Find the surface area of a triangle prism side of the right triangular base measure 9 cm 12 cm and 15 cm the height Prism is 20 cm

The view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

The view factor (F) from Surface A to Surface B can be calculated using the formula:

F = A / (A + B)

where A and B are the areas of Surface A and Surface B, respectively.

The area of a triangle can be calculated using Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter of the triangle and a, b, and c are the side lengths of the triangle.

For Surface A:

a = 2 cm

b = 3 cm

c = 4 cm

s = (a + b + c) / 2 = (2 + 3 + 4) / 2 = 4.5 cm

Area_A = sqrt(4.5 * (4.5 - 2) * (4.5 - 3) * (4.5 - 4))

= √(4.5 * 2.5 * 1.5 * 0.5)

=√(5.625) ≈ 2.37 cm²

For Surface B:

a = 2 cm

b = 4 cm

c = 3 cm

s = (a + b + c) / 2 = (2 + 4 + 3) / 2 = 4.5 cm

Area_B = √(4.5 * (4.5 - 2) * (4.5 - 4) * (4.5 - 3))

= √(4.5 * 2.5 * 0.5 * 1.5)

=√(5.625) ≈ 2.37 cm²

Now we can calculate the view factor (F):

F = Area_A / (Area_A + Area_B)

= 2.37 / (2.37 + 2.37)

≈ 0.5

Therefore, the view factor from the 2 cm side to the 4 cm side of the infinitely long three-sided triangular enclosure is approximately 0.5.

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The number of terms required to evaluate the expression π = 48 \(tan^{-1}\)(1/18) + 32 \(tan^{-1}\)(1/57) - 20 \(tan^{-1}\)(1/239) with an error magnitude less than a given threshold cannot be determined without specifying the threshold value. The accuracy of the evaluation depends on the threshold chosen, and the number of terms needed in the Taylor series for \(tan^{-1}\) x will vary accordingly.

The Taylor series expansion for \(tan^{-1}\) x is given by the formula:

\(tan^{-1}\) x = x - (\(x^{3}\))/3 + (\(x^{5}\))/5 - (\(x^{7}\))/7 + ...

To estimate the number of terms needed, we can analyze the size of the remaining terms in the series. We want the magnitude of the error to be less than a specified threshold.

By comparing the terms of the series with decreasing powers of x, we can observe that as x becomes smaller, the terms in the series become smaller as well. Therefore, to ensure the error is within the desired threshold, we need to evaluate the terms until the magnitude of the next term is smaller than the threshold.

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The equation, rearranged to isolate c, is: c = (a + bd) / b

In order to isolate c, we need to get c by itself on one side of the equation. Here's how we can do that:

First, we can distribute the b to get:
a = bc - bd

Next, we can add bd to both sides of the equation:
a + bd = bc

Finally, we can divide both sides by b to isolate c:
(a + bd) / b = c

The equation, rearranged to isolate c, is: c = (a + bd) / b

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The maximum distance the dog can be from the house is 8 meters and the minimum distance the dog can be from the house is also 8 meters on the basis of the equation |x - 500|.

The equation |x - 500| can be used to find the maximum and minimum distances that Morgan's dog may be from her house while walking on an 8-meter-long leash.
The equation |x - 500| represents the absolute value of the difference between the dog's distance from the house (x) and 500 meters. The absolute value ensures that the result is always positive.
To find the maximum distance, we need to consider the scenario where the dog is as far away from the house as possible. In this case, the dog would be at the end of the 8-meter-long leash, which means x would equal 500 + 8 = 508 meters. Plugging this value into the equation gives us |508 - 500| = 8 meters which is the maximum distance.
To find the minimum distance, we need to consider the scenario where the dog is as close to the house as possible. In this case, the dog would be at the other end of the leash, which means x would equal 500 - 8 = 492 meters. Plugging this value into the equation gives us |492 - 500| = 8 meters which is maximum distance.
In summary, the maximum and minimum distances that the dog may be from the house while walking on an 8-meter-long leash are both 8 meters.

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Answer:

b. 8

Step-by-step explanation:

Simplify the left side by dividing the top and bottom by 5

35/5 = 7

40 /5 = 8

7/8

Hey there!

35/40 = 7/x

Cross Multiply the fraction

35(x) = (7)(40)

→ 35x = 280

DIVIDE 35 to BOTH SIDES

35x/35 = 280/35

CANCEL out: 35/35 because that gives you 1

KEEP: 280/35 because that helps solve for the x-value

→ x = 280/35

x = 8

Therefore, your answer is most likely: 8 (Option B)

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

If two sides and the included angle of one triangle are congruentto the corresponding parts of another triangle, the triangles are congruent.

Since:

Then, in order to the triangles be congruent:

Answer:

A

Refer to the attachment! v

The emphasis is on the Counting and Cardinality standard in the early childhood years according to the National Council of Teachers of Mathematics.

The National Council of Teachers of Mathematics emphasizes the following standards in the early childhood years:

- Counting and Cardinality

- Operations and Algebraic Thinking

- Number and Operations in Base Ten

- Measurement and Data

- Geometry

The National Council of Teachers of Mathematics recognizes that all five math standards are important in the early childhood years. However, they place a particular emphasis on the standards related to counting and cardinality. This includes developing skills in counting, understanding numbers, and recognizing numerical relationships.

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To critically evaluate the solution of the differential equation obtained in the previous part, we can model the equation in Simulink and analyze its behavior.

To critically evaluate the solution of the differential equation, we can use Simulink to model the equation and visualize the system's behavior. By connecting the appropriate blocks and specifying the values of the constants, we can simulate the system and observe its response over time. By plotting the relation between the distance in meters and the force applied on the mass, we can analyze the characteristics of the system's behavior.

The solution of the differential equation may include terms that represent the transient state, which describe the initial response of the system before it settles into a steady state. These terms decay over time and eventually vanish. On the other hand, the terms representing the steady state remain constant once the system has reached a stable equilibrium.

The time needed for the system to reach a steady state value depends on the characteristics of the system and the initial conditions. It can be evaluated by observing the behavior of the system in the simulation and determining when the response stabilizes.

The speed of the system's response is influenced by various constants in the differential equation, such as the coefficients and parameters. For example, increasing the coefficient of a damping term can lead to a faster decay of transient oscillations, resulting in a faster response. Similarly, adjusting the parameters related to stiffness or inertia can impact the system's response time.

To demonstrate the effect of different constants on the speed of the system's response, we can model various cases by varying the values of these constants. By comparing the responses of the different cases, we can observe how changes in the constants affect the system's behavior and determine the conditions that lead to a faster response.

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The probability that the three pieces can be assembled into a triangle is 25%

Let the length of the stick be 1, so each break can occur at a position in the interval [0,1]. Let x and y be the two breaks in the stick. Then the area of the region in the square bounded x=0, x=1, y=0, y=1, which represents combinations of x and y, for which we can form a triangle. Since the area of the whole square is 1, the area of the region inside is the probability of the triangle.

If y>x, then the lengths of the pieces are x, y-x, and 1-y.

The triangle inequality must hold for each combination of edges.

for  y>x ...

x+y−x≥1−y

x+1−y≥y−x

y−x+1−y≥x

these simplify to...

for  y>x ...

y≥1/2

x+1/2≥y

x≤1/2

If we cut our 1x1 square into two triangles along the line x=y,

then the region in the upper triangle which satisfies the inequalities above forms a smaller triangle which connects the midpoints of the upper triangle.

The lower triangle (x>y), is just a reflection about x=y of the upper triangle, so together, the entire region looks like a bow-tie at a 45 degree angle.

This region takes up 25% of the square,

Thus, the probability that the three pieces can be assembled into a triangle is 25%

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Answer:

15x+10

Step-by-step explanation:

All you need to do is multiply 5 by 3x and 5 by 2

Step-by-step explanation:

\(5(3x + 2) \\ 15x + 10\)

if you want to find the value of x then

\(15x + 10 = 0 \\ 15x = - 10 \\ \\ x = - \frac{10}{15} \\ \\ x = - \frac{2}{3} \)

Answer:

Honestly I don't know but I hope you have a good day

Answer:

Part A:

d - 0.05 = c

Part B:

$59.85

Answer:

- 9 + 12x

Step-by-step explanation:

- 3(3 - 4x) ← multiply each term in the parenthesis by - 3

= - 9 + 12x

Answer:

12\(\sqrt{x}\)

Step-by-step explanation:

(144x)^1/2

(ab) ^ 1/2 = a^1/2 b^1/2

144 ^ 1/2  x^1/2

12 x^1/2

In radical form

12\(\sqrt{x}\)

The table has a greater rate of change.

The rates of change are equal.

In the given problem, we have a table showing the relationship between x and y values. By comparing the change in y with the change in x, we can determine the rate of change. Looking at the table, we observe that for every increase of 1 in x, there is a corresponding increase of 1 in y. Therefore, the rate of change for this table is 1.

The slopes are equal.

The equation has a greater slope.

In problem 2, we are given a linear equation in the form y = mx + b, where m represents the slope. The given equation is y = 2x + 7, which means the slope is 2. To compare the rates of change, we compare the slopes. If the slopes are equal, the rates of change are equal. In this case, the slopes are equal to 2, so the rates of change are the same.

The function rule has a greater slope.

The slopes are equal.

In problem 3, we are told that as x increases by 1, y increases by 3. This information gives us the rate of change between x and y. The slope of a function represents the rate of change, and in this case, the slope is 3. Comparing the slopes, we find that they are equal, as both have a value of 3. Therefore, the rates of change are the same.

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Answer:

65

Step-by-step explanation:

Answer:

the opposite of 9

Step-by-step explanation:

the absolute value of nagative 9, is positive 9.

the absolute value of postive 9, is postive 9.

the distance between 0 and nagative 9 on a line would be a count of postive 9.

the opposite of postive 9 is negative 9 (the only one with a diffrent outcome)

Cans of regular Coke probably weigh more than cans of Diet Coke due to the extra metal present in a regular Coke can but not a Diet Coke can. The correct answer is A.

Regular Coke contains sugar, which means that it has a higher density than Diet Coke, which uses artificial sweeteners. However, the difference in density alone would not account for a noticeable difference in weight between the two types of cans.

The primary reason that cans of regular Coke weigh more than cans of Diet Coke is that regular Coke cans are made of thicker metal than Diet Coke cans. This is because regular Coke contains acids that can corrode the metal over time, and the thicker metal helps prevent this from happening. Diet Coke, on the other hand, does not contain these acids, so the cans can be made with thinner metal.

Therefore, due to the extra metal present in regular Coke cans but not in Diet Coke cans, cans of regular Coke would weigh more than cans of Diet Coke.

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The surface area of the right prism with right triangular bases and height of 15 inches is bh + 15(a + b + c).

It can be found by adding the area of the two triangular bases and the area of the three rectangular faces:

Surface area = 2(Area of base triangle) + (Perimeter of base triangle x height of prism)

To find the area of the base triangle, we can use the formula A = 1/2bh, where b is the base of the triangle and h is its height. The perimeter of the triangle is simply the sum of its three sides.

So, if we let the base of the triangle be b, and the height of the triangle be h, then the area of the base triangle is A = 1/2bh. The perimeter of the triangle is P = a + b + c, where a, b, and c are the lengths of its sides.

Thus, the surface area of the prism is given by:

Surface area = 2(1/2bh) + (a + b + c) x 15

Simplifying the expression gives us the final answer:

Surface area = bh + 15(a + b + c)

Therefore, the surface area of the right prism with right triangular bases and height of 15 inches is bh + 15(a + b + c).

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Answer

There are 12 more yellow apples than red.

Step-by-step explanation:

How exactly?

First find how many bags of YELLOW apples. 9 bags in total and there is 1 bag of green apples and 3 bags of red apples so 9-(3+1)= 5 bags of YELLOW apples.

So we know there is 1 bag of GREEN apples and since each bag holds/ contains 6 apples we also know that 1x6= 6 so  g or GREEN apples is 6.

Now lets find how many RED apples there are :D. There are 3 bags of RED apples each containing 6 apples so we know 6+6+6= so r or RED apples is 18.

So, now we find how many YELLOW apples there are. 6 apples in each bag and there are 5 bags remaining for YELLOW apples we do 6x5 which equals 30 apples ( WOW My girl PAM?! She looove her yellow apples)

Lastly we know there are 30 yellow apples and 18 red apples we also know the question asked " How many MORE yellow apples are there than red apples?" so this means we subtract. 30-18= 12 MORE YELLOW APPLES THAN RED APPLES

Thee value 150 kilograms is equal to 330.69 pounds. The units pound and kilogram are the units of measurements.

The pound (lb) and kilogram (kg) are both units of measurement used to express weight, but they are part of different systems of measurement. The pound is part of the imperial system commonly used in the United States and the United Kingdom, while the kilogram is part of the International System of Units (SI).

This can be calculated by multiplying 150 by the conversion factor of 2.20462.

To perform the conversion, simply multiply the number of kilograms by 2.20462.

1 Kg = 2.20462

150 Kg = 150 x 2.20462 = 330.69 lb

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Answer:

3 2 /5 ×3

change 3 2 /5 into an improper fraction

then you will get 17 /5

after that you say 17/5 ×3/1

=(17×3)/ (5x1)

=51/5 (51÷5)

=10.2/ 10 1/5

\(3 \frac{2}{5} \times 3 \\ = \frac{17}{5} \times 3 \\ = \frac{51}{5} \\ = 10 \frac{1}{5} \)

\(10 \frac{1}{5} \)

Hope it helps.

Do comment if you have any query.

The graph indicate the difference between the paths will be zero at distances of 2 feet and 7 feet.

Function is a type of relation, or rule, that maps one input to specific single output.

The path of the first player's ball can be represented by the function as;

g(x) = –2x² + 11x + 6,

where x represents the distance from the coach.

The path of the second player's ball can be represented by the function as;

h(x) = –x² + 4x + 12.

We are interested in the values of x such that; g(x) = h(x). These will be solutions of the difference SHOWN AS g(x) -h(x) = 0.

Hence, the x-intercepts of a graph of the difference g(x) -h(x) will be solutions.

The graph indicate the difference between the paths will be zero at distances of 2 feet and 7 feet.

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Answer:

G

Step-by-step explanation:

• The intersection of lines n and k is point V.

• Point X is the intersection of line m and plane A.

We can infer  the following from the diagram :

We can see that the intersection of any two planes will produce a line at the intersection point of plane A and plane S, the line CW is formed and also the lines intersect at a point, the intersection point of line n and line k is point V.

• The point X in the diagram is brought about by the intersection of line m on the plane A .

In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or another line.

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