company Alpha. You find that the mean time between calls to the center is 6 minutes with standard deviation of 4 minutes. The effective response time is 11 minutes with a standard deviation of 20 minutes. (a) Identify the following parameters: ta
tθ
∂a
∂θ
ra:
rθ:
Answers
The identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
ta: Mean time between calls to the center
tθ: Effective response time
∂a: Standard deviation of the time between calls to the center
∂θ: Standard deviation of the effective response time
ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)
rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)
Given information:
Mean time between calls to the center (ta) = 6 minutes
Standard deviation of time between calls (∂a) = 4 minutes
Effective response time (tθ) = 11 minutes
Standard deviation of effective response time (∂θ) = 20 minutes
Using this information, we can determine the values of the parameters:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/ta = 1/6 minutes^(-1)
rθ = 1/tθ = 1/11 minutes^(-1)
So, the identified parameters are:
ta = 6 minutes
tθ = 11 minutes
∂a = 4 minutes
∂θ = 20 minutes
ra = 1/6 minutes^(-1)
rθ = 1/11 minutes^(-1)
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help meeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
DStep-by-step explanation:
1 is incorrect so the answer must be D
Question content area the calculation for annual depreciation using the units-of-output method is:________
Answers
Content area the calculation for annual depreciation using the units-of-output method is yearly output.
What are the output method's units?
The productive output, units of production, or units of activity methods are other names for the units of output approach. Depreciation is computed based on the output of the equipment over a given period of time, taking into account the equipment's anticipated lifetime output units.What is the annual depreciation formula?
The formula for calculating the annual depreciation rate is (100 x Number of Periods in Year)/Number of Periods in Expected Life. The formula annual depreciation rate/number of periods in the year is used to determine the amount of depreciation for each period.Learn more about yearly output.
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y= 3 x+2
y= -2x-8
find the solution to the following system by subsitution
Answers
The solution to the system of linear equations is x = -2 and y = -4
What is an Algebraic equation?An Algebraic equation is a mathematical statement that shows the equality between two or more quantities.
An Algebraic equation may be linear, quadratic or Polynomic depending on the highest degree on the variables.
y = 3x + 2 ---------------1
y = -2x - 8 ---------------2
Equating equations 1 and 2 to find the value of x
3x + 2 = -2x - 8
Collecting like terms
3x + 2x = -8 - 2
5x = -10
x = -10/5
x = -2
Substitute x = -2 in equation 1
y = 3(-2) + 2
y = -6 +2
y = -4
In conclusion, the solution to the system of equations is x = -2 and x = -4
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solve and show work 1.32 x 4
Answers
Answer: 5.28
Step-by-step explanation: 1.32 times 4 is 5.28 because 4 times 2 is 8 4 times 3 is 12 1 over 1 and 4 times 1 is 4 plus 1 is 5 and put the dot in between 5 and 2 because there is one only dot
a cell phone plan has a basic charge of $45 a month. the plan includes 600 free minutes and charges 10 cents for each additional minute of usage. write the monthly cost c (in dollars) as a function of the number x of minutes used.
Answers
The monthly Cost C (in dollars) as a function of the number of minutes x used will be a C=$45 when less than 600 minutes are used and C= $45 + 0.1(x -600) when more than 600 minutes are used.
It is given that, The charge of the plan is $45, so our function of Cost C must include this price. Now, the plan includes 600 minutes of usage for free, So our definition of function should include this information as well.
Now, There will be 2 cases, Case 1 : when the minutes of usage is less than or equal to 600 and Case 2 : when the minutes of usage is greater than 600.
For the first case, the equation will be a simple constant function as no other additional cost is required :
⇒ C = 45
For the 2nd case, there is a 10 cent charge for every extra minute of usage + the plan charge of $45 and to find the number of extra minutes of usage we simply subtract 600 from 'x' (total minutes used). Therefore, our equation will be :
⇒C = 45 + 0.1 (x-600)
In conclusion, we can write our equation with proper format like this :
\(C = \left \{ {{45}\atop {45 + 0.1(x-600)}} \right.\)
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Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 to describe the relationship.
Answers
In the given equation r = 2/5 t "r" is the dependent variable.
Dependent variables:In mathematics, a variable is a symbol that represents a quantity that can take on different values. In many cases, variables can be divided into two types: dependent variables and independent variables.
An independent variable is a variable that can be changed freely, and its value is not dependent on any other variable in the equation.
A dependent variable is a variable whose value depends on the value of one or more other variables in the equation
Here we have
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups.
She writes the equation r = 2/5 t to describe the relationship.
In the equation, r = 2/5 t, "t" represents the total number of cups, while "r" represents the number of cups of red paint.
Here "t" is the independent variable because it represents the total number of cups, which can be changed arbitrarily.
The value of "r" depends on the value of "t" because the number of cups of red paint is always 2/5 of the total number of cups.
Therefore,
In the given equation r = 2/5 t "r" is the dependent variable.
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Complete Question:
Lin notices that the number of cups of red paint is always 2/5 of the total number of cups. She writes the equation r = 2/5 t to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know.
he length of a rectangle is 7/8 inches, and it has a width of 16/21 inches. Calculate the area for this rectangle in square inches.
Answers
Answer:
28 is the answer when I did the math :)
Answer:
i think the answer is 2/3
Step-by-step explanation:
Well, *clicks tounge* didn’t expect to be awake late, but time flies when your crying and panicing. :)
Answers
Answer: The first two
Step-by-step explanation:
A yogurt shop has a half-price mystery scoop special. The scoop could have vanilla or chocolate yogurt. It will also include either hot fudge, caramel, or marshmallow topping. Which list shows all the possible outcomes of the mystery scoop special?
a) S = {vanilla, chocolate, hot fudge, caramel, marshmallow}
b) S, = {(vanilla, hot fudge), (vanilla, caramel), (vanilla, marshmallow)}
c) S = {(vanilla, hot fudge), (vanilla, caramel), (vanilla, marshmallow), (chocolate, hot fudge), (chocolate, marshmallow)}
d) S = {(vanilla, hot fudge), (vanilla, caramel), (vanilla, marshmallow), (chocolate, hot fudge), (chocolate, caramel), (chocolate, marshmallow)}
Answers
Answer:
the answer would be D
Step-by-step explanation:
Answer:
d)s
Step-by-step explanation: