Old Martha has 5 children, each of whom
has 4 children, each of whom has 3
children, each of whom is childless. How
many descendants does Old Martha have?
descendants

Answer:

50

4 were incorrect

44/50 would make it 88%

Step-by-step explanation:

Answer:

1. There are 50 questions on the test.

2. He answered 4 questions incorrectly.

3. To make an 88 he would have gotten 44/50 questions right.

Answer:

m = 5

a = -3

b = -15

Step-by-step explanation:

(m - 2) = 3 for x^2

(2a + 3) = - (m - 2) = (2 - m) for x^1

(b + 6) = (2a - 3) for x^0

Shawndra is correct

(A) It is not possible to draw a trapezoid that is a rectangle true.

(B) it is possible to draw a square that is a rectangle true.

A. A trapezoid cannot be drawn as a rectangle.

The statement is true because we cannot draw a trapezoid that is a rectangle as a rectangle is a parallelogram with two pairs of parallel sides having opposite sides equal in length whereas a trapezoid is a quadrilateral with exactly one pair of parallel sides.

B. A square can be drawn as a rectangle.

The statement is true because we can draw a square that is a rectangle as any parallelogram with right angles is referred to be a rectangle whereas a parallelogram with right angles that has two pairs of opposite sides is a square. Despite being a unique type of rectangle with equal-length sides, squares are all rectangles.

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Answer:

x = 5

Step-by-step explanation:

Take your starting equation:

5x - 6 = 2x + 9

Your first step should be to isolate the variable, X, by having it on only one side of the equation. This can be done by subtracting one of the X values (either 5x or 2x) from either side, but I recommend the side with 2x since it's a smaller value and won't result in a negative.

(This is the right side of the equation)

2x + 9

- 2x

= 9

We need to do the same thing on the other side of the equation too, to balance both sides:

(This is the left side of the equation)

5x - 6

- 2x

= 3x - 6

This is our equation now:

3x - 6 = 9

The next step is to isolate X further by removing any constants (regular numbers) from the side with X. Since the constant on that side is -6, we need to add 6 to that side so that it's cancelled out, and do the same on the other side to balance.

(This is the left side of the equation)

3x - 6

+ 6

= 3x

And now for the other side:

(This is the right side of the equation)

9

+ 6

= 15

This is our current equation:

3x = 15

The final step is to get X completely isolated. X is being multiplied by 3, so we need to divide both sides of the equation by 3 to finally get the value of X.

(This is the left side of the equation)

3x

÷ 3

= x

And now for the other side:

(This is the right side of the equation)

15

÷ 3

= 5

Our final equation:

x = 5

We can check our answer by taking the final X value, 5, and inserting it into our beginning equation.

This is the beginning equation, as a reminder:

5x - 6 = 2x + 9

Replace all instances of X with its value, 5:

(5 · 5) - 6 = (2 · 5) + 9

After simplifying, the result is:

19 = 19, which means the X value is correct.

The error made in subtracting the two rational expressions 1/(x - 2) - 1/x is that the common denominator is not correctly identified and applied.

To subtract rational expressions, we need to find a common denominator and then subtract the numerators. In this case, the common denominator should be (x - 2) * x. However, the error lies in neglecting the parentheses in the first expression, leading to a miscalculation of the common denominator.

The correct subtraction of the given expressions should be: (x - 2)/(x - 2) - 1/(x * (x - 2)). Simplifying this expression further would result in (x - 2 - 1)/(x * (x - 2)), which can be simplified as (x - 3)/(x * (x - 2)).

Therefore, the error made in the subtraction lies in incorrectly identifying and applying the common denominator, which resulted in an inaccurate calculation of the expression.

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Answer: Elm Street Bookstore has 1,272 books.

Step-by-step explanation:

Read the problem: Main Street Bookstore has 3,132 books. They have 4 times as many books as Water Street Bookstore. Water Street Bookstore has 489 fewer books than Elm Street Bookstore. How many books does Elm Street Bookstore have?

Highlight facts: Main Street Bookstore has 3,132 books. They have 4 times as many books as Water Street Bookstore. Water Street Bookstore has 489 fewer books than Elm Street Bookstore. How many books does Elm Street Bookstore have?

Draw a picture: I drew a diagram to represent the relationships between the bookstores.

Assign variables: Let x be the number of books that Elm Street Bookstore has, y be the number of books that Water Street Bookstore has, and z be the number of books that Main Street Bookstore has.

Write equations: Based on the facts, I can write three equations:

z = 4y (Main Street Bookstore has 4 times as many books as Water Street Bookstore)

y = x - 489 (Water Street Bookstore has 489 fewer books than Elm Street Bookstore)

z = 3,132 (Main Street Bookstore has 3,132 books)

Solve for x: I can substitute y and z in the first equation with the expressions from the second and third equations:

3,132 = 4(x - 489)

Simplify and solve for x:

3,132 = 4x - 1,956

5,088 = 4x

x = 1,272

Check the answer: I can plug in x = 1,272 in the other equations and see if they are true:

y = x - 489

y = 1,272 - 489

y = 783

z = 4y

z = 4(783)

z = 3,132

All the equations are true, so x = 1,272 is the correct answer.

Hope this helps, and have a great day! =)

Step-by-step explanation:

\( \sqrt{(60 \div 10) {}^{2} } \\ = \sqrt{(6) {}^{2} } \\ = \sqrt{36 } \\ = 6\)

6 is your answer

Answer:

\(\sqrt{\left(\frac{60}{10}\right)^2}\)

\(\sqrt{\left(\frac{60}{10}\right)^2}=\frac{60}{10}\)

\(\frac{60}{10}=6\)

----------------------

hope it helps..

have a great day!!

Answer:

A

Step-by-step explanation:

The geometric series among the given options are:

B. ∑n=0[infinity]6n29n and D. ∑=0[infinity]63.

A geometric series is a series in which each term is obtained by multiplying the previous term by a constant ratio.

In option B, the series ∑n=0[infinity]6n29n is a geometric series because each term is obtained by multiplying the previous term by the constant ratio of 6/29. The first term is 6^0/29⁰ = 1, and each subsequent term is obtained by multiplying the previous term by 6/29.

In option D, the series ∑=0[infinity]63 is also a geometric series because each term is the same constant value of 63. In this case, the common ratio is 1 because each term is equal to the previous term.

The other options (A, C, E, and F) do not exhibit the pattern of a geometric series, either due to the lack of a constant ratio between terms or a constant term value.

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The correct choice is B

Let's solve the following triangle using the Law of Cosines for this given information, b = 10, c = 12, A = 59°. The Law of Cosines is expressed as;c² = a² + b² - 2ab cosCUsing the given values,

we can calculate the measure of the missing side of the triangle;a² = b² + c² - 2bc cosAa² = (10)² + (12)² - 2(10)(12) cos(59°)a² ≈ 144.1a ≈ 12 (rounded to one decimal place)Now we can use the Law of Sines to find the values of B and C.

The Law of Sines is expressed as;a/sinA = b/sinB = c/sinCa/sinA = b/sinBsinB = b (sinA / a)sinB = 10 (sin59° / 12)sinB ≈ 0.6914B ≈ sin⁻¹(0.6914)B ≈ 44.2°(rounded to one decimal place)C = 180° - A - BC = 180° - 59° - 44.2°C ≈ 76.8°(rounded to one decimal place),

the solution with the smaller angle B is;a ≈ 12, B ≈ 44.2°, C ≈ 76.8°.Hence, the correct choice is;B. There are two possible solutions for the triangle. The measurements for the solution with the smaller angle B are as follows. a ≈ 12, B ≈ 44.2°, C ≈ 76.8°.

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The quotient of 7/8 divided by 2/5 will be C. 35/16.

The quotient simply means that we have to divide.

Therefore, the quotient of 7/8 divided by 2/5 will be:

= 7/8 ÷ 2/5

= 7/8 × 5/2

= 35/16

In conclusion, the correct option is C

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Answer:

∠ 1 = 120°

Step-by-step explanation:

5x + 15 and 3x - 3 are same- side interior angles and sum to 180° , then

5x + 15 + 3x - 3 = 180 , that is

8x + 12 = 180 ( subtract 12 from both sides )

8x = 168 ( divide both sides by 8 )

x = 21

Then

5x + 15 = 5(21) + 15 = 105 + 15 = 120

∠ 1 and 5x + 15 are corresponding angles and are congruent , so

∠ 1 = 120°

Answer:

The bottom right !

Step-by-step explanation:

10 + 2 TIMES 10 + 1 (shown on the model)

10 + 2 = 12

10 + 1 = 11

Those two numbers become: 12 and 11 (12 x 11)

And the bottom-right is the one of two models that you can actually use for multiplication; the other models are not even rectangles in the first place ..

Hope this helped ~~

Answer:

5x+3=8

Step-by-step explanation:

this is the answer

The approximately 1.5% of the items will be classified as good.

The probability that an item is defective given that it was classified as good is around 1.96%.

When we consider the production process, we know that 15% of all items produced are defective. However, the inspector misclassifies an item 10% of the time. This means that out of the 85% of non-defective items, approximately 10% will be falsely classified as defective.

Hence, the proportion of items classified as good can be calculated as 100% - 10% = 90% of non-defective items. Considering that 85% of all items produced are non-defective, we can estimate that 85% * 90% = 76.5% of all items will be classified as good.

To determine the probability that an item is defective given that it was classified as good, we need to consider the misclassification rate. Since the inspector misclassifies an item 10% of the time, it means that out of the 15% defective items, around 10% will be incorrectly classified as good. Thus, the proportion of items classified as good but are actually defective can be calculated as 15% * 10% = 1.5%.

Therefore, the probability that an item is defective given that it was classified as good is approximately 1.5% out of the total items classified as good, which is 76.5%. Consequently, the probability that an item is defective given that it was classified as good is approximately 1.5% / 76.5% = 1.96%.

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The function does not have any

B. There is no local maxima

B. There is no local minima, but it has a

A. saddle point at (0, 0).

To find the local maxima, local minima, and saddle points of the function f(x, y) = \(5e^{(-y(x^2 + y^2))}\) + 6, we can analyze its critical points and determine the nature of those points. The function does not have any local maxima or local minima, but it has a saddle point at (0, 0).

To find the critical points of the function, we need to calculate the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = \(-10xye^{(-y(x^2 + y^2)})\) = 0

∂f/∂y = \(-5(x^2 + 2y^2)e^{(-y(x^2 + y^2)}) + 5e^{(-y(x^2 + y^2)})\) = 0

Simplifying the first equation, we get xy = 0, which implies that either x = 0 or y = 0. Substituting these values into the second equation, we find that when x = 0 and y = 0, the equation is satisfied.

To determine the nature of the critical point (0, 0), we can use the second partial derivative test. Calculating the second partial derivatives, we have:

\(∂^2f/∂x^2 = -10ye^{(-y(x^2 + y^2)}) + 20x^2y^2e^{(-y(x^2 + y^2)})\)

\(∂^2f/∂y^2 = -5(x^2 + 6y^2)e^{(-y(x^2 + y^2)}) + 10y^3e^{(-y(x^2 + y^2)})\)

Substituting x = 0 and y = 0 into the second partial derivatives, we find that both ∂\(^2]\)f/∂\(x^{2}\) and ∂\(^2]\)f/∂\(y^2\) are equal to 0. Since the second partial derivatives are inconclusive, we need to further analyze the function.

By observing the behaviour of the function as we approach the critical point (0, 0) along various paths, we can determine that it exhibits a saddle point at that location.

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In order to demonstrate that ψ2​(x)=(4πα​)1/4[2αx2−1]exp(−αx2/2) is an eigenfunction of the quantum harmonic oscillator, let's make use of the equation provided below:

Schrödinger equation for the system:

2μ−ℏ2​dx2d2ψn​(x)​+21​kx2Ψn​(x)=En​ψn​(x)

Given eigenfunction: \(ψ2​(x)=(4πα​)1/4[2αx2−1]exp(−αx2/2)\)

Let's differentiate the given equation and find the second derivative.

\(ψ2​(x)=(4πα​)1/4[2αx2−1]exp(−αx2/2)\)

\(ψ′(x)=∂∂xψ2​(x)=2α(4πα​)1/4xexp(−αx2/2)[2αx2−1]\)

\(ψ′′(x)=∂2∂x2​ψ2​(x)=2α(4πα​)1/4exp(−αx2/2)[2αx2−3]\)

Let's substitute the above values into the Schrödinger equation to solve for the energy eigenvalue.

Enψ2​(x)=(2μ−ℏ2​dx2+21​kx2)ψ2​(x)

Substituting the above values in the Schrodinger equation,

\(2μ−ℏ2​dx2d2ψn​(x)​+21​kx2Ψn​(x)\)=\(En​ψn​(x)2μ−ℏ2​2α(4πα​)1/4exp(−αx2/2)[2αx2−3]+21​kx2(4πα​)1/4[2αx2−1]exp(−αx2/2)\)

\(=En​(4πα​)1/4[2αx2−1]exp(−αx2/2)\)

Further simplifying,

\(2μ(4α2πα)1/4exp(−αx2/2)[2αx2−3]−2αℏ2​(4α2πα)1/4xexp(−αx2/2)[2αx2−1]+12kx2(4α2πα)1/4[2αx2−1]exp(−αx2/2)\)

\(=E(4α2πα)1/4[2αx2−1]exp(−αx2/2)\)

We can easily solve for the eigenvalue by comparing the above equation with the harmonic oscillator equation:\(2\mu\omega^2x^2\)=ℏω(1+n)

This comparison shows that the energy eigenvalue for the given wave function is given by (1/2+2n)ℏω.

ψ2​(x)=(4πα​)1/4[2αx2−1]exp(−αx2/2) is indeed an eigenfunction of the quantum harmonic oscillator with an eigenvalue of (1/2+2n)ℏω. To show this, the Schrödinger equation was used, and the wave function was differentiated twice to find the second derivative. The energy eigenvalue was determined by comparing the obtained equation with the harmonic oscillator equation.

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The value of the integral is 1710. To evaluate the integral S1 0 (1+1/2u⁴ - 2/5u⁹)du, we need to integrate each term separately.

∫1du = u + C, where C is the constant of integration.

To integrate 1/2u⁴, we can use the power rule of integration:

∫1/2u⁴ du = (1/2) ∫u⁴ du = (1/2) * u⁵/5 + C = u⁵/10 + C

To integrate -2/5u⁹, we can also use the power rule of integration:

∫(-2/5)u⁹ du = (-2/5) ∫u⁹ du = (-2/5) * u¹⁰/10 + C = -u¹⁰/25 + C

Putting everything together, we have:

∫(1+1/2u⁴ - 2/5u⁹)du = ∫1du + ∫1/2u⁴ du - ∫2/5u⁹ du

= u + u⁵/10 - (-u¹⁰/25) + C

= u + u⁵/10 + u¹⁰/25 + C

Now, we can evaluate the definite integral by plugging in the limits of integration:

S1 0 (1+1/2u⁴ - 2/5u⁹)du = [u + u⁵/10 + u¹⁰/25]₁⁰

= (10 + 10⁵/10 + 10¹⁰/25) - (0 + 0⁵/10 + 0¹⁰/25)

= 10 + 1000 + 400000/25

= 10 + 1000 + 16000

= 1710

Therefore, the value of the integral is 1710.

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Gary would need 15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bottles   Glue   Glitter

1              3.8       1.9

This means,

1 bottle = 3.8 oz of glue and 1.9 oz of glitter

Now,

1 bottle = 3.8 oz of glue

Multiply 4 on both sides.

4 bottle = 4 x 3.8 oz

4 bottle = 15.2 oz

1 bottle = 1.9 oz of glitter

Multiply 4 on both sides.

4 bottle = 7.6 oz

Thus,

15.2 oz of glue and 7.6 oz of glitter to make 4 bottles.

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False. the statement "If a variable x does not depend on a variable y, both coefficients are equal to zero" is false.

The coefficient of determination (R-squared) and the coefficient of correlation (Pearson's correlation coefficient) are related but distinct measures.

The coefficient of determination, denoted as R², measures the proportion of the variance in the dependent variable (y) that can be explained by the independent variable(s) (x). It ranges from 0 to 1, where a value of 0 indicates that the independent variable(s) do not explain any of the variance in the dependent variable, and a value of 1 indicates that the independent variable(s) completely explain the variance in the dependent variable.

On the other hand, the coefficient of correlation, denoted as r, measures the strength and direction of the linear relationship between two variables (x and y). It also ranges from -1 to 1, where a value of -1 indicates a perfect negative linear relationship, a value of 0 indicates no linear relationship, and a value of 1 indicates a perfect positive linear relationship.

If a variable x does not depend on variable y, it means there is no linear relationship between the two variables. In this case, the coefficient of correlation (r) would be 0, indicating no linear relationship. However, the coefficient of determination (R²) could still be non-zero if there are other independent variables that explain the variance in the dependent variable y.

Therefore, the statement "If a variable x does not depend on a variable y, both coefficients are equal to zero" is false.

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a) equation will be 0.5x + 3 = 18.50

b)  equation will be (0.75x - 0.10x) + 3 = 21.00

a) Sydney made $18.50 selling lemonade.

she sold each cup for $0.50 and received a $3 tip from a neighbor.

let x be the cost of cup she sold.

equation will be 0.5x + 3 = 18.50

b) Daria made a profit of $21.00 selling lemonade

she sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbor.

equation will be (0.75x - 0.10x) + 3 = 21.00

c) Sydney don't have to pay for the cups used while Daria paid.

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A. An equation to represent the situation in part A is 18.50 = (0.50) x + 3.

B. An equation to represent the situation in part B is 21.00 = (0.75) y - (0.10) y + 3.

C. The equations differ in the fact that one accounts for the cost per cup while the other does not.

In general, the profit is defined as the amount gained by selling a product, which should be more than the cost price of the product.

Part A: Let x be the number of cups of lemonade sold.

Then, the total amount of money Sydney made is given by:

Total money = (selling price per cup) × (number of cups sold) + tip

Substituting the given values, we get:

18.50 = (0.50) x + 3

Part B: Let y be the number of cups of lemonade sold.

Then, the total profit made by Daria is given by:

Total profit = (selling price per cup) × (number of cups sold) + tip - (cost per cup) × (number of cups sold)

Substituting the given values, we get:

21.00 = (0.75) y - (0.10) y + 3

Part C: The equation for Sydney's lemonade stand only takes into account the total amount of money she made, which includes the selling price per cup and a fixed tip.

On the other hand, the equation for Daria's lemonade stand takes into account both the total profit made (which includes the selling price per cup and a fixed tip) and the cost per cup of lemonade sold. So, the equations differ in the fact that one accounts for the cost per cup while the other does not.

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Complete question is

Part A : Sydney made $18.50 selling lemonade, by the cup, at her yard sale. She sold each cup for $0.50 and received a $3 tip from a neighbour. Write an equation to represent this situation.

Part B : Daria made a profit of $21.00 selling lemonade. She sold her lemonade for $0.75 per cup, received a tip of $3 from a neighbour, but also had to buy each plastic cup she used for $0.10 per cup. Write an equation to represent this situation.

Part C: Explain how the equation from part A and part B differ.

Answer:

See below

Step-by-step explanation:

9 x 1/8 = 1.125

10 x 1/8 = 1.25

9 1/2 x 1/8 = 1.1875

12 x 1/8 = 1.5

8 1/2 x 1/8 = 0.5

For detailed, step-by-step explanations you can visit my fiverr account: kesja_

I provide detailed explanations for math questions for as little as $1!

Answer:

9 x 1/8 = 9/8

10 x 1/8 = 10/8 ≈ 5/4

9 1/2 x 1/8 = 19/16

12 x 1/8 = 12/8 ≈ 3/2

8 1/2 x 1/8 = 17/16

you can either turn them to decimals by dividing through or you leave them in Improper fractions or mixed fractions

Answer:

Hi there!

Your answers are:

a) x= 10

b) x= 4

c) x= 2

Step-by-step explanation:

a) 5+2x=25

-5

2x= 20

/2

x= 10

Plug back in!

5+2(10)= 25

5+20=25

25=25✓✓✓

b) 14= 5x-6

+6

5x= 20

/5

x= 4

14= 5(4)-6

14= 20-6

14=14✓✓✓

c) 15= 4x+7

-7

8= 4x

/4

2=x

15= 4(2)+7

15= 8+7

15= 15✓✓✓

Hope this helps!

Answer:

2 because id you take 3 times 2 its 6 divided by 3 is 2

Step-by-step explanation:

5/9×3/10= 15/90 simplification is 1/6

the correct is 1/6

Answer:

The 4th answer is correct

Step-by-step explanation:

\(\frac{5}{9} *\frac{3}{10} \\\\\)

\(\frac{5*3}{9*10}\)

\(\frac{15}{90}\)

Now you can make the answer as the simplest form divide both sides by 15

\(\frac{15}{90} =\frac{1}{6}\)

ANSWER IS,

\(\frac{1}{6}\)

Hope this helps you.

Let me know if you have any other questions :-)

H(Y∣X=X)H(Y) holds for the given joint random variable X and Y.

Given that we have to provide an example of a joint random variable X and Y such that

(i) the entropy of Y given X = x is smaller than the overall entropy of Y.

H(Y∣X=X)H(Y)We have to choose X and Y in such a way that it fulfills the above condition. The entropy of Y given that X = x (H(Y|X = x)) can be defined as follows:

H(Y|X=x) = − ∑i p(Y=yi|X=x) log p(Y=yi|X=x) .Therefore, we must choose X and Y such that H(Y) < H(Y|X=x), or in other words, the entropy of Y given X = x is smaller than the overall entropy of Y.

Example:

Let us take X and Y as 2 random variables such that X takes values -1,0,1 and Y takes values 0,1 such that P(X = -1) = 1/3, P(X = 0) = 1/3, P(X = 1) = 1/3, P(Y = 0) = 1/2, P(Y = 1) = 1/2.

The joint distribution can be represented in the following table:

Therefore, H(Y) = −(1/2 log(1/2) + 1/2 log(1/2)) = 1 bit And,H(Y|X=-1) = −(1/2 log(1/2) + 0 log(0)) = 1/2 bit Similarly,H(Y|X=0) = −(1/2 log(1/2) + 1/2 log(1/2)) = 1 bit And,H(Y|X=1) = −(0 log(0) + 1/2 log(1/2)) = 1/2 bit

Hence, H(Y∣X=X)H(Y) holds for the given joint random variable X and Y.

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Answer:

$54.01

Step-by-step explanation:

All you have to do is $300.00-$245.99 .

Answer:

hi am sorry and am trying to help you but I don't now the answer

Let l be the length of the rectangle and w be the width of the rectangle. Therefore, the area of the rectangle is given by the formula:

We know that the area of the rectangle is given as 81m².

So, 81 = lw

Let's solve for w: w = 81/l

The perimeter of the rectangle is given by the formula: Perimeter of Rectangle = 2(Length + Width)P

= 2(l + w)

Substituting the value of w from the above equation: P = 2(l + 81/l) This is the required expression to calculate the perimeter of the rectangle in terms of length. In order to find the perimeter of a rectangle, we need to know the length and width of the rectangle. We can then use the formula for the perimeter of a rectangle, P = 2(l + w), and substitute the value of w that we just found: P = 2(l + 81/l) This is the required expression to calculate the perimeter of the rectangle in terms of length l.

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