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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

2x + (x(dy/dx) + y) + 2y(dy/dx) = 0

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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Answer:

the answer to the problem is h=7

The graphs have been correctly dragged to the table to show the image of the triangle after it is reflected over the x-axis, the y-axis, and the line y = x.

By applying a reflection over the x-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (x, -y)

(1, -3)             →      (1, -(-3)) = (1, 3)

(3, -2)             →      (3, -(-2)) = (3, 2)

(4, -5)             →      (4, -(-5)) = (4, 5)

By applying a reflection over the y-axis to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (-x, y)

(1, -3)             →        (-1, -3)

(3, -2)             →      (-3, -2)

(4, -5)             →      (-4, -5)

By applying a reflection over the line y = x to the coordinates of this triangle, we have the following coordinates of the image triangle;

(x, y)                →      (y, x)

(1, -3)             →        (-3, 1)

(3, -2)             →      (-2, 3)

(4, -5)             →      (-5, 4)

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Step-by-step explanation:

2.25

6.4

4

1.333

Hope is will help you

Answer: 3 hours

Step-by-step explanation:

Bottle = 3.6 liters / 3600 milliliters

Rate = 20 ml a minute

3600 / 20 = 180 minutes

60 minutes = 1 hour

180 / 60 = 3 hours

For $3.00, the pounds of bananas that can be bought are 2.

How to derive equation of line from graph using two point form?
A line's equation can take many different shapes in a two-dimensional coordinate plane. The point-slope form, slope-intercept form, and general or standard form of the equation of a line are the three most often used techniques.
The formula of two point form of a equation is given below:
Let (x₁, y₁) and (x₂, y₂) be the two points such that the equation of line passing through these two points is given by the formula:
(y-y₁)/(x-x₁) = (y₂-y₁)/(x₂-x₁) -- (i)
Rearranging (i), we get: y - y₁ = [(y₂-y₁)/(x₂-x₁)] (x-x₁) --(ii)

Given, the graph has y co-ordinate as cost in $ of bananas and the x co-ordinate as pounds in lb.
From graph in question, the two points that can be assumed are (0.5,0.75) and (3,4.5); thus using two point form we get the equation as:
y - 0.75 = [(4.5 - 0.75)/(3 - 0.5)] *(x - 0.5) ⇒ y - 0.75 = 1.5 (x - 0.5)
⇒ y - 0.75 = 1.5x - 0.75 ⇒ y = 1.5x ⇒ x = y/1.5 --(ii)
From (ii),
thus for y = 3, value of x will be x = 3/1.5 = 2

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The population parameter of interest in this study is the proportion or percentage of all female adults in the entire population who support a ban on public smoking. The Gallup poll was conducted to estimate this proportion or percentage by collecting data from a sample of female adults. By using statistical inference methods, the researchers can use the sample data to make inferences about the population parameter with a certain level of confidence.

Answer:

\(6,10\)

Step-by-step explanation:

Method 1:

\(\mathrm{Let\ two\ numbers\ be\ x\ and\ y\ such\ that:}\\\mathrm{x:y=3:5\ \ \ \ and\ \ \ \ x+y=16}\\\mathrm{or,\ \frac{x}{y}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3y..........(1)}\\\mathrm{Also\ we\ have}\\\mathrm{x+y=16}\\\mathrm{or,\ 5(x+y)=5(16)}\\\mathrm{or,\ 5x+5y=80}\\\mathrm{or,\ 3y+5y=80\ [From\ equation\ 1]}\\\mathrm{or,\ 8y=80}\\\mathrm{or,\ y=10}\\\mathrm{From\ equation\ 1,}\\\mathrm{5x=3y}\\\mathrm{or,\ 5x=3(10)=30}\\\mathrm{\therefore x=6}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Alternative method 1:

\(\mathrm{Let\ the\ two\ numbers\ be\ x\ and\ 16-x.}\\\mathrm{Then,\ we\ have}\\\mathrm{x:(16-x)=3:5}\\\\\mathrm{or,\ \frac{x}{16-x}=\frac{3}{5}}\\\\\mathrm{or,\ 5x=3(16-x)=48-3x}\\\mathrm{or,\ 5x+3x=48}\\\mathrm{or,\ 8x=48}\\\mathrm{\therefore x=6}\\\mathrm{So,\ the\ other\ number=16-x=16-6=10}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

Alternative method 2:

\(\mathrm{Let\ the\ two\ numbers\ be\ 3x\ and\ 5x.}\\\mathrm{Then,}\\\mathrm{3x+5x=16}\\\mathrm{or,\ 8x=16}\\\mathrm{or,\ x=2}\\\mathrm{So,\ first\ number=3x=3(2)=6}\\\mathrm{Second\ number=5x=5(2)=10}\)

\(\mathrm{So,\ the\ two\ numbers\ are\ 6\ and\ 10.}\)

The tip was $7.77

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Answer:about 8 dollars

Step-by-step explanation:

Answer:

4/100

Step-by-step explanation:

% or per cent means "in a hundred"

\(y \propto \dfrac 1x\\\\\implies y = \dfrac kx \\\\\implies \dfrac 14 = \dfrac k{8}\\\\\implies k=2\\\\\text{When}~ x =-4\\\\y = \dfrac{k}{x} = \dfrac{2}{-4}= -\dfrac 12\)

A mean is an arithmetic average of a set of observations. The average cost of ten classes is $14.

A mean is an arithmetic average of a set of observations. it is given by the formula,

Mean = (Sum of observations)/Number of observations

Given that there is a $40 initiation fee. It costs an additional $10 for every spinning class you attend. Therefore, the Cost of ten classes is,

Cost of ten classes = Fixed cost + Varible cost

                                = $40 + $10(10)

                                = $40 + $100

                                = $140

Now, the average cost of ten classes can be written as,

Average cost = Cost of ten classes / Number of classes

                      = $140 / 10

                      =$14

Hence, the average cost of ten classes is $14.

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The area of the rectangle is 27/70 square feet.

The area of a rectangle is given by the formula:

Area = base x height

Plugging in the given values, we get:

Area = (3/7) x (9/10)

Simplifying, we get:

Area = (27/70) square feet

Therefore, the area of the rectangle is 27/70 square feet.

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The time and electricians it would take the remaining 3 electricians 8 hours to complete the job if one electrician does not report.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

If x men take y time for a work,

We can define a constant as "Manpower" needed for doing that specific work.

Let we define:

Manpower needed for a work = y + y + y + .. + y = Time per man × count of men

Manpower needed for a work = xy

We are given that;

Number of electricians= 4

Number of hours= 6

Now,

We can use the formula:

workers × time = work

where "workers" is the number of electricians, "time" is the number of hours they work, and "work" is the amount of work done.

In this case, we know that 4 electricians can complete the job in 6 hours. So:

4 × 6 = work

work = 24

This means that the total amount of work required to complete the job is 24 "units".

Now, if one electrician doesn't show up, we have only 3 electricians to do the work. Let's call the time it takes for the 3 electricians to complete the job "t".

So we have:

3 × t = 24

Dividing both sides by 3, we get:

t = 8

Therefore, by work and time answer will be 3 electricians and 8 hours.

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Answer:

17000

Step-by-step explanation:

17^1 * 10^3

17 * 10*10*10

17*1000

17000

the answer is 17,000

the exponent shows how many times you multiply the number by itself

here is an image for an explanation

hope I helped ❤

Answer:

Step-by-step explanation:

The expression 2x - 11x - 6 can be simplified as follows:

2x - 11x - 6 = -9x - 6

So, the equivalent expression is -9x - 6.

The answer is:

-9x - 6

Work/explanation:

To simplify this expression, we combine the like terms :

\(\huge\text{2x - 11x - 6} \\ \\ \\ \text{-9x - 6}\)

There's nothing that we can do for this expression. It's been simplified as much as possible.

The distance between the points G and H is D = 8 units

Given data ,

Let the distance between 2 points be represented as D

Now , let the first point be G ( 0 , 8 )

Let the second point be H ( 8 , 8 )

Now , let the distance between G and H be D , where

D = √( ( x₂ – x₁ )² + ( y₂ – y₁ )²)

D = √ ( 0 - 8 )² + ( 8 - 8 )²

D = √64 units

D = 8 units

Hence , the distance is 8 units

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Answer:

f(f(5)) = 11

Step-by-step explanation:

\(f(f(5)) \\ from \: the \: table \: f(5) = 9 \\ so \: f(f(5)) = f(9) \\ also \: from \: the \: table f(9) = 11 \\ so \: f(f(5)) = 11\)

I hope that is useful for you

Answer:

  (a)  2%

Step-by-step explanation:

A score of 60 is 2 standard deviations below the mean (80 -2·10 = 60). The empirical rule tells you that 95% of the distribution is within 2 standard deviations of the mean. The remaining 5% is split evenly between those that are more than 2 SD above the mean and those that are more than 2 SD below the mean.

That tells you the percentage who failed is about 2.5%. The best answer choice is 2%.

_____

Additional comment

The empirical rule is a little bit sloppy, but it gets you in the ballpark. The actual percentage is closer to 2.275%.

Answer:

3

−

+

2

=

Step-by-step explanation:

The solution of the expression will be;

⇒ x = 2/7

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 3x / (3x-1) + 2 / x = 1

Now,

Solve the equation as;

The expression is,

⇒ 3x / (3x-1) + 2 / x = 1

⇒ 3x × x + 2 (3x - 1) / x (3x - 1) = 1

⇒ 3x² + 6x - 2 = x (3x - 1)

⇒ 3x² + 6x - 2 = 3x² - x

⇒ 6x - 2 = - x

⇒ 6x + x = 2

⇒ 7x = 2

⇒ x = 2/7

Thus, The solution of the expression will be;

⇒ x = 2/7

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Answer:

The measure of CD is 46

Step-by-step explanation:

From the midpoint theorem, we have,

FG = (1/2)CD

so,

\(13+5x=(1/2)(-3x+52)\\So,\\2(13+5x)=-3x+52\\26+10x=-3x+52\\13x=52-26\\13x=26\\x=26/13\\x=2\)

Now,

\(CD = -3x+52\\since \ x=2\\we \ get\\CD=-3(2) +52\\CD=-6+52\\CD=46\)

The steps that Patel could he use to solve the quadratic equation include:

8(x² + 2x) = –3

8(x² + 2x + 1) = –3 + 8

x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

It is preferred to solve quadratic equations without the use of the known quadratic formula solver. This can be completing squares and solving for x.

The equation given is:

8x² + 16x + 3 = 0

8(x² + 2x) = -3

Completing squares in the brackets and balancing the equation:

8(x² + 2x + 1) = -3 + 8

Factoring the perfect square will give 8(x + 1)² = 5.

This is illustrated in the options picked for the step.

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Answer:

answer in picture

Step-by-step explanation:

Yep, sounds like you're going virtual.

Answer:

3(m+7)

Step-by-step explanation:

solution,

3 times

the sum of m amd 7

= 3(m+7)

Answer:

its 3 x (m + 7)

Step-by-step explanation:

sue me if im wrong