The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In ( - x3 + 9x2 +21x + 1) (0 sxs 10). a) Find the number of units that should be sold in order to maximize the total profit. b) What is the maximum profit? a) The number of units that should be sold in order to maximize the total profit is (Simplify your answer.) b) The maximum profit is approximately $. (Do not round until the final answer. Then round to the nearest dollar as needed.)

The best step when constructing a tangent to the circle is to strike an arc on bq with a center of b that has a length the same as the radius of circle q. The correct answer is option a.

When constructing a tangent to a circle with a center point of Q that passes through point B, and having already connected points Q and B to form line segment BQ, the best next step is to: A) Strike an arc on BQ with a center of B that has a length the same as the radius of circle Q.

This will help you find the point where the tangent line intersects the circle, allowing you to complete the tangent construction. The tangent line will be perpendicular to the radius at the point of tangency.

Therefore option a is correct.

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The coordinates of point D would be (0,y) where y is the vertical distance between points A and D.

Without knowing the exact location of point A and the dimensions of the rectangle, it is impossible to determine the coordinates of points B and D with certainty.

However, if we assume that point A is located at (0,0), and the length and width of the rectangle are given by the horizontal and vertical distances between points A and B, and between points A and D, respectively, we can find the coordinates of points B and D.

For example, if the length of the rectangle is 5 and the width is 3, then point B would be located at (5,0) and point D would be located at (0,3).

In general, the coordinates of point B would be (x,0) where x is the horizontal distance between points A and B, and the coordinates of point D would be (0,y) where y is the vertical distance between points A and D.

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45% is the experimental probability that only 1 of 4 children in a family is a girl.

To find the experimental probability that only 1 of 4 children in a family is a girl, we need to count the number of times this outcome occurs in the sample and divide it by the total number of outcomes. In this case, we have 20 coin tosses, and we are looking for sequences with exactly 1 "tails" (girl) and 3 "heads" (boys).

Here are the sequences with exactly 1 girl:
HTHH
HHTT
HHHT
THHT
HTTH
TTHH
THTT
TTHH
THTT

There are 9 such sequences out of the total 20 coin tosses. Therefore, the experimental probability is:

(9/20) * 100% = 45%

The experimental probability that only 1 of 4 children in a family is a girl is 45%.

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To determine the scale factor of the dilation between the green parallelogram and the black parallelogram, you would need to compare the corresponding side lengths of the two parallelograms. For example, if the green parallelogram has a side length that is half of the black parallelogram's side length, the scale factor would be 1/2 (Option B).

If the green parallelogram's side length is twice the black parallelogram's side length, the scale factor would be 2 (Option C). And if the green parallelogram's side length is one-third of the black parallelogram's side length, the scale factor would be 1/3 (Option A). Without specific measurements or a visual representation, it is not possible to accurately identify the scale factor between the two parallelograms. Please provide the side lengths or a diagram to help determine the correct scale factor.

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the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters. So the dimensions of the rectangle are 10 meters by 11 meters.

what is  rectangle ?

A rectangle is a geometric shape that has four straight sides and four right angles (90-degree angles) between them. The opposite sides of a rectangle are parallel and have the same length, so the shape is symmetrical along its horizontal and vertical axes.

In the given question,

Let's assume that the width of the rectangle is x meters. Then, according to the problem, the length of the rectangle is x + 1 meters, since the length and width are consecutive integers.

The perimeter of a rectangle is the sum of the lengths of all its sides. In this case, the perimeter is given as 42 meters, so we can write:

2(length + width) = 42

Substituting the expressions for the length and width in terms of x, we get:

2(x + x + 1) = 42

Simplifying this equation, we get:

4x + 2 = 42

Subtracting 2 from both sides, we get:

4x = 40

Dividing both sides by 4, we get:

x = 10

Therefore, the width of the rectangle is x = 10 meters, and the length is x + 1 = 11 meters.

So the dimensions of the rectangle are 10 meters by 11 meters.

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Answer: 80

Step-by-step explanation: The question is tell us that a certain company  we don't know which one, but it says a certain company has 400 shoes. that is important to note. also 20% of the shoes are black. and One shoe is chosen and replaced. Then the second shoe is chosen. The question is What is the probability that the shoes chosen are black?

Well, take 400 and mutipy it by 20% which changes to 0.20 in decimal form then mutiply your answer by one and you get 80. so the answer is the probability that shoes chosen are black is 80%.

The expression that represents a strategy for estimating the farm's output for 2015 is 1.153w, where w is the farm's wheat output in 2013.

Let w be the farm's wheat output in 2013. We know that the output increased by 9.8% from 2013 to 2014, so the output in 2014 can be estimated as:

w + 0.098w = 1.098w

This expression represents a strategy for estimating the farm's output for 2014.

Similarly, the output in 2015 can be estimated as:

(1.098w) + 0.051(1.098w) = (1 + 0.051)(1.098w)

Simplifying this expression, we get:

1.153w

Therefore, the expression that represents a strategy for estimating the farm's wheat output for 2015 is:

1.153w

where w is the farm's wheat output in 2013 (i.e., 19.8 tons).

So we can estimate the farm's wheat output in 2015 as:

1.153(19.8) = 22.82 tons (rounded to two decimal places)

Note that this is only an estimate, based on the assumption that the percentage increases from 2013 to 2014 and from 2014 to 2015 will continue to hold in the future.

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The value of x in the variation is -2/9

y varies inversely as x and the value of y is 18 and x is 1/2

the first step is to calculate the constant k

k= y/x

k= 18 ÷ 1/2

k= 18 × 2/1

k= 36

From the calculation above the value of k which is the constant is 36

The next step is to calculate x. The value of x can be calculated as follows

k = y/x

36= -10/x

cross multiply

36x= -10

x= -10/36

x= -2/9

Hence the value of x in the variation is -2/9

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The transformation of the function g(x) is g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, a shift of 3 units to the left, and a downward shift of 1 unit applied to the original function f(x) = 5^x.

- Vertical stretch by a scale factor of 2: Multiply the output by 2.

- Shift 3 units to the left: Replace x with x + 3.

- Shift 1 unit down: Subtract 1 from the output.

Thus, the function g(x) can be written as:

g(x) = 2 * f(x + 3) - 1

Substituting f(x) = 5^x, we get:

g(x) = 2 * 5^(x + 3) - 1

Simplifying:

g(x) = 2 * 125 * 5^x - 1

g(x) = 250 * 5^x - 1

The function g(x) is given by g(x) = 250 * 5^x - 1. It represents a vertical stretch by a scale factor of 2, followed by a shift of 3 units to the left, and a downward shift of 1 unit, applied to the original function f(x) = 5^x.

The transformation increases the steepness of the graph, shifts it to the left, and shifts it downward. The expression 250 * 5^x represents the vertical scaling, and the -1 accounts for the vertical shift downward. Overall, g(x) is a modified version of f(x) with these transformations applied.

Therefore, the function g(x) is g(x) = 250 * 5^x - 1.

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The angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s

To calculate the angular velocity of the elbow during an elbow flexion exercise, we'll use the information given about the relative angle at different times. Here's the step-by-step explanation:
First, find the change in relative angle: Δθ = Final angle - Initial angle = 120 degrees - 10 degrees = 110 degrees.
Next, find the change in time: Δt = Final time - Initial time = 0.71s - 0.5s = 0.21s.
Now, calculate the angular velocity: ω = Δθ / Δt = 110 degrees / 0.21s ≈ 523.81 degrees/s.
So, the angular velocity of the elbow during the elbow flexion exercise was approximately 523.81 degrees/s.

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Therefore, two possible values of α are approximately 138.19° and 221.81°.

Sin 180 has a precise value of zero. One of the fundamental trigonometric functions is sine, which is used to calculate the angle or sides of a right-angled triangle.

Given that cos = -8/17, we must determine two potential values for.

We can construct a right triangle with the adjacent side equal to -8 and the hypotenuse equal to 17, and then use the Pythagorean theorem to calculate the opposite side since cos = adjacent/hypotenuse.

The Pythagorean theorem gives us:

opposite² = hypotenuse² - adjacent²

opposite² = 17² - (-8)²

opposite² = 225

opposite = ±15

Both the x and y coordinates are negative in the second quadrant, resulting in:

cos α = -8/17

sin α = -15/17

Consequently, may have the following value: = 180° - arccos(-8/17) 138.19° (rounded to two decimal places)

The x coordinate is negative and the y coordinate is positive in the third quadrant, resulting in:

cos α = -8/17

sin α = 15/17

Therefore, another possible value of α is:

α = 360° - cos(-8/17)

≈ 221.81°

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It took Franny 5 minutes to walk each lap. The correct option is B.

Franny spent a total of 35 minutes walking around the track and made 7 laps around the track, so the total time for all 7 laps is 35 minutes. Let's assume it took Franny t minutes to walk each lap. Then, we can set up the following equation:

7t = 35

We can solve for t by dividing both sides of the equation by 7:

t = 35/7 = 5

Therefore, the correct option is B.

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Answer:

0 hrs 32 mins

Step-by-step explanation:

The image point of (6, 4) after the transformation R₉₀ T₁,₅ is (-3, 11).

The transformation R₉₀ T₁,₅  represents a rotation of 90° counterclockwise around the origin followed by a translation of 1 unit to the right and 5 units up.

To find the image point of (6, 4) under this transformation, we can apply the two transformations in order.

First, let's find the image of (6, 4) after rotating 90° counterclockwise around the origin.

Easy way to do this is by switching the x and y coordinates and negate the new x-coordinate. So, the image of (6, 4) after the rotation is (-4, 6).

Next, we apply the translation of 1 unit to the right and 5 units up. This moves the point (-4, 6) one unit to the right to get (-3, 6), and five units up to get the final image point:

Image point = (-3, 11)

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The value of the missing side is 58. 75

To determine the value of the missing side, we need to know the different identities and their ratios.

These trigonometric identities are;

We have their ratios as;

sin θ = opposite/hypotenuse

tan θ = opposite/adjacent

cos θ = adjacent/hypotenuse

We have that the;

Angle = 57 degrees

Adjacent = 32

Hypotenuse side = x

Then, we have;

Substitute the values for the cosine identity, we get

cos 57 = 32/x

cross multiply

x = 58. 78

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when t=1, y is approximately equal to 5.

To solve for y when t=1 in the equation y=1.5 In(et.t+5), we first need to plug in t=1:

y=1.5 In(e(1)(1)+5)

We simplify the exponent e(1)(1) to just e:

y=1.5 In(e+5)

Using the properties of natural logarithms, we can simplify this further:

y=1.5(1+ln(5+e))

We can use a calculator to evaluate ln(5+e) to be approximately 2.063, so we can plug that in and simplify:

y=1.5(1+2.063)

y=1.5(3.063)

y=4.5945

Rounding this answer to the nearest whole number, we get:

y=5

Therefore, when t=1, y is approximately equal to 5.

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The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.

Money spend =  $400

Time = 120 months

Loan amount = $30,000

Interest rate = 6.5%.

The formula is given P = [tex]PV*(i / (1 - (1+i)^{-n}))[/tex]

The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.

i = 0.065/12 = 0.00541667  

Substituting the values into the formula,

P = [tex]30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})[/tex]

P = $328.05

Therefore, we can conclude that the monthly payment for the loan is $328.05.

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We know that the solutions to the quadratic equation are x=21 or x=-12.

To solve the quadratic equation x^2-19x-39=0 using the method of completing the square, the number that would have to be added to "complete the square" is 91.

First, move the constant term to the right side: x^2-19x=39.

Then, take half of the coefficient of x, square it, and add it to both sides: x^2-19x+90.25=129.25.

This can be factored as (x-9.5)^2=129.25.

Taking the square root of both sides, we get x-9.5=±√129.25.

Solving for x, we get x=9.5±√129.25, which simplifies to x=9.5±11.5.

Therefore, the solutions to the quadratic equation are x=21 or x=-12.

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The length of the rectangle is 15 cm and the width is 9 cm.

Let's start by setting up the equations we need to solve:

L = 2W - 3 (the length is 3 cm less than twice the width)

2L + 2W = 48 (the perimeter is 2 times the length plus 2 times the width)

Now we can substitute the first equation into the second equation and solve for W:

2(2W - 3) + 2W = 48

4W - 6 + 2W = 48

6W = 54

W = 9

Now that we know the width is 9 cm, we can substitute this value back into the first equation and solve for L:

L = 2(9) - 3

L = 15

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It is also possible that there may not be a clear relationship between the two variables or that there may be other factors that influence the number of coats sold, such as seasonal trends or fashion trends.

In mathematics, a variable is a symbol or letter that represents a quantity that can vary or take on different values in a given situation or equation. Variables are commonly denoted by letters such as x, y, z, a, b, c, etc. They are used to represent unknown or changing quantities in mathematical expressions or equations.

For example, in the equation y = 2x + 3, x and y are variables. x represents an unknown value, while y represents the value that results from the equation for a particular value of x. In this case, the variable x can take on different values, and the corresponding value of y will change accordingly.

Variables are used in a wide range of mathematical concepts, such as algebra, calculus, and statistics, to represent and manipulate different quantities and relationships between them.

It is reasonable to expect that there is a negative correlation between the number of coats sold and the outside temperature. In other words, as the temperature gets colder, the number of coats sold would increase, and as the temperature gets warmer, the number of coats sold would decrease. This is because colder temperatures would typically prompt people to buy more coats to stay warm, while warmer temperatures would make people less likely to buy coats. However, it is also possible that there may not be a clear relationship between the two variables or that there may be other factors that influence the number of coats sold, such as seasonal trends or fashion trends.

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The measure of ∠L in Triangle JKL is 56.1 degrees.

In geometry, the measures in triangles refer to the angles and sides within a triangle. Triangles are three-sided polygons, and the measures of their angles and sides are important properties that determine their shape and characteristics.

In a triangle, the sum of the measures of all three angles is always 180 degrees. Therefore, to find the measure of ∠L in Triangle JKL, we can use the information given:

∠J is congruent to ∠L, which means they have the same measure.

∠K is given as 67.8 degrees.

Since ∠J is congruent to ∠L, we can denote their measure as "x".

So, the sum of the measures of ∠J, ∠K, and ∠L is 180 degrees:

∠J + ∠K + ∠L = 180

Substituting the given values:

x + 67.8 + x = 180

Simplifying the equation:

2x + 67.8 = 180

Subtracting 67.8 from both sides:

2x = 180 - 67.8

2x = 112.2

Dividing both sides by 2:

x = 112.2 / 2

x = 56.1

Hence, the measure of ∠L in Triangle JKL is 56.1 degrees.

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Answer: 4

Step-by-step explanation:

[tex]\frac{1}{3} \pi 3^{2} h=12\pi \\3h=12\\h=4[/tex]

[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{\text{x}+2} = -2+5\\\\\sqrt{\text{x}+2} = 3\\\\(\sqrt{\text{x}+2})^2 = 3^2\\\\\text{x}+2= 9\\\\\text{x}= 9-2\\\\\text{x}= 7\\\\[/tex]

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

Check:

[tex](\text{x}+2)^{1/2}-5 = -2\\\\\sqrt{\text{x}+2}-5 = -2\\\\\sqrt{7+2}-5 = -2\\\\\sqrt{9}-5 = -2\\\\3-5 = -2\\\\-2 = -2 \ \ \ \checkmark\\\\[/tex]

The answer is confirmed.

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

The maximum value of s is 9261, which is obtained when x = y = z = 7.

To find the maximum value of s=xyz, we can use the AM-GM inequality, which states that the arithmetic mean of a set of non-negative numbers is greater than or equal to the geometric mean of the same set of numbers.

Mathematically, this can be represented as:[tex](1/3)(x + y + z) \geq (xyz)^(1/3)[/tex]Multiplying both sides of the inequality by[tex]3(xyz)^(1/3)[/tex],

we get: [tex](x + y + z) \geq 3(xyz)^(1/3)[/tex] Now,

we can substitute the given value of x + y + z = 21, to obtain: 21 ≥ [tex]3(xyz)^(1/3)[/tex]

Cubing both sides of the inequality, we get: [tex]21^3 \geq 27(xyz)[/tex]

Simplifying the expression, we obtain: s=[tex]xyz \leq (21^3)/27[/tex]= 9261.

The maximum value of s=xyz is obtained when x = y = z = 7, and the value of s is equal to 9261. This result is obtained using the AM-GM inequality, which is a useful tool for solving optimization problems involving non-negative numbers.

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Answer: To determine if the series –128 + 96 – 72 + 54 – ... is a geometric series, we need to check if the ratio between consecutive terms is constant.

Let's calculate the ratio between the second and first terms:

96 / (-128) = -3/4

Now let's calculate the ratio between the third and second terms:

-72 / 96 = -3/4

The ratio between the fourth and third terms is:

54 / (-72) = -3/4

We can see that the ratio between consecutive terms is always the same: -3/4. Therefore, the series –128 + 96 – 72 + 54 – ... is a geometric series with a common ratio of -3/4.

So the answer is r equals negative three fourths.

Step-by-step explanation:

The series provided is a geometric series because each term after the first is found by multiplying the previous term by -3/4. Therefore, the common ratio 'r' equals -3/4.

In a geometric series, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. In the series given –128 + 96 – 72 + 54 – …, the second term (96) divided by the first term (-128) equals -3/4, the third term (-72) divided by the second term (96) also equals -3/4, and so on. This constant ratio between successive terms demonstrates that this is indeed a geometric series. Therefore, the statement that proves this is a geometric series is 'r equals negative three fourths' where r represents the common ratio.

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For question 2, the zoologists can conduct an analysis of variance (ANOVA) test to investigate whether the four different diets impact the weight gains of the 6-month baby elephants. The ANOVA test will compare the mean weight of each diet group to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the zoologists can conclude that the diets are impacting the weight gains of the baby elephants.

For question 3, the researchers can also conduct an ANOVA test to investigate whether the nursery locations affect the growth of oak trees. The test will compare the mean circumference growth of the oak trees at each nursery location to determine if there is a statistically significant difference between them. If the test shows that there is a significant difference, then the researchers can conclude that the nursery locations are impacting the growth of the oak trees.

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For a normal distribution with a mean of 68 and a standard deviation of 9, the percentage of scores less than 50 is 2.28%.

It is given that scores on a psychology exam have a normal distribution with a mean of 68 and a standard deviation of 9. The percentage of scores less than 50 can be determined as follows.

1. Calculate the z-score for 50 using the formula:

z = (X - μ) / σ

where

X = 50 (the value we're comparing to)

μ = 68 (mean)

σ = 9 (standard deviation)

2. Plug in the values:

z = (50 - 68) / 9 = -18 / 9 = -2

3. Use a z-table or calculator to find the area to the left of z = -2. This represents the percentage of scores less than 50.

4. Based on the z-table or calculator, the area to the left of z = -2 is approximately 0.0228, which means that around 2.28% of scores were less than 50.

So, about 2.28% of scores on the psychology exam were less than 50.

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After 50 minutes, you will have placed 675 pieces

Given, you are doing a 5000 piece puzzle. You have already placed 175 pieces, and every minute you place 10 more pieces. After 50 minutes, we need to find how many pieces you will have placed.

We can start by finding the number of pieces you place in 50 minutes.

Every minute, you place 10 more pieces, so in 50 minutes, you will place:

10 x 50 = 500 pieces

Adding the pieces you have already placed, we get:

175 + 500 = 675 pieces

Therefore, after 50 minutes, you will have placed 675 pieces

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DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

In the given figure, we have a triangle DEF, where EF is a transversal intersecting DE and DF at points X and Y, respectively, such that XY || DE.

    D

   / \

  /   \

 /     \

E-------F

Given that XF = 10, YF = 5, and EF = 13, we need to find DY.

We can start by using the property of similar triangles. Since XY || DE, we have the following similarity ratios:

EF / ED = EY / EJ  (where J is the intersection of XY and DF)

EF / DF = EJ / EY

Substituting the given values, we get:

13 / ED = EY / EJ

13 / DF = EJ / (13 - EY)

Multiplying the above two equations, we get:

13 / ED * 13 / DF = EY / EJ * EJ / (13 - EY)

169 / (ED * DF) = EY / (13 - EY)

Substituting the values of XF = 10 and YF = 5, we get:

169 / (ED * DF) = 5 / 8

ED / DF = 135 / 169

Using the Pythagorean theorem on triangles DEX and DFY, we get:

ED^2 = EX^2 + DX^2

DF^2 = FY^2 + DY^2

Since EX + DX = EF = 13, we have DX = 13 - EX. Substituting this in the first equation and simplifying, we get:

ED^2 = EX^2 + (13 - EX)^2

ED^2 = 2EX^2 - 26EX + 170

Similarly, substituting FY = 13 - EY in the second equation and simplifying, we get:

DF^2 = FY^2 + DY^2

DF^2 = 170 - 26EY + EY^2 + DY^2

Now, using the fact that ED/DF = 135/169, we can substitute ED^2 = (135/169)^2 * DF^2 in the above equation for ED^2, and simplify to get:

(135/169)^2 * DF^2 = 2EX^2 - 26EX + 170

DF^2 = 170 * 169^2 / (135^2 + 2EX^2 - 26EX)

DF^2 = 170 * 169^2 / (135^2 + 2(10^2) - 26EX)   (Substituting XF = 10)

Similarly, we can substitute EY = 5 in the above equation for DF^2 and simplify to get:

FY^2 + DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY)   (Substituting YF = 5)

DY^2 = 170 * 169^2 / (135^2 + 2(5^2) - 26EY) - FY^2

Substituting the given values, we get:

DF^2 = 170 * 169^2 / (135^2 + 200 - 26EX) = 106.7027

DY^2 = 170 * 169^2 / (135^2 + 50 -

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