Mathematics help nedd​

1) The relationship between the side lengths in ΔABD is c² = x² + h² by the Pythagorean Theorem.

2) . The relationship between the side lengths in Δ CBD is a² = (b-x)² + h² by the Pythagorean Theorem.

3) The expanded equation is e² = x² -12x + 36 + h²
4) the expanded equation is a² = b²-x²+32

According to the Pythagorean theorem, the square of the hypotenuse (c) of a right triangle equals the sum of the squares of the other two sides  (a² + b²).

So

1) The relationship between the side lengths in ΔABD is c² = x² + h² by the Pythagorean Theorem.

2) The relationship between the side lengths in Δ CBD is a² = (b-x)² + h² by the Pythagorean Theorem.

3) The equation is e² = (6 - x)² + h² when expanded

e² = 36 - 12x + x² + h²
or

e² = x² -12x + 36 + h²

4) Using this equation, we can solve for h² by subtracting (b-x)² from both sides:

a² - (b-x)² = h²

Now we can substitute this expression for h² into the equation given in step 3

2² = 6² - 2bx + (a² - (b-x)²)

Simplifying this equation, we get:

4 = 36 - 2bx + a² - (b-x)²

Expanding the square term, we get:

4 = 36 - 2bx + a² - (b² - 2bx + x²)

Simplifying further, we get:

4 = 36 - b² + x² + a²

Rearranging, we get:

a² = b² - x² + 32

So the equation expanded  is a² = b² - x² + 32.

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Full Question:

For 1 and 2, see attached image.
3)  The equation e²= (6 – x)² + h² is expanded y to become ?
4) Using the equation from step 1, the equation

2² = 6² - 2bx +32+ h becomes a = 62 - 2bx + 2

by substitution

22 = 62 - 2x + x2 +h?

By using trigonometry,

we have shown that tan(15°) = 2 - √3.

One of the most significant areas of mathematics, trigonometry has a wide range of applications. T

he study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry."

Hence, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle.

Angles in trigonometry can be expressed as either degrees or radians. 0°, 30°, 45°, 60°, and 90° are some of the trigonometric angles that are most frequently employed in computations.

We can use the half-angle formula for tangent to show that:

tan(15°) = tan(30°/2) = (1 - cos(30°)) / sin(30°)

We know that cos(30°) = √3/2 and sin(30°) = 1/2, so we can substitute those values in:

tan(15°) = (1 - √3/2) / 1/2

Simplifying the denominator and multiplying by the reciprocal:

tan(15°) = 2(1 - √3/2)

Simplifying the expression:

tan(15°) = 2 - √3

Therefore, we have shown that tan(15°) = 2 - √3.

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To solve the exact differential equation (5t^2 + 8y) dy + (10yt + 9t^2) = 0, we need to check if it is exact or not. We do so by taking partial derivatives with respect to y and t:

∂/∂y (5t^2 + 8y) = 8
∂/∂t (10yt + 9t^2) = 10y + 18t

Since these partial derivatives are not equal, the equation is not exact. To make it exact, we can multiply the entire equation by a integrating factor, which is given by:

μ = e^(∫(∂/∂t)(10yt + 9t^2) dt) = e^(∫(10y + 18t) dt) = e^(10yt + 9t^2)

Multiplying both sides of the equation by μ, we get:

(5t^2 + 8y)e^(10yt + 9t^2) dy + (10yt + 9t^2)e^(10yt + 9t^2) dt = 0

Now, we can check if this equation is exact:

∂/∂y (5t^2e^(10yt + 9t^2) + 8ye^(10yt + 9t^2)) = 10te^(10yt + 9t^2)
∂/∂t ((10ye^(10yt + 9t^2)) + (9t^2e^(10yt + 9t^2))) = 10ye^(10yt + 9t^2) + 18t^2e^(10yt + 9t^2)

These partial derivatives are equal, so the equation is exact. Therefore, we can find a potential function Φ such that:

∂Φ/∂y = 5t^2e^(10yt + 9t^2) + 8ye^(10yt + 9t^2)
∂Φ/∂t = (10ye^(10yt + 9t^2)) + (9t^2e^(10yt + 9t^2))

Integrating the first equation with respect to y, we get:

Φ = ∫(5t^2e^(10yt + 9t^2) + 8ye^(10yt + 9t^2)) dy = (5t^2/10)e^(10yt + 9t^2) + (4y/10)e^(10yt + 9t^2) + C(t)

where C(t) is an arbitrary constant of integration that depends only on t.

Now, we can differentiate this expression with respect to t and compare it to the second equation:

∂Φ/∂t = (10t/10)e^(10yt + 9t^2) + C'(t)
(10ye^(10yt + 9t^2)) + (9t^2e^(10yt + 9t^2)) = (10t/10)e^(10yt + 9t^2) + C'(t)

Comparing the two expressions, we get:

C'(t) = 10ye^(10yt + 9t^2)

Integrating both sides with respect to t, we get:

C(t) = ∫10ye^(10yt + 9t^2) dt = e^(10yt + 9t^2) + K

where K is another arbitrary constant of integration.

Therefore, the solution to the exact differential equation (5t^2 + 8y) dy + (10yt + 9t^2) = 0 is given by:

(5t^2/10)e^(10yt + 9t^2) + (4y/10)e^(10yt + 9t^2) + e^(10yt + 9t^2) + K = 0

or simplifying:

y = (-5t^2/4) - (1/2)e^(-10yt - 9t^2) - (K/4)e^(-10yt - 9t^2)

where K is an arbitrary constant of integration.

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There are no points of inflection.

To determine the intervals on which the function S(x) = (x - 10)(1 - x) is concave up or down and find the points of inflection, we need to find the second derivative and analyze its sign.

First, find the first derivative, S'(x):
S'(x) = (x - 10)(-1) + (1 - x)(1) = -x + 10 - 1 + x = 9

Next, find the second derivative, S''(x):
S''(x) = d(S'(x))/dx = d(9)/dx = 0

Since the second derivative S''(x) is constant and equal to 0, there is no concavity, and the function is neither concave up nor concave down. There are no points of inflection.

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To determine the range and sample standard deviation of tornadoes that touched down during each month of one year, we need to use the data in the table.

However, the table is not provided in the question.

Please provide the table with the number of tornadoes that touched down during each month of one year so I can help you with your question.
To determine the range and sample standard deviation of the number of tornadoes that touched down each month, you'll first need to provide the data in a table format.

Once you provide the data, I can help you calculate the range and sample standard deviation.

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Correct question:

Each​ year, tornadoes that touch down are recorded. The following table gives the number of tornadoes that touched down during each month of one year. Determine the range and sample standard deviation.

3 2 41 115 197 95

70 85 68 64 110 91

Range?

Sample Standard Deviation?

Weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.

Let's assume that Gina has n boxes in total, and let x be the weight of each box in pounds. We can then express the weight of the boxes that weigh less than [tex]1/2[/tex] pound as [tex](1/2)*w1[/tex], where [tex]w1[/tex] is the number of boxes that weigh less than [tex]1/2[/tex] pound. Similarly, we can express the weight of the boxes that weigh more than 1/2 pound as [tex](1/2)*w2[/tex], where [tex]w2[/tex] is the number of boxes that weigh more than [tex]1/2[/tex] pound.

Since Gina puts all the boxes weighing less than [tex]1/2[/tex] pound into a small box, the weight of the small box will be the sum of the weights of all the boxes that weigh less than [tex]1/2[/tex] pound, which is [tex](1/2)*w1[/tex].

Similarly, since Gina puts all the boxes weighing more than [tex]1/2[/tex] pound into a large box, the weight of the large box will be the sum of the weights of all the boxes that weigh more than [tex]1/2[/tex] pound, which is [tex](1/2)*w2[/tex].

The weight difference between the large box and the small box will be:

[tex](1/2)*w2 - (1/2)*w1[/tex]

Simplifying this expression, we get:

[tex](1/2)*(w2 - w1)[/tex]

Therefore, the weight difference between the large box and the small box is [tex](1/2)*(w2 - w1)[/tex] pounds.

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The percentage by which the median earnings of college degree exceed that of high school degreed for 1973 for men is 17.9%

College: Women= 4400

H.School: Women = 3300

Solving we have

The base number is the high  school women.

The difference is 4400 - 3300 = 1100

So the % = (1100/3300) * 100% = 33.3%

1973

The base number is again high school 5600

Difference: 6600 - 5600 = 1000

% = (1000/5600) * 100% = 17.9

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See the aattached image.

Answer:

The first one is - 5 and the other is - 40

Answer:

1024

Step-by-step explanation:

I hope everything I wrote is clear, I really need to sharpen my pencil oof

To multiply the polynomials (1-2t)(5t+t^2), we can use the distributive property and multiply each term in the first polynomial by each term in the second polynomial:

(1-2t)(5t+t^2) = 1(5t+t^2) - 2t(5t+t^2)

Multiplying the first term by each term in the second polynomial, we get:

5t + t^2

Multiplying the second term by each term in the second polynomial, we get:

-10t^2 - 2t^3

Combining like terms, we get:

-2t^3 - 10t^2 + 5t

Therefore, the answer is D. -2t^3 - 9t^2 + 5t.

Your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.

The amount a lender charges a borrower for the use of assets, such as money, consumer goods, or physical assets, is known as an interest rate. It is a fraction of the loan's principal, which is the amount borrowed to cover the cost of the purchase or the deposit made with a bank or other financial institution.

If your best friend is charging you an extra ₹3 for every three months that pass before you return the money, then after nine months, you will owe her an extra ₹9 in addition to the original ₹300.

So the total amount you must pay her if you return the ₹300 after nine months would be ₹309.

To calculate the annual rate of interest she is charging you, we can use the formula:

Annual Interest Rate = (Total Interest / Principal) x (12 / Number of Months)

Where the Principal is the original amount borrowed (₹300), the Total Interest is the extra amount you owe her (₹9), and the Number of Months is the time period for which you borrowed the money (9 months).

Plugging in the values, we get:

Annual Interest Rate = (9 / 300) x (12 / 9) = 0.04 or 4%

So, your best friend is charging you an annual interest rate of 4% for lending you ₹300 for nine months with a quarterly interest rate of 1%.

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The complete question is:

You ask your best friend to lend you ₹300 to buy your favourite toy. She says she can lend you the money only if you give her an extra ₹3 for every three months that pass before you return it. What is the total amount you must pay her if you return it after nine months? What is the annual rate of interest she is charging you?

To multiply these fractions, we can simplify each fraction first:

64e^2/5e * 3e/8e = (8*8*e*e)/(5*e) * (3*e)/(2*2*2*e)

Next, we can cancel out common factors between the numerators and denominators:

= (8*8*1*1)/(5*1) * (1*1)/(2*2*2*1)

= 64/5 * 1/8

= 8.

Answer:

24e^2/5e my answer needs to be 20+characters sooooooooooo

Therefore, the surface area of the mailer is approximately 229.3 square inches.

Total surface area refers to the sum of the areas of all the faces or surfaces of a three-dimensional object. It includes the area of all the faces including the bases, top and sides.

Here,

To find the total surface area of the mailer, we need to find the area of all the faces and then add them up.

First, let's find the area of the rectangular faces. The length of the mailer is 18 inches and the height is 4 inches, so the area of each rectangular face is:

Area of rectangle = length x height

= 18 x 4

= 72 square inches

Since there are 3 rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = 3 x 72

= 216 square inches

Next, let's find the area of the triangular faces. The triangular side is 4.7 inches and the base is 5 inches. To find the area of a triangle, we use the formula:

Area of triangle = (1/2) x base x height

where base is the length of the triangle's base and height is the perpendicular distance from the base to the opposite vertex.

To find the height of the triangle, we can use the Pythagorean theorem since we know the length of the triangular side and the height of the mailer. The Pythagorean theorem states that:

c² = a² + b²

where c is the hypotenuse (the triangular side), and a and b are the other two sides (the height of the mailer and the height of the triangle).

Solving for b, we get:

b = √(c² - a²)

= √(4.7² - 4²)

= 2.66 inches

Now we can find the area of each triangular face:

Area of triangle = (1/2) x base x height

= (1/2) x 5 x 2.66

= 6.65 square inches

Since there are 2 triangular faces, the total area of the triangular faces is:

Total area of triangular faces = 2 x 6.65

= 13.3 square inches

Finally, we add up the areas of all the faces to get the total surface area:

Total surface area = area of rectangular faces + area of triangular faces

= 216 + 13.3

= 229.3 square inches (rounded to one decimal place)

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Answer:

no solution

Step-by-step explanation:

There are no values of x that make the equation true.

Based on the information on the number line, the numbers that represent the percentages are: 42 (100%), 21 (50%), 63 (150%).

To calculate the number that is equivalent to each percentage we must carry out the following procedure: Rule of three. In this case we must take into account that 42 represents 100% of the people.

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Answer:

  A)  x < 15

Step-by-step explanation:

You want the solution to x/3 < 5.

The steps to solving an inequality are basically identical to the steps for solving an equation. There are a couple of differences:

If this were and equation, it would be a "one-step" equation. That step is to multiply both sides by the inverse of the coefficient of x.

The coefficient of x is 1/3. Its inverse is 3. Multiplying both sides by 3, we have ...

  3(x/3) < 3(5)

  x < 15 . . . . . . . . . simplify

Note that 3 is a positive number, so we leave the inequality symbol pointing the same direction.

__

Additional comment

We can swap the sides of an equation based on the symmetric property of equality:

  a = b   ⇔   b = a

When we swap the sides of an inequality, we need to preserve the relationship between them. (This is the meaning of "respect the direction of the inequality symbol".)

  a < b   ⇔   b > a

Besides multiplying and dividing by a negative number, there are other operations that affect the order of values.

Note that the 1/x function is another one that has negative slope, which is why it reverses the ordering for values with the same sign. (It has no effect on ordering of values with opposite signs.)

The Unique or Many for each description by placing a check or X in the appropriate box is given below.

We are given that;

Measurements=  30°, 60°, 90°

Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4.

Now,

If three angle measures are given, and they add up to 180 degrees, then there are infinitely many similar triangles with those angle measures, but they differ in size. This is called the AAA (angle-angle-angle) similarity criterion.

If two angles and a non-included side are given, then there may be zero, one, or two possible triangles with those measurements, depending on the length of the side and the position of the angles. This is called the AAS (angle-angle-side) or SSA (side-side-angle) criterion.

Using criteria, we can fill in the table as follows:

Conditions | Unique | Many Side lengths 3 cm, 6 cm, 7 cm | ✓ | Angle measures 30°, 60°, 90° | | ✓ Angle measures 35º, 35°, 110° | | ✓ Side lengths 5 cm, 5 cm, 5 cm | ✓ | Side lengths 3 in and 4 in with an included 95° angle | ✓ |

Therefore, by the angle the answer will be given.

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The cost of 15 meters of ribbon at the factory is:

15 meters / 3 meters per $7 = 5 times $7 = $35

The cost of 15 meters of ribbon at the store is:

15 meters x $2.50 per meter = $37.50

Therefore, the amount saved by buying 15 meters of ribbon at the factory rather than at the store is:

$37.50 - $35 = $2.50

The theoretical probability of rolling less than 9 on a 12-sided die is 0.6667 or approximately 67%.

To find the theoretical probability of rolling less than 9 on a 12-sided die, we need to count the number of outcomes that satisfy this condition and divide by the total number of possible outcomes.

There are 8 outcomes that satisfy this condition, namely 1, 2, 3, 4, 5, 6, 7, and 8. The total number of possible outcomes is 12, since the die has 12 sides. Therefore, the theoretical probability of rolling less than 9 on a 12-sided die is:

P(less than 9) = Number of outcomes that satisfy the condition / Total number of possible outcomes

= 8 / 12

= 2 / 3

= 0.6667

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There are 39 red blocks out of 65 total blocks.

To solve this problem, we need to find the total number of blocks in each repeating pattern. The pattern is three red blocks followed by two blue blocks. So in each pattern, there are five blocks total.

To find the number of red blocks in 65 total blocks, we need to figure out how many times the pattern repeats. We can do this by dividing the total number of blocks (65) by the number of blocks in each pattern (5):

65 ÷ 5 = 13

So the pattern repeats 13 times.

In each pattern, there are three red blocks. So to find the total number of red blocks, we need to multiply the number of red blocks in each pattern (3) by the number of times the pattern repeats (13):

3 x 13 = 39

Therefore, there are 39 red blocks out of 65 total blocks.

The correct answer is option B.

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The amount of interest earned by Mr. Jones's retirement account over 5 years is $79,025.

Mr. Jones has invested $410,000 in a retirement account that earns 3.85% simple interest per year. Simple interest is calculated by multiplying the principal amount by the annual interest rate and the time period in years.

In this case, the time period is 5 years. Using the formula for simple interest, we can calculate the amount of interest earned on this investment as:

I = P * r * t = $410,000 * 0.0385 * 5 = $79,025

Therefore, the amount of interest earned by Mr. Jones's retirement account over 5 years is $79,025. This means that the total value of his retirement account after 5 years would be $489,025 ($410,000 + $79,025).

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The solution to the problems using trigonometric ratios are:

12a) x = 16.09

12c) x = 7 and y = 7

13a) Time it takes to reach the ground is: 8 seconds

13b) Highest point reached is: 80 ft

12a) Using the law of sines, we can say that:

x/sin 90 = 9/sin 34

x = (9 * sin 90)/sin 34

x = 16.09

12c) Using the law of sines, we can say that:

x/sin 45 = 7√2/sin 90

x = (7√2 * 1/√2)/1

x = 7

Similarly, because it is an isosceles triangle, y = 7

13a) The equation of the height above the ground is :

h = 40t - 5t²

where:

h is height

t is time in seconds

Thus:

Time it takes to reach the ground is at h = 0.

40t - 5t² = 0

5t² = 40t

5t = 40

t = 8 seconds

b) Highest point reached:

h'(t) = 40 - 10t

h'(t) = 0

40 - 10t = 0

t = 4 seconds

Thus:

h_max = 40(4) - 5(4)²

h_max = 80 ft

c) Time at which ball was 35ft off ground is:

35 = 40t - 5t²

5t² - 40t + 35 = 0

Using quadratic equation calculator gives us:

t = 1 and 7 seconds

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The volume of the large box is 120[tex]s^3[/tex].

If Frank can fit 15 cube-shaped containers in each layer and stack 8 layers into one box, then the total number of containers he can fit in one box is:

15 containers/layer x 8 layers = 120 containers

Since each container is cube-shaped, we can assume that it has the same length, width, and height. Let's represent the length of one side of the container as "s". Then, the volume of one container is:

Volume of one container = [tex]s^3[/tex]

The volume of 120 containers that can fit in one box is:

Volume of 120 containers = 120 x Volume of one container

Substituting the expression for the volume of one container, we get:

Volume of 120 containers = 120[tex]s^3[/tex]

Therefore, the volume of the large box that can hold 120 cube-shaped containers with side length "s" is 120[tex]s^3[/tex].

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Statements C and D are statements of causation, while statements A, B, E, and F are not.

Causation refers to the relationship between cause and effect, where a change in one variable causes a change in another variable. Statements of causation imply a cause-and-effect relationship between two variables.

Based on the given statements, the statements of causation are C and D. Statement C implies that higher clarity causes an increase in the price of a diamond, and statement D implies that a higher weight causes an increase in the price of a diamond.

Statements A, B, E, and F are not statements of causation. Statement A only provides information about the cost of a particular diamond and does not explain the reason behind the cost. Statement B suggests a relationship between color and clarity, but it does not imply a cause-and-effect relationship.

Statement E also suggests a relationship between color and price, but it does not imply causation. Statement F only suggests an observation about the relationship between cut grade and price, but it does not imply causation.

In summary, statements C and D are statements of causation, while statements A, B, E, and F are not.

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Answer:

Callum’s method is incorrect because he is confusing the conversion of linear units with the conversion of square units. There are indeed 100 cm in 1 m, but when converting square units, you need to square the conversion factor. So 1 m² is equal to (100 cm)² or 10,000 cm². Therefore, 300 cm² is equal to 0.03 m², not 3 m².

Step-by-step explanation:

Answer:

The answer is wrong because the 3m is still squared if you divided it by 100 then it should only be 3m not 3m^2.

Step-by-step explanation:

I am not 100% sure this is correct so please dont get mad at me.

The situation in which Shawn's activity will result in a final value of zero is Shawn travels east ten feet and then travels south ten feet. The correct option is D.

This is because when Shawn travels east ten feet, he moves horizontally to the right of his starting point. When he travels south ten feet after that, he moves vertically downwards from his previous position, cancelling out the horizontal movement he made earlier.

The displacement caused by Shawn's movement in the east direction is equal in magnitude but opposite in direction to the displacement caused by his movement in the south direction.

The net displacement of Shawn's movement is zero, and he ends up back at his starting point. Options A, B, and C do not involve any movements that result in a net displacement of zero.

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The old plan is cheaper for a customer who writes 10 checks per month.

To determine how many checks a customer must write per month before the new plan is cheaper than the old plan, we need to set up an equation to compare the two plans. Let x be the number of checks written per month. The cost of the old plan is given by:

C_old = 0.08x + 2

The cost of the new plan is given by:

C_new = 3 + 0.15x

To find out when the new plan becomes cheaper, we need to set the two costs equal to each other and solve for x:

0.08x + 2 = 3 + 0.15x

0.07x = 1

x ≈ 14.29

Therefore, a customer would need to write 15 checks per month for the new plan to be cheaper than the old plan.

For a customer who writes 10 checks per month, the cost of the old plan is:

C_old = 0.08(10) + 2 = 2.80

The cost of the new plan is:

C_new = 3 + 0.15(10) = 4.50

Therefore, the old plan is cheaper for a customer who writes 10 checks per month.

The formula for the cost of any number of checks for the old plan is:

C_old = 0.08x + 2

where x is the number of checks written per month

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To evaluate the double integral I = ∬D xy dA, where D is the triangular region with vertices (0,0),(1,0), (0,6), we need to set up the limits of integration for x and y.

Since D is a triangular region, we can integrate over the two sides that meet at the origin and then integrate over the third side. Let's integrate over the sides that form the right angle at (0,0).

For the side along the x-axis, y = 0 to y = 6x.

For the side along the y-axis, x = 0 to x = 1.

Thus, the double integral becomes:

I = ∫0^1 ∫0⁶x xy dy dx

Evaluating the inner integral with respect to y, we get:

I = ∫0^1 [x(y²/2)]0⁶x dx

Simplifying and evaluating the outer integral with respect to x, we get:

I = ∫0^1 18x⁴ dx

I = 18/5

Therefore, the value of the double integral I = ∬D xy dA over the triangular region with vertices (0,0),(1,0), (0,6) is 18/5.
To evaluate the double integral I = ∬_D xy dA for the triangular region D with vertices (0,0), (1,0), and (0,6), we first need to set up the limits of integration.

The base of the triangle lies on the x-axis, from x = 0 to x = 1. The height of the triangle lies on the y-axis, from y = 0 to the line y = 6(1-x), since the slope of the hypotenuse is -6 and passes through (1,0).

Now we can set up the integral:

I = ∬_D xy dA = ∫_(0 to 1) ∫_(0 to 6(1-x)) xy dy dx

Let's first integrate with respect to y:

∫_(0 to 6(1-x)) xy dy = [x(y²)/2]_(0 to 6(1-x)) = 18x(1-x)²

Next, integrate with respect to x:

I = ∫_(0 to 1) 18x(1-x)² dx

Using integration by substitution or expanding and integrating term by term, we get:

I = 2

So, the value of the double integral is 2.

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