1. ΔABD ≅ ΔCBD by SAS congruence theorem.
2. ΔABD ≅ ΔCBD by SSS congruence theorem.
What is the SAS and the SSS Congruence Theorem?The SAS Congruence Theorem and the SSS Congruence Theorem are two postulates used in geometry to determine whether two triangles are congruent. The SAS Congruence Theorem requires that two sides and the included angle of one triangle be congruent to two sides and the included angle of another triangle for them to be congruent.
The SSS Congruence Theorem requires that all three sides of one triangle be congruent to the corresponding sides of another triangle for them to be congruent.
1. With the given information, we can deduce that, both triangles have two pairs of congruent sides which are:
BD ≅ BD (based on reflexive property)
AB ≅ CB (midpoint definition)
<ABD ≅ <CBD (right angles are congruent)
Thus, we can conclude that ΔABD ≅ ΔCBD by SAS congruence theorem.
2. Given the new information, it means that the two triangles have three pairs of congruent sides which are:
AD ≅ CD (given)
BD ≅ BD (based on reflexive property)
AB ≅ CB (midpoint definition)
Therefore, ΔABD ≅ ΔCBD by SSS congruence theorem.
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A plastic bag contains 0.80 mol of gas and occupies a volume of 18 L. A leak in the bag allows gas to escape until the volume becomes 16 L. How many moles of gas remain in the bag?
0.31 mol
0.91 mol
0.51 mol
0.71 mol
To find the moles of gas remaining in the bag, we can use the initial and final volumes and the initial moles of gas. Since the temperature and pressure remain constant, we can use the formula:
Initial moles × Initial volume = Final moles × Final volume
0.80 mol × 18 L = Final moles × 16 L
Solve for the final moles:
(0.80 mol × 18 L) / 16 L = Final moles
14.4 mol / 16 L = Final moles
Final moles = 0.9 mol
So, 0.9 moles of gas remain in the bag after the leak. The closest answer is 0.91 mol, so the correct option is:
0.91 moles of gas remain in the bag.
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a list of numbers is considered increasing if each value after the first is greater than or equal to the preceding value. the following procedure is intended to return true if numberlist is increasing and return false otherwise. assume that numberlist contains at least two elements.
Option C is the correct option for the given problem; let’s consider all options and identify the different reasons in the number list.
How would we write this code?From the second element (index 1) through the last element, this procedure iterates through the list of numbers using a for loop. It determines whether the current number is lower than the previous number after each repetition. If it is, the process gives a prompt False response, meaning that the list is not growing.
The procedure returns True, indicating that the list is growing, if the for loop concludes without running into a number that is less than the number it encountered before.
According to the issue definition, this technique implies the list has at least two elements. This guarantees that the for loop will always have a previous number to compare to.
Comments are written in italic to explain the code
Line 1: PROCEDURE Is Increasing(numberList)//start Is Increasing procedure with a list number List
Line 2: {//start procedure
Line 3: count<-2//set count to be 2
Line 4: REPEAT UNTIL (count -> LENGTH(numberList)//repeat from element 2 to last
Line 5: {//start repeat
Line 6: IF(numberList[count] < numberList[count-1]//if previous number is greater
Line 7: {//start if
Line 8: RETURN(true)//return true as next is greater than
Line 9: }//end if
Line 10: count<- count +1//increment to next element
Line 11: }//end repeat
Line 12: RETURN (false)//return false
Line 13: }//end procedure
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Complete question is:
A list of numbers is considered increasing if each value after the first is greater than or equal to the preceding value. The following procedure is intended to return true if numberList is increasing and return false otherwise. Assume that numberList contains at least two elements. PROCEDURE isIncreasing(numberList) Tue 61 Line 1: Line 2: { Line 3: count 2 Line 4: REPEAT UNTIL(count > LENGTH(numberList)) Line 5: } IF(numberList[count] < numberList[count - 1]) Line 6: Line 7: To entd Line 8: RETURN(true) :80 onij { count count + 1 Line 9: Line 10: er onil Line 11: } Line 12: RETURN(false) BELAS(ConuE) Line 13: } Which of the following changes is needed for the program to work as intended? Lines 8 and 12 should be interchanged. c. In line 6, < should be changed to >=. a. b. Lines 10 and 11 should be interchanged. d. In line 3, 2 should be changed to 1. 3.
Sally left the city for vacation. Sandy left six hours later going 82 miles faster to catch up. After 5 hours Sandy caught up. What was Sally's average speed?
Answer: It took Sandy 11 hours to travel the same distance that Sam took 5 hours. {{{R[s]*11=5*75}}}
{{{R[s]=(5/11)*75}}}
{{{R[s]=34.9}}}{{{mph}}}
Don't ask sometimes i don't make sense...
The final answer is 11 hours... Hope this helps... Stay safe and have a great weekend!!! :D
Answer:
68 1/3
Step-by-step explanation:
Going 82 mph faster for 5 hours, Mary closed a (82 mi/h)×(5 h) = 410 mile gap. That gap was created in 3 hours by Sandy going.
(410 mi)/(6 h) = 68 1/3 mi/h
please mark me as brainliest. l am bagging you please.
Solve the system using substitution:
y = -6x + 7
3x – 2y = 16
helppp
Answer:
x=-6 y=-1
Step-by-step explanation:
// Solve equation [2] for the variable y
[2] y = -x - 7
// Plug this in for variable y in equation [1]
[1] 3x - 2•(-x -7) = -16
[1] 5x = -30
// Solve equation [1] for the variable x
[1] 5x = - 30
[1] x = - 6
// By now we know this much :
x = -6
y = -x-7
// Use the x value to solve for y
y = -(-6)-7 = -1
Solution :
{x,y} = {-6,-1}
Answer: 1 .x=-1/6y+7/6 (2.x=2/3y+16/3
Step-by-step explanation:
I need help with this practice problem solving from the trig section in my ACT prep guide
Step 1
Find the polar coordinates of the rectangular coordinates
\((-\sqrt[]{3},1)\)To convert from the cartesian coordinates (x,y) to polar coordinates (r,θ), we use the following equation.
\(r^2=x^2+y^2\)\(\theta=arc\tan (\frac{y}{x})\)Step 2
We have;
\((x,y)=(-\sqrt[]{3},1)\)\(\begin{gathered} r^2=(-\sqrt[]{3})^2+1^2 \\ r^2=3+1 \\ r=\sqrt[]{4} \\ r=2 \\ \end{gathered}\)\(\begin{gathered} \theta=arc\tan (\frac{y}{x}) \\ \theta=arc\tan (\frac{1}{-\sqrt[]{3}}) \\ \theta=\arctan (\frac{1}{-\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}) \\ \theta=\arctan \frac{\sqrt[]{3}}{-3} \\ \theta=-\frac{\pi}{6}+\pi \\ \theta=\frac{5}{6}\pi \end{gathered}\)The answer therefore is;
\((2,\frac{5\pi}{6})\)Another easy question need fast please
Answer:
30.25
Step-by-step explanation:
All angles of a line must add up to 180. Since we already know that one angle is 90 degrees, we know that the other angles should add up to 90 degrees in order for all of the angles to add up to 180 degrees:
(3x-7)+(x+8)=90
4x+1=90
4x=89
x=22.25
22.25+8= 30.25
IM GIVING 100PTS & BRAINLIEST! -- ]
You are paid $10 per hour. You work 13 hours each week. Your taxes are federal, 10%; FICA, 7.65%; and state, 3%. You also contribute $30 to your company's retirement plan.
If you are paid weekly, how much is your realized income?
If i paid weekly, I realized my income is $73.155.
Answer:
Solution given;
1 hour =$10
13 hour = 13*10=$130
Taxes
federal :10%
FICA:7.65%
state: 3%
contribute to company: $30
now
My income each week :
$130-10%of $130-7.65% of $130-3% of $130-$30$130-$30-$13-$9.945-$3.9$73.155Three objective functions for linear programming problems are 7A+10B,6A+4B, and −4A+7B. Show the graph of each for objective function values equal to 420 .
Graph of each objective function using linear programming.
Here,
Putting the equation equal to 420 and plotting the graph by finding the value of A and By putting A=0 and finding B then putting B=0 and finging A.
For example putting A=0 in 7A+10B=420 will yield (0,42) and Putting B=0 will yield (60, 0). plotting theses points on graph and joining them to generated the line.
Repeating thin step for each objective function and plotting the graph.
7A + 10B = 420 is labelled as a.
6A+4B = 420 is labelled as b.
-4A + 7B = 420 is labelled as c .
The graph of each function is attached below.
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If an Australian contractor ordered $340,000 U.S. Dollars worth of steel from an American company, what is the cost of the steel in Australian dollars? (Enter a number as an exact integer or decimal.)
Answer:
466895
Step-by-step explanation:
If you know the conversion, it's easy.
1 US dollar is about 1.37322 Australian.
so, you multiply 340,000 times 1.37322 and get about 466895 Australian dollars
The formula for relating a man's shoe size S and the length of his foot L in inches is
S3L
26. Find the length of a man's foot if he wears a size 12 shoe.
Answer:
12 5/6 inches
Step-by-step explanation:
You want to find the value of L when S=12 1/2, using the formula S = 3L -26.
Foot lengthYou can substitute for S in the formula before or after you solve for L. Here, we'll solve for L first:
S +26 = 3L . . . . add 26 to both sides
(S +26)/3 = L . . . . divide both sides by 3
Substituting 12 1/2 for S, this becomes ...
L = (12 1/2 +26)/3 = (38 1/2)/3 = (77/2)/3 = 77/6 = 12 5/6
A man's foot is 12 5/6 inches long if he wears a size 12 1/2 shoe.
Answer:
the length of his foot in inches is 12
Please help me answer this question, it was due yesterday .
Answer:
FA=7.29
Step-by-step explanation:
\(FD=\sqrt{10^{2}-8^{2} } \\FD=\sqrt{36} \\FD=6\\\)
∠EDF=53° (properties of retangle)
∠EAD=180-90-53 (∠ sum of Δ)
=37
\(\frac{AD}{sin90} =\frac{8}{sin37} \\AD=13.29\)
FA=AD-FD
FA=7.29
Evaluate the triple integral of
f(x,y,z)=z(x2+y2+z2)−3/2f(x,y,z)=z(x2+y2+z2)−3/2 over the part of
the ball x2+y2+z2≤81x2+y2+z2≤81 defined by z≥4.5z≥4.5.
The value of the triple integral is 21π/8.
To evaluate the triple integral, we use spherical coordinates since we are dealing with a ball. The bounds for the radius r are 0 to 9, the bounds for the polar angle θ are 0 to 2π, and the bounds for the polar angle φ are arccos(4.5/9) to π. Substituting these bounds into the integral expression, we integrate the function
\(f(x, y, z) = z(x^2 + y^2 + z^2)^(-3/2)\)
over the given region. After performing the calculations, the value of the triple integral is found to be 21π/8, representing the volume under the function over the specified region of the ball.
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There are 5 pencils in a pack.
Catalina has 2 packs. How many
pencils in all?
(unit)
Reese has 20 packs. How many
pencils in all?
(unit)
Answer:
Catalina has 10 pencils total. (2 x 5 = 10)
Reese has 100 pencils total. (20 x 5 = 100)
Answer:
1. 10 2. 100
Step-by-step explanation
5 x 2= 10
20x 5= 100
for adults in the town of bridgeport, systolic blood pressure is normally distributed with a mean of 137 mmhg and a standard deviation of 9 mmhg. what percentage of adults in the town have a systolic bloo pressure less than 110 mmhg
99.85% of adults in the city have a systolic blood pressure of less than 110 mmHg.
Using 68-95-99.7 rule, we know that
99.7% of values lie between the interval (mean - 3 × standard deviation, mean + 3 × standard deviation)
(100 - 99.7) = 0.3% values lie outside the interval (mean - 3 × standard deviation, mean + 3 × standard deviation).
Since the normal distribution is bell-curved and symmetrical,
we can say
0.3/2 = 0.15% values are less than the mean - 3 × standard deviation
and 0.3/2 = 0.15% values are greater than mean + 3 × standard deviation.
Here,
Mean + 3 × standard deviation.
= 110 + 3 × 10 = 140
So, 0.15% of values are greater than 140
So, (100 - 0.15) = 99.85% values are less than 140.
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a sphereical balloon is inflating with helium at a rate of 128pi ft^3/min. how fast is the balloon's radius increasing at the instant the radius is 4 ft
A sphereical balloon is inflating with helium at a rate of \(128\pi ft^3/min\).The balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.
To find the rate at which the balloon's radius is increasing, we can use the relationship between the volume of a sphere and its radius. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius.
We are given that the volume is increasing at a rate of 128π ft³/min. Taking the derivative of the volume formula with respect to time, we have dV/dt = 4πr²(dr/dt), where dV/dt represents the rate of change of volume and dr/dt represents the rate of change of the radius.
At the instant when the radius is 4 ft, we can substitute r = 4 into the equation. Solving for dr/dt, we have 128π = 4π(4)²(dr/dt), which simplifies to dr/dt = 8 ft/min.
Therefore, the balloon's radius is increasing at a rate of 8 ft/min when the radius is 4 ft.
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Khalil has a game board as shown below, which is a square with 20 cm sides. The area of the largest circle is 314
square centimeters
What is the probability of scoring 1, 3, or 5 points with one randomly thrown dart?
O 50%
O 62.5%
O75%
O78.5%
Answer:
78.5
Step-by-step explanation:
The probability of scoring 1 , 3 or 5 points is 78.5% ( optionD)
What is probability?A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty of an event is 1 and it's 100% in percentage.
probability is expressed as;
probably = sample space/total outcome
The area of the square is expressed as;
A = l²
= 20 × 20
= 400cm²
The area of the biggest circle is 314 cm²
The probability of scoring 1, 3 or 5
= 314/400 = 0.785
in percentage = 0.785 × 100
= 78.5%
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Simplify 3x + 5y + 2x – 4y
Answer:
5x + yStep-by-step explanation:
3x + 5y + 2x – 4y=> 5x + yConclusion:
Therefore:
5x + yHoped this helped.
\(GeniusUser\)
The simplified form of the given expression is 7x+y.
The given expression is 3x+5y+2x-4y.
An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
Group the like terms and simplify, we get
(3x+2x)+(5y-4y)
= 7x+y
Therefore, the simplified form of the given expression is 7x+y.
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Under what circumstances is an atomic electron's probability density distribution spherically symmetric? Why?
An atomic electron's probability density distribution is in a symmetrical three-dimensional electron cloud around the nucleus under certain circumstances.
When the electron is in a spherically symmetric orbital, such as an s orbital (e.g., 1s, 2s, 3s), its probability density distribution is spherically symmetric.
S orbitals have a spherical shape, with the highest probability of finding the electron at the nucleus, gradually decreasing as we move away from the nucleus in all directions.
This spherically symmetric distribution occurs because s orbitals have no angular momentum and are characterized by a single quantum number, indicating a spherical symmetry.
In contrast, other atomic orbitals, such as p, d, and f orbitals, have different shapes and are not spherically symmetric due to their angular momentum and additional quantum numbers.
The spherically symmetric probability density distribution of an atomic electron in an s orbital allows for an equal likelihood of finding the electron in any direction from the nucleus, resulting in a symmetrical three-dimensional electron cloud around the nucleus.
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Is (–39, 42) a solution to the equation y = x + 81?
Answer:
Yes
Step-by-step explanation:
Yes because if you insert -39 for x and 42 for y then your equation is:
42 = -39 + 81
If you were to solve this equation it would be true.
please help me with this ixl please
Answer:
plot these points on the graph and connect them
Step-by-step explanation:
T(5,-10)
U(9,-10)
V(2,0)
a scatter plot would be useful for question 17 options: showing the trend of sales, over time, of five different brands of blank dvds showing the relationship between the sales of blank cds and blank dvds showing the top selling brands of blank dvds showing the relative number of sales of four different brands of blank dvds
A scatter plot would be useful for showing the trend of sales, over time, of five different brands of blank DVDs. So, the correct answer is B).
A scatter plot is a type of graph that represents the relationship between two variables. It is particularly useful for showing the trend or pattern in data over time.
In this case, option B is the most appropriate because it involves plotting the sales data of different brands of blank DVDs over time. The scatter plot would allow for visualizing how the sales of each brand vary over different time periods, enabling the identification of any trends or patterns in the sales data.
So, the correct option is B).
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--The given question is incomplete, the complete question is given below " A scatter plot would be useful for
A. Showing the relative number of sales of four different brands of blank DVDs
B. Showing the trend of sales, over time, of five different brands of blank DVDs
C. Showing the relationship between the sales of blank CDs and blank DVDs
D. Showing the top selling brands of blank DVDs"--
5.4 cm
12.8 cm
x cm
Work out the value of x.
Give your answer correct to 3 significant figure
Answer:
890w
bro if i know i will tell u but the problem that d
Suppose an odd function f has a local minimum at c. Does f have a local maximum or minimum at - c? If f is odd with a local minimum at c, f has a local at -
If f is an odd function and it has a local minimum at c, then f has a local maximum at -c. Since f is an odd function, we know that f(-c) = -f(c).
Given that f has a local minimum at c, we know that there exists an interval (c-d, c+d) containing c such that f(x) ≥ f(c) for all x in (c-d, c+d).
For simplicity, let's say that d = 1 (i.e., we have an interval (c-1, c+1) that contains c).
Then we know that f(c-1) ≤ f(c) and f(c+1) ≤ f(c). Using the fact that f is odd, we have:
f(-c-1) = -f(c+1) ≥ -f(c) = f(-c)f(-c+1) = -f(c-1) ≥ -f(c) = f(-c)
We can rewrite these inequalities as -f(-c) ≤ f(-c+1) and -f(-c) ≤ f(-c-1).
Thus, there exists an interval (-c-1, -c+1) containing -c such that f(x) ≤ f(-c) for all x in (-c-1, -c+1).
Therefore, f has a local maximum at -c.
Therefore, if an odd function f has a local minimum at c, then f has a local maximum at -c. This is true for any odd function f with a local minimum at any point c in its domain.
Thus, if an odd function f has a local minimum at c, it has a local maximum at -c. The proof uses the definition of an odd function, which is a function that satisfies f(-x) = -f(x) for all x in the domain of f.
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Fractions 7/8+ 1/5
Evaluate the expression shown below and write your answer as a fraction in simplest form
The simplest form of fraction of the given terms is 43/40.
According to the statement
we have to find that the simplest form of the fraction by evaluating.
So, For this purpose, we know that the
A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole.
The given expression is
7/8+ 1/5
Now, to solve it take a LCM of it then
35+8/40
Now solve the term then the equation become
43/40.
Now, The simple form of the fraction become the 43/40.
So, The simplest form of fraction of the given terms is 43/40.
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Your sock drawer has two white socks, four brown socks, and two black socks. You randomly pick a sock and put it on your left foot and then pick another sock and put it on your right foot. You leave the house with a white sock on your left foot and a brown sock on your right foot. Find the probability of this occuring.
Answer:
The probability of this occurring is 1/7
Step-by-step explanation:
Okay, here is a probability question.
From the question, we can identify the following;
Total number of socks = 2 + 4 + 2 = 8 socks
Since we are not given the order in which the socks was worn, we can assume any order.
Let’s say the right leg socks was worn first.
From the question, the socks on the right leg is a brown one.
So now let’s calculate the probability of selecting a brown socks out of the mix
That would be ;
number of brown socks/ total number of socks = 4/8 = 1/2
Now, for the left foot, we are having white sock here.
Kindly recall that since we already have a sock on the right foot, we have 7 socks left to pick from.
Now we need the probability of picking a white sock from the total 7. That would be ; 2/7
So the probability of both action occurring is simply the product of both probabilities and that is ;
1/2 * 2/7 = 1/7
George's dog ran out of its crate. It ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate. How far away from its crate is George's dog? Round to the nearest hundredth.
George's dog is approximately 32.41 meters away from its crate, if it ran 22 meters, turned and ran 11 meters, and then turned 120° to face its crate.
To determine the distance from George's dog to its crate after the described movements, we can use the concept of a triangle and trigonometry.
The dog initially runs 22 meters, then turns and runs 11 meters, forming the two sides of a triangle. The third side of the triangle represents the distance from the dog's final position to the crate.
To find this distance, we can use the Law of Cosines, which states that in a triangle with sides a, b, and c and angle C opposite side c, the equation is c² = a² + b² - 2abcos(C).
In this case, a = 22 meters, b = 11 meters, and C = 120°. Plugging these values into the equation, we have
c² = 22² + 11² - 2(22)(11)cos(120°).
Evaluating the expression, we get
c ≈ 32.41 meters.
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what is 20% of 24cm?
Answer:
20% of 24cm=20/100×24=4.8cm
Answer:
4.8cm
Step-by-step explanation:
24x20%=20×0.20=4.8cm
14. Find the reciprocal of 20.95 to4 decimal places using the tables of reciprocals (1mk)
The reciprocal of 20.95 to 4 decimal places using the table of reciprocals is 0.0478.
Reciprocal of a numberTo find the reciprocal of 20.95, we can look up the reciprocal of 20.9 or 21 in the table and then interpolate to get a more accurate value for 20.95.
reciprocal of 20.9 = 0.04784reciprocal of 21 = 0.04762To interpolate, we can calculate the difference between 20.95 and 20.9, which is 0.05, and the difference between the reciprocals of 20.95 and 20.9, which is 0.00009.
Then we can use the formula:
reciprocal of 20.95 = reciprocal of 20.9 + (difference / interval) x (reciprocal of 21 - reciprocal of 20.9)
where interval is the difference between the numbers in the table (which is 0.1 in this case).
Thus:
reciprocal of 20.95 = 0.04784 + (0.05 / 0.1) x (0.04762 - 0.04784)
= 0.04784 + 0.025 x (-0.00022)
= 0.04784 - 0.0000055
= 0.0478345
In other words, the reciprocal of 20.95 to 4 decimal places using the tables of reciprocals is 0.0478.
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A man in a lighthouse tower that is 30 ft. He spots a ship at sea at an angle of depression of 10°. How far is the ship from the base of the lighthouse?
Answer:
170.16 ft
Step-by-step explanation:
tan10° = 30/x
x = 30x/ tan 10° = 30/0.1763
=170.16 ft
The distance from the vertex to the centroid of the equilateral triangle is 12√3 cm. Calculate the volume.
2,304 cubic centimetres is the required volume of the regular tetrahedron.
The distance from the vertex to the centroid of the equilateral triangle.Let's denote the side length of the equilateral triangle as "s". We know that the distance from the vertex (pointing downwards) to the centroid (the center of mass) is 12√3 cm.
Since the centroid divides each median in a 2:1 ratio, we know that the distance from the centroid to the midpoint of a side is 1/3 of the total distance from the centroid to the vertex. Therefore, the distance from the centroid to each side is:
(1/3) * 12√3 = 4√3 cm
Let's draw an altitude from the centroid to one of the sides of the triangle, creating a right triangle. The length of the altitude is:
h = 4√3 cm
The length of the base of the right triangle (half of one side of the equilateral triangle) is:
b = s/2
The length of the hypotenuse of the right triangle (the distance from the centroid to the vertex) is:
c = 12√3 cm
Using the Pythagorean theorem, we can write:
c^2 = b^2 + h^2
Solving for s, we get:
s = 2b = 2√(c^2 - h^2)
s = 2√((12√3)^2 - (4√3)^2)
s = 2√(1443 - 163)
s = 2√(128*3) = 32√3
Now we can calculate the area of the equilateral triangle:
A = √(3)/4)s^2 = √((3)/4)(32√3)^2 = 192√3 cm^2
Finally, we can use the formula for the volume of a regular tetrahedron:
V = (1/3)Ah
where A is the area of the equilateral triangle and h is the height of the tetrahedron, which is the distance from the vertex to the centroid.
Plugging in the values we have found, we get:
V = (1/3)192√312√3 = 2,304 cm^3
Therefore, the volume of the regular tetrahedron with the given properties is 2,304 cubic centimeters.
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