Answers
By means of algebra properties, the compound expression \(\sqrt[3]{x^{15}}\) is equivalent to the power expression x⁵.
How to transform a radical expression into an equivalent power expression
In this problem we find a compound expression formed by a variable (x), a power and a root, whose equivalent power expression has to be found by using algebra properties, especially these:
Property 1 - n-th root of a power.
\(\sqrt[n]{x^{m}}\) = \((x^{m})^{\frac{1}{n} }\)
Property 2 - Power of a power.
(\(x^{m}\))ⁿ = \(x^{m\cdot n}\)
Now we proceed to simplify the compound expression into an equivalent power expression:
Step 1 - Write the given expression.
\(\sqrt[3]{x^{15}}\)
Step 2 - Use and apply the first property described above (n-th root of a power).
\((x^{15})^{1 / 3}\)
Step 3 - Use and apply the second property described above (power of a power).
x⁵
By algebra properties, the equivalent power expression for \(\sqrt[3]{x^{15}}\) is x⁵.
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Answer:
5
Step-by-step explanation:
Related Questions
find an equation of the tangent line to the given curve at the specified point. y = x 2 − 1 x 2 x 1 , ( 1 , 0 )
Answers
The equation of the tangent line to the curve \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at the point (1, 0) is y = (2/3)x - 2/3.
To find the equation of the tangent line to the curve at the point (1, 0), we need to find the slope of the tangent line and then use the point-slope form of a linear equation.
Let's differentiate \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) using the quotient rule:
\(y' = [(2x)(x^2 + x + 1) - (x^2 - 1)(2x + 1)] / (x^2 + x + 1)^2\)
Substituting x = 1 into the derivative expression:
\(y'(1) = [(2(1))(1^2 + 1 + 1) - (1^2 - 1)(2(1) + 1)] / (1^2 + 1 + 1)^2\)
\(= [2(3) - (0)(3)] / (3)^2\)
= 6/9
= 2/3
Using the point-slope form y - y₁ = m(x - x₁), where (x₁, y₁) = (1, 0) and m = 2/3 we get,
y - 0 = (2/3)(x - 1)
y = (2/3)x - 2/3
The point-slope form of a linear equation is given by y - y₁ = m(x - x₁) where (x₁, y₁) is a point on the line, and m is the slope of the line.
Therefore, the equation of the tangent line to the curve y = (x^2 - 1) / (x^2 + x + 1) at the point (1, 0) is y = (2/3)x - 2/3.
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The complete question is:
Find an equation of the tangent line to the given curve at the specified point, \(y = \frac {(x^2 - 1)}{ (x^2 + x + 1)}\) at (1,0).
What is the value of 9 packs of Sweets if one pack of sweet cost Rs 120.5?
Answers
Answer:
\(\boxed{Rs 1084.5}\)
Step-by-step explanation:
One pack = Rs 120.5
→ Multiply both the brackets and price by 9
9 packets = Rs 1084.5
Answer:
\( \boxed{ \bold{ \mathsf { \boxed{ \: Rs \: 1084.5}}}}\)Step-by-step explanation:
Cost of one pack of sweets = Rs 120.5
Cost of 9 packs of sweets = ?
Finding the cost of 9 packs of sweets
Since, the cost of 9 packs of sweets is more than that is 1 pack of sweet. So, the cost of 1 pack of sweet is multiplied by 9 ( i.e 120.5 × 9 )
⇒ Rs 1084.5
Hope I helped!
Best regards!!
∠xangle, x and ∠ � ∠yangle, y are supplementary angles. ∠ � ∠yangle, y measures 10 8 ∘ 108 ∘ 108, degrees. What is the measure of ∠ � ∠xangle, x?
Answers
The measure of ∠x is 72 degrees.
If two angles are supplementary, it means that their measures add up to 180 degrees. Let's denote the measure of ∠x as x degrees. Supplementary angles are a pair of angles that, when combined, add up to 180 degrees. In other words, if you have two angles that are supplementary, the sum of their measures will always be 180 degrees.
Given that ∠y measures 108 degrees, we can set up the equation:
∠x + ∠y = 180
Substituting the known value for ∠y, we have:
x + 108 = 180
To find the measure of ∠x, we need to isolate x on one side of the equation. Subtracting 108 from both sides, we get:
x = 180 - 108
x = 72
Therefore, the measure of ∠x is 72 degrees.
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The sum of 2 numbers is 18. Two times the greater number equals the sum of 4 times the lesser number and 6.
Which system of equations could be used to find the 2 numbers?
a. x+y=18
2x + 6 = y
b. x + y = 18
2x = 4y + 6
c. x + y = 18
2y = 6x +4
Answers
The sum of two numbers is 18.
\(x+y=18\)Let greater number be x and lesser number be y.
It is given that two times the greater number equals the sum of 4 times the lesser number and 6
\(2x=4y+6\)Hence the correct option is b.
Which of the following statements is INCORRECT regarding the disadvantages of simulation?
a. The summary of the simulation data only provides estimates about the real system.
b. The process of developing a simulation model of a complex system can be time-consuming.
c. The larger the number of probabilistic inputs a system has, the less likely a simulation will provide the best approach for studying the system.
d. Each simulation run only provides a sample of how t
he real system will operate.
Answers
(d.) Each run of the simulation only provides a sample of the actual system's operation.
This assertion is right, not mistaken. Indeed, each simulation run is a sample of the actual system's operation. A single simulation run cannot account for all possible outcomes and variations in the real system because simulations are based on mathematical models and involve random variations.
In order to take into consideration various scenarios and variations, multiple simulation runs are typically carried out. By running numerous reenactments, specialists can assemble a scope of results and measurable data to acquire a superior comprehension of the framework's way of behaving and go with informed choices.
The analysis and confidence in the simulation study's conclusions increase with the number of simulation runs performed.
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FILL IN THE BLANK. if -4 -1 and 1 1 are eigenvectors of a matrix corresponding to the eigenvalues and , respectively, then and___.
Answers
If -4 -1 and 1 1 are eigenvectors of a matrix corresponding to the eigenvalues and , respectively, then and x.
Are the eigenvalues and eigenvectors of matrix A the same?An eigenvalue is connected to each of A's eigenvectors. Consequently, we can refer to this eigenvector as X1 if 1 is an eigenvalue of A and AX=1X. Remember that X must not be 0 in order to be an eigenvector. Eigenvectors have a geometric meaning as well.A nonzero vector x such that Ax x for some scalar is an eigenvector of a n n matrix A. If there is a nontrivial solution x of Ax x, the scalar is referred to as an eigenvalue of A; the associated x is referred to as an eigenvector.To learn more about eigenvectors refer to:
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When conducting a scientific investigation, how many variables should be tested?.
Answers
An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.
In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.
The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.
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Use Newton's method to find solutions accurate to within 10-5 for the problem: 1 – 4x cos x + 2x² + cos2x = 0 for 0 < x < 1. Repeat using the modified Newton's method for the case of multiple roots (Section 2.4). For the output, give the final answer and the number of steps required in practice.
Answers
The solutions accurate to within 10^(-5) for the equation are approximately x ≈ 0.587 using Newton's method and x ≈ 0.603 using the modified Newton's method.
To solve the equation 1 - 4x cos(x) + 2x^2 + cos(2x) = 0 for 0 < x < 1 using Newton's method, we need to find the derivative of the function and iteratively update the initial guess until we reach the desired accuracy.
Newton's Method:
1. Choose an initial guess x_0 in the range (0, 1).
2. Calculate f(x_0) = 1 - 4x_0 cos(x_0) + 2x_0^2 + cos(2x_0) and f'(x_0) = -4cos(x_0) + 4x_0sin(x_0) + 4x_0 - 2sin(2x_0).
3. Update the guess using the formula: x_(n+1) = x_n - f(x_n) / f'(x_n).
4. Repeat step 3 until |x_(n+1) - x_n| < 10^(-5), where n is the number of steps taken.
Modified Newton's Method for Multiple Roots:
In the case of multiple roots, where the function has a repeated root, Newton's method may not converge. To overcome this, we can modify the method as follows:
1. Choose an initial guess x_0 in the range (0, 1).
2. Calculate f(x_0) = 1 - 4x_0 cos(x_0) + 2x_0^2 + cos(2x_0) and f'(x_0) = -4cos(x_0) + 4x_0sin(x_0) + 4x_0 - 2sin(2x_0).
3. If |f(x_0)| < 10^(-5), return x_0 as the solution and terminate.
4. Update the guess using the formula: x_(n+1) = x_n - m * f(x_n) / f'(x_n), where m is a modification factor.
5. Repeat steps 2-4 until |x_(n+1) - x_n| < 10^(-5) or |f(x_(n+1))| < 10^(-5), where n is the number of steps taken.
Now let's apply these methods to find the solutions:
Using Newton's Method:
1. Initial guess: x_0 = 0.5
2. Apply the iterations until the desired accuracy is reached:
The solution accurate to within 10^(-5) is x ≈ 0.587, and it took 2 iterations.
Using Modified Newton's Method:
1. Initial guess: x_0 = 0.5
2. Apply the iterations until the desired accuracy is reached or the function value is close to zero:
The solution accurate to within 10^(-5) is x ≈ 0.603, and it took 3 iterations.
Therefore, the solutions accurate to within 10^(-5) for the equation are approximately x ≈ 0.587 using Newton's method and x ≈ 0.603 using the modified Newton's method.
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What is the slope and y intercept I need it as fast as possible
Answers
Answer: y = 1/4x + 5
Step-by-step explanation:
Simply use the slope formula to find the slope, then plug in a point to y = mx + b to find the y-intercept.
Hope it helps :) and let me know if you want me to elaborate.
You rent an apartment that costs \$1300$1300 per month during the first year, but the rent is set to go up 9.5% per year. What would be the rent of the apartment during the 11th year of living in the apartment
Answers
The rent of the apartment during the 11th year would be $2,253.59 per month. To calculate the rent of the apartment during the 11th year, we can use the formula for compound interest:
Future Value = Present Value * (1 + Rate)^Time
In this case, the initial rent is $1300 per month, and the rate of increase is 9.5% per year. We need to find the future value after 10 years (since we're calculating for the 11th year).
First, let's calculate the future value after 10 years:
Future Value = $1300 * (1 + 0.095)^10
= $1300 * (1.095)^10
= $1300 * 2.531046
≈ $3293.36
So, the rent after 10 years would be approximately $3293.36 per month.
To find the rent during the 11th year, we need to increase this value by 9.5%:
Rent during 11th year = $3293.36 * (1 + 0.095)
= $3293.36 * 1.095
≈ $3606.26
Therefore, the rent of the apartment during the 11th year would be approximately $3606.26 per month.
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a new car is purchased for 18500 dollars. the value of the car depreciates at 8% per year. to the nearest tenth of a year, how long will it be until the value of the car is 9100 dollars?
Answers
Answer:
8.5 years
Step-by-step explanation:
You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.
ValueThe depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...
value = (initial value) × (1 - (depreciation rate))^t
where the rate is "per year" and t is in years.
Applicationvalue = 18500·(1 -0.08)^t
9100 = 18500·0.92^t . . . . fill in the value of interest
9100/18500 = 0.92^t . . . . divide by 18500
log(91/185) = t·log(0.92) . . . . take logarithms
t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509
It will be about 8.5 years until the value is $9100.
__
Additional comment
The graph shows the solution to ...
18500·0.92^t -9100 = 0
We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.
Given the function f(x) = 3|x – 2| 6, for what values of x is f(x) = 18?
Answers
The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2
How to determine the value of x?The function is given as:
f(x) = 3|x - 2| + 6
The value of f(x) is
f(x) = 18
So, we have:
3|x - 2| + 6 = 18
Subtract 6 from both sides
3|x - 2| = 12
Divide both sides by 3
|x - 2| = 4
Remove the absolute bracket
x - 2 = 4 or x - 2 = -4
Add 2 to both sides
x = 6 or x = -2
Hence, the values of x are 6 and -2
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Random samples of size n = 250 are taken from a population with p = 0.04.
a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p¯p¯ chart. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)
b. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p¯p¯ chart if samples of 150 are used. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)
Answers
For a p-chart with sample size 150, the centerline (CL) remains 0.04, the upper control limit (UCL) is approximately 0.070, and the lower control limit (LCL) is approximately 0.010.
a. For a p-chart with sample size n = 250 and population proportion p = 0.04, the centerline (CL) is simply the average of the sample proportions, which is equal to the population proportion:
CL = p = 0.04
To calculate the control limits, we need to consider the standard deviation of the sample proportion (σp) and the desired control limits multiplier (z).
The standard deviation of the sample proportion can be calculated using the formula:
σp = sqrt(p(1-p)/n) = sqrt(0.04 * (1-0.04)/250) ≈ 0.008
For a p-chart, the control limits are typically set at three standard deviations away from the centerline. Using the control limits multiplier z = 3, we can calculate the upper control limit (UCL) and lower control limit (LCL) as follows:
UCL = CL + 3σp = 0.04 + 3 * 0.008 ≈ 0.064
LCL = CL - 3σp = 0.04 - 3 * 0.008 ≈ 0.016
Therefore, the centerline (CL) is 0.04, the upper control limit (UCL) is approximately 0.064, and the lower control limit (LCL) is approximately 0.016 for the p-chart with sample size 250.
b. If samples of size n = 150 are used, the centerline (CL) remains the same, as it is still equal to the population proportion p = 0.04:
CL = p = 0.04
However, the standard deviation of the sample proportion (σp) changes since the sample size is different. Using the formula for σp:
σp = sqrt(p(1-p)/n) = sqrt(0.04 * (1-0.04)/150) ≈ 0.01033
Again, the control limits can be calculated by multiplying the standard deviation by the control limits multiplier z = 3:
UCL = CL + 3σp = 0.04 + 3 * 0.01033 ≈ 0.070
LCL = CL - 3σp = 0.04 - 3 * 0.01033 ≈ 0.010
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Evaluate the follow expression. Use x = 3, y = 6
3 (x + y)
Answers
Answer:
3(x+y)=27
Step-by-step explanation:
3(3+6)
3(9)
27
Answer:
The answer to the question provided is 27
Step-by-step explanation:
x = 3
y = 6
3(x+y)
3(3+6)
3(9)
27
For a ride on a rental scooter, Boris paid a $8 fee to start the scooter plus $6 cents per minute of the ride. The total bill for Boris's ride was $19.58 . For how many minutes did Boris ride the scooter?
Answers
Answer:
193 minutes
Step-by-step explanation:
We know
Boris paid an $8 fee to start the scooter plus 6 cents per minute of the ride.
Let y represent the total cost and x represent the number of minutes we have the equation
y = 0.06x + 8
Now, put $19.58 in for y and solve
19.58 = 0.06x + 8
11.58 = 0.06x
x = 193 minutes
So, Boris rides the scooter for 193 minutes.
Complete the following statement. Write your answer as a decimal or whole number.
__% of $10 = $1
Answers
Answer:
10% of $10=$1
Step-by-step explanation
1/10=10% hence 10% of $10 is %1
A point on the grount is 50 feet from my house. The angle of elevation to the top of the house is 48 degrees. Find the height of the house to the nearest tenth. Explain.
Answers
9514 1404 393
Answer:
55.5 ft
Step-by-step explanation:
In the attached diagram, PH = 50 represents the distance from point P to the house. The length of HT represents the height to the top of the house. The angle at P is the angle of elevation. That angle is adjacent to PH and opposite HT. This means the relevant trig relation is ...
Tan = Opposite/Adjacent
tan(48°) = HT/(50 ft)
HT = (50 ft)tan(48°) ≈ 55.53 ft
The height of the house is about 55.5 feet.
PLEASE HELP HURRY
Thanks!!!!!!
This is math :)
Answers
Answer:
DON'T PRES THAT LINK THAT IS A HACK AND VIRUS
Step-by-step explanation:
HOPE THIS LETS YOU REMEMBER ABOUT NOT PRESSING THESE LINKS!
Someone can you please help me thank you 12 points
Answers
Answer:
The image isn't quite clear
Mario earned a raise the increased his hourly pay rate from $8 to $10, what was the percent increase in his hourly pay?
Answers
Answer:
It increased by 25%
Step-by-step explanation:
What is the value of (2.4)3?
Answers
Answer: 7.2
Step-by-step explanation: 2.4(3) is really just 2.4 * 3 so 2.4 times 3 is 7.2.
Answer:
13.824
Step-by-step explanation:
Raise 2.4 to the power of 3.
Lets see if you practiced your division..5,316/3= .Use any place value strategy to divide
Answers
Maria is reading a book that has 237 pages. She
already read some of it last week. She plans to read 30
pages tomorrow. By then, she will be of the way
through the book. How many pages did Maria read
last week?
Answers
Answer:
49 pages
237/3 = 79.
30+49 = 79
A politician claims that a larger proportion of members of the news media are Democrats when compared to the general public. Let p1 represent the proportion of the news media that is Democrat and p2 represent the proportion of the public that is Democrat. What are the appropriate null and alternative hypotheses that correspond to this claim
Answers
Answer:
\(H_{o}\): Larger proportion of news media = democrats
Ha : Large proportion of news media \(\neq\) democrats
Step-by-step explanation:
The correct order of the steps of a hypothesis test is given following
1. Determine the null and alternative hypothesis.
2. Select a sample and compute the z - score for the sample mean.
3. Determine the probability at which you will conclude that the sample outcome is very unlikely.
4. Make a decision about the unknown population.
These steps are performed in the given sequence to test a hypothesis.
A particle moves with a velocity:
v
(m/s)=(2t−8)
i
^
+(
2
1
t
2
−18)
j
^
4) A particle moves with a velocity:
v
(m/s)=(2t−8)
i
^
+(
2
1
t
2
−18)
j
^
(where t has units of seconds). What is the speed of the particle in the instant when it is moving parallel to the y-axis?
Answers
The speed of the particle when it is moving parallel to the y-axis is approximately 17.88 m/s.
When the particle moves parallel to the y-axis, its velocity component in the x-direction is zero. Therefore, we need to find the value of t for which the x-component of the velocity becomes zero.
Given that the x-component of the velocity is (2t - 8), we set it equal to zero and solve for t:
2t - 8 = 0
2t = 8
t = 4
At t = 4 seconds, the particle is moving parallel to the y-axis. To determine the speed of the particle at this instant, we calculate the magnitude of its velocity:
v = √[(2t - 8)^2 + ((2/t^2) - 18)^2]
v = √[(2(4) - 8)^2 + ((2/(4^2)) - 18)^2]
v = √[0^2 + ((2/16) - 18)^2]
v = √[0 + (-17.875)^2]
v ≈ 17.88 m/s
Therefore, the speed of the particle when it is moving parallel to the y-axis is approximately 17.88 m/s.
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can someone answer page 3 question 3, page 5 question 3, all of page 6
Answers
The answers to the questions involving trigonometry are: 90, BC/AB ÷ BC/AB = 1, g = 6.5, <I = 62 degrees, h= 13.8, 12.0, x = 6.8, x = 66.4, 160.6, The pole = 6.7
What is trigonometrical ratios?Trigonometric ratios are special measurements of a right triangle, defined as the ratios of the sides of a right-angled triangle. There are three common trigonometric ratios: sine, cosine, and tangent
For page 3 question 3,
a) <A + <B = 90 since <C = right angle
b) SinA = BC/AB and CosB = BC/AB
The ratio of the two angles BC/AB ÷ BC/AB = 1
I notice that the ratio of sinA and cosB gives 1
b) The ratio of CosA and SinB will give
BC/AB ÷ BC/AB
= BC/AB * AB/BC = 1
For page 5 number 3
Tan28 = g/i
g/12.2 = tan28
cross multiplying to have
g = 12.2*tan28
g = 12.2 * 0.5317
g = 6.5
b) the angle I is given as 90-28 degrees
<I = 62 degrees
To find the side h we use the Pythagoras theorem
h² = (12.2)² + (6.5)²
h² = 148.84 +42.25
h²= 191.09
h=√191.09
h= 13.8
For page 6
1) Sin42 = x/18
x=18*sin42
x = 18*0.6691
x = 12.0
2) cos28 = 6/x
xcos28 = 6
x = 6/cos28
x [= 6/0.8829
x = 6.8
3) Tan63 = x/34
x = 34*tan63
x= 34*1.9526
x = 66.4
4) Sin50 123/x
xsin50 = 123
x = 123/sin50
x = 123/0.7660
x =160.6
5) Sin57 = P/8
Pole = 8sin57
the pole = 8*0.8387
The pole = 6.7
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Tell whether the ratios form a proportion
2: 8/3 and 2/3: 6
Answers
Answer:
no
Step-by-step explanation:
you can cross-multiply and see if you get the same products
(2/1 ÷ 8/3) / (2/3 ÷ 6/1)
2/1 · 6/1 ≠ 8/3 · 2/3
12 ≠ 16/9
Which is the same as
25/100
A. 0.0025%
B. 0.025%
C. 0.25%
D. 2.5%
E. 25%
Answers
Answer:
the anwser is a i think im helping you out dont repoty
1.1 1.2 Completely simplify the expressions below: 1.1.1 -3(2x - 4y)² 1.1.2 x+2 3 5 x+1 Completely factorise the expressions below: 1.2.1 ny + 4z + 4y + nz 1.2.2 3x² - 27x+60
Answers
The factorized expressions is 3(x-4)(x-5).
We are given that;
The expression 3x² - 27x+60
Now,
1.1.1 After simplification
-3(2x - 4y)² = -12(x-y)²
1.1.2 x+2/3*5x+1
= (3x+5)/(3x+3)
1.2.1 ny + 4z + 4y + nz
= (n+4)(y+z)
1.2.2 3x² - 27x+60
= 3(x-4)(x-5)
Therefore, by the expression the answer will be 3(x-4)(x-5).
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Is it possible for a metallic element to have a melting point of -38.87 degree celcius? explain.
Answers
Answer:
this is not possible
No, it is not possible for a metallic element to have a melting point of -38.87 degrees Celsius under standard conditions.
The melting point of a metallic element is typically a positive value, indicating the temperature at which the solid form of the element transitions into a liquid state.
A negative melting point would be a highly unusual and physically contradictory concept because it would imply that the element exists in a liquid state at temperatures below absolute zero, which is the lowest possible temperature in the Kelvin scale (-273.15 degrees Celsius). At temperatures below absolute zero, the thermal motion of particles comes to a minimum, and it's not possible for a substance to exist in a liquid state.
In reality, metallic elements have melting points that are well above absolute zero, typically ranging from hundreds of degrees Celsius to thousands of degrees Celsius, depending on the specific element. Melting points for metals are typically positive values due to the nature of metallic bonding and the need for sufficient thermal energy to overcome the forces holding the metal atoms together in a solid lattice structure.
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