Find each function value and the limit for f(x) = 14 - 8x^4 / 4+x^4 Use -[infinity] or [infinity] where appropriate. (A) f(-10) (B) f(-20) (C) lim f(x)
Answers
The given function is f(x) = (14 - 8x4) / (4 + x4).
Let us find each Find each function value and the limit for f(x) = 14 - 8x^4 / 4+x^4
Use -[infinity] or [infinity] where appropriate.
(A) f(-10) (B) f(-20) (C) lim f(x) and the limit for this function value:
(a) When x = -10:f(-10) = (14 - 8(-10)4) / (4 + (-10)4)f(-10) = (14 - 80000) / (4 + 10000)f(-10) = -79986 / 10004= -7.99422 (approx)
Therefore, when x = -10, f(x) = -7.99422.
(b) When x = -20:f(-20) = (14 - 8(-20)4) / (4 + (-20)4)f(-20) = (14 - 2560000) / (4 + 160000)f(-20) = -2559986 / 160004= -159.993
Therefore, when x = -20, f(x) = -159.993.
(c) Let us find the limit of the given function f(x) as x approaches infinity and negative infinity.
Let x approach infinity:f(x) = (14 - 8x4) / (4 + x4)
Since the highest degree of the polynomial in the denominator is x4,
let us divide the numerator and denominator by x4f(x) = [(14/x4) - 8] / (4/x4 + 1)As x approaches infinity,
the terms 14/x4 and 4/x4 both approach zero.
Therefore:f(x) = -8/1= -8
Thus, when x approaches infinity,
f(x) approaches -8.Let x approach negative infinity:
f(x) = (14 - 8x4) / (4 + x4)
Since the highest degree of the polynomial in the denominator is x4,
let us divide the numerator and denominator by x4f(x) = [(14/x4) - 8] / (4/x4 + 1)As x approaches negative infinity,
the terms 14/x4 and 4/x4 both approach zero.
Therefore:f(x) = -8/1= -8
Thus, when x approaches negative infinity, f(x) approaches -8.
Thus, the value of f(-10) is approximately -7.99422 and the value of f(-20) is approximately -159.993.
When x approaches infinity and negative infinity,
the limit of f(x) is -8.
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Related Questions
a slice of pizza supplies 217 kcal (217 cal). if a person weighing 140 lb expends 80 kcal per mile when walking at 2.0 miles per hour, approximately how long will it take to use up the calories from the pizza?
Answers
The required time consumed to burn the calories gained from the slice of pizza is 1.36 hr.
Given that,
A slice of pizza supplies 217 kcal (217 cal). if a person weighing 140 lb expends 80 kcal per mile when walking at 2.0 miles per hour.
here,
1 mile = 80 kcal used,
1 kcal used = 1/80 mile
217 kcal used = 217/80 mile = 2.71 miles
Now,
2 miles = 1 hour,
2.71 miles = 2.71/2 hours
2.71 miles = 1.36 hours
Thus, the required time consumed to burn the calories gained from the slice of pizza is 1.36 hr.
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In 1905 R. Pearl published the article "Biometrical Studies on Man I. Variation and Correlation in Brain Weight". According to the study, brain weights of Swedish men are normally distributed with a mean of 1. 4 kg and a standard deviation of 0. 11 kg. Determine the sampling distribution of the sample mean for samples of size 12
Answers
The sampling distribution of the sample mean for samples of size 12 from the given population will have a mean of 1.4 kg (same as the population mean) and a standard deviation of approximately 0.0317 kg.
How to determine the sampling distribution of the sample mean for samples of size 12For a normally distributed population with mean (μ) and standard deviation (σ), the sampling distribution of the sample mean (xbar) follows a normal distribution with the same mean (μ) and a standard deviation (σxbar) given by:
σ xbar = σ / sqrt(n)
Where:
σxbar is the standard deviation of the sample mean
σ is the population standard deviation
n is the sample size
In this case, the population mean (μ) of brain weights of Swedish men is 1.4 kg, and the population standard deviation (σ) is 0.11 kg. We are interested in the sampling distribution of the sample mean for samples of size 12.
Substituting the values into the formula, we have:
σxbar = 0.11 / sqrt(12)
Calculating this, we find:
σxbar ≈ 0.0317 kg
Therefore, the sampling distribution of the sample mean for samples of size 12 from the given population will have a mean of 1.4 kg (same as the population mean) and a standard deviation of approximately 0.0317 kg.
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While solving an equation, if the variable term becomes zero, and the equation makes a true statement, then the solution is
Answers
The equation's remaining constant is the answer if the variable term eventually equals zero and the equation can be said to be true.
By isolating the variable on one side of the equation, we can arrive at a numerical value that satisfies the equation. However, in rare circumstances, the variable term may become zero while the equation is being simplified.
When a common factor is eliminated or an expression containing the variable is simplified, this can take place. The equation has a solution, and that solution is the constant value left over if, after removing the variable element, we arrive at a true assertion.
This is due to the equation's ability to be simplified to a declaration of equality between two constants if the variable term is zero. The constant value is the answer to the equation if the aforementioned assertion is accurate.
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If n=25,x(x-bar)=30, and s=5, find the margin of error at a 90% confidence level. Give your answer to two decimal places. _______
Answers
To find the margin of error at a 90% confidence level, given n = 25, x-bar = 30, and s = 5, we can use the formula for the margin of error in estimating a population mean.
The margin of error can be calculated using the formula: Margin of Error = (Critical Value) * (Standard Deviation / sqrt(n)), where the critical value is determined based on the desired confidence level. For a 90% confidence level, the critical value can be found from the t-distribution table with degrees of freedom (n-1). Since n = 25, the degrees of freedom is 24. By looking up the critical value in the t-distribution table, the corresponding value is approximately 1.711. Plugging in the values, the margin of error can be calculated as (1.711) * (5 / sqrt(25)) = 1.711.
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In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate?a. +1b. 0c. Infinityd. -1
Answers
Answer:
In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, what is the standard error of the estimate b. 0
Step-by-step explanation:
If the plots on a scatter diagram lie on a straight line in a simple linear regression model, it indicates a perfect fit between the predictor variable and the response variable. In this case, the standard error of the estimate would be 0.
The standard error of the estimate represents the average distance between the observed values and the predicted values by the regression model. When the scatter diagram forms a perfect straight line, it means that the regression model can precisely predict the response variable using the predictor variable without any error.
Consequently, the residuals, which are the differences between the observed and predicted values, become zero for all data points, resulting in a standard error of 0. It is important to note that this scenario of a perfect fit on a scatter diagram is rare in real-world data, as there are typically variations and uncertainties in the relationship between variables.
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Cheryl is creating a rectangular garden in her backyard. The length of the garden is 11 feet. The perimeter of the garden must be at least 36 feet and no more than 38 feet. Use a compound inequality to find the range of values for the width w of the garden.
Answers
Answer:
The range of values for the width is within 7 to 8 feet i.e 7 feet, 7.5 feet, 8 feet.
Step-by-step explanation:
The formula for the perimeter of a rectangle is 2( L + W)
Perimeter = P ≥ 36 and P ≤ 38
hence, the perimeter is within the range of 36 and 38 feet ( i.e 36, 37, 38).
L = 11 feet
When Perimeter is 36 feet
36 = 2L + 2 W
36 = 2(11)+ 2 W
36 = 22 + 2W
36 - 22 = 2W
14 = 2W
W = 14/2
W = 7 feet
When Perimeter is 37 feet
37 = 2L + 2 W
37 = 2(11)+ 2 W
37 = 22 + 2W
37 - 22 = 2W
15 = 2W
W = 14/2
W = 7.5 feet
When Perimeter is 38 feet
38 = 2L + 2 W
38 = 2(11)+ 2 W
38 = 22 + 2W
38 - 22 = 2W
16 = 2W
W = 16/2
W = 8 feet
The range of values for the width is within 7 to 8 feet i.e 7 feet, 7.5 feet, 8 feet.
The density of a certain material is such that it weighs 5 ounces per gallon of volume. Express this density in pounds per cubic meter. Round your answer to the nearest tenth.
Answers
Answer:
82.6 pounds per cubic meter
Step-by-step explanation:
A grocery store sells a bag of 3 oranges for $1.71. How much does one orange cost?
Answers
Answer: 57 cents each
Answer:
57 cents
Step-by-step explanation:
divide the amount of money by the amount of oranges to find the amount each of them are. so if each of them are 57 then 1 is 57.
A train travels a total of 38 km at a constant speed of 90 km/h.
How long is its journey? Give your answer in minutes and seconds, to the nearest second. Pls Help Maybe I will give you brainiest
Answers
Answer:
25 minutes and 33 seconds
Step-by-step explanation:
please brainiest
Give examples of Inverses (ex: are 3 and -3 inverses?)
Answers
Answer:
3, -3 ; 4, -4
Step-by-step explanation:
Yes, 3 and -3 are inverse because positive is the inverse of negative.
You could also write
\( {3}^{2} \)
and
\( \sqrt{3} \)
because squares and square roots are inverse operations.
25 points) Every year, 20% of the residents of New York City move to Los Angeles, and 25% of the residents of Los Angeles move to New York. Suppose, for the sake of he problem, that the total populations are otherwise stable: that is, the change in the NYC population yearly is determined entirely by the number of residents moving to represent the number of residents of New York and LA, respectively. LA and the number moving from LA. Let (1) (a) (3 points) Write down a 2 x 2 matrix A so that A (1) outputs a 2-vector repre- senting the number of residents of New York and Los Angeles after one year. (b) (9 points) Diagonalize A: that is, find a diagonal matrix D and an invertible matrix X such that A = X-DX. (c) (5 points) Compute A4 using your diagonalization. (d) (8 points) Suppose there are initially 9 million residents of NYC and 9 million residents of LA. Find the steady state vector the populations of NYC and LA stabilize toward? (*): that is, as n + oo, what do
Answers
The steady state vector for the populations of New York City (NYC) and Los Angeles (LA) stabilizes towards [15 million, 15 million].
How do the populations of NYC and LA stabilize over time?In this problem, we can represent the populations of NYC and LA using a 2-vector [NYC, LA]. The given information states that every year, 20% of NYC residents move to LA, and 25% of LA residents move to NYC. To analyze the long-term population trends, we need to find the steady state vector, which represents the population distribution that remains unchanged over time.
To find the steady state vector, we can consider the population changes as matrix operations. Let A be the 2 x 2 matrix representing the yearly population changes. The first row of A will have the percentage of residents moving from NYC to NYC and LA, respectively, while the second row will have the percentage of residents moving from LA to NYC and LA, respectively. In this case, A is given by: A = [[0.8, 0.25],
[0.2, 0.75]]
To find the steady state vector, we need to diagonalize matrix A. Diagonalization involves finding a diagonal matrix D and an invertible matrix X such that \(A = XDX^(^-^1^)\). After diagonalization, the diagonal elements of D will represent the eigenvalues of A, while the columns of X will represent the corresponding eigenvectors.
By diagonalizing matrix A, we find that:
D = [[1, 0],
[0, 0.55]]
X = [[-0.993, -0.707],
[0.119, -0.707]]
To compute \(A^4\) using diagonalization, we can use the formula \(A^n\) = X D^n X^(-1). Since D is a diagonal matrix, raising it to the power of 4 is simply done by raising each diagonal element to the power of 4. Thus:
\(D^4 = [[1^4, 0]\),
\([0, (0.55)^4]] = [[1, 0],\)
[0, 0.0915]]
Now we can compute \(A^4:\)
\(A^4 = X D^4 X^(^-^1^)\)
By substituting the values of X, \(D^4\), and \(X^(^-^1^)\) into the equation, we get:
\(A^4 = [[0.8, 0.25],\)
\([0.2, 0.75]]^4 = [[0.816, 0.233],\)
[0.184, 0.767]]
After four years, the population distribution stabilizes towards [0.816, 0.233] for NYC and [0.184, 0.767] for LA. Considering the initial populations of 9 million for both NYC and LA, the steady state vector represents approximately [15 million, 15 million].
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4x(x + y) - y (x + y)
=
Answers
Answer:
=4x2+3xy−y2
Hope this helps you
min 8x₁ + 6x₂ subject to
a. 4x₁ + 2x₂ ≥ 20
b. −6x₁ + 4x₂ ≤ 12
c. x₁ + x₂ ≥ 6
d. x₁ + x₂ ≥ 0
Answers
The minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).
The given problem is:
min 8x₁ + 6x₂ subject to4x₁ + 2x₂ ≥ 20−6x₁ + 4x₂ ≤ 12x₁ + x₂ ≥ 6x₁ + x₂ ≥ 0
The feasible region is as follows:
Firstly, plot the following lines:4x₁ + 2x₂ = 20-6x₁ + 4x₂ = 12x₁ + x₂ = 6x₁ + x₂ = 0On plotting, the following graph is obtained:
Now, let's check each option one by one:
a. 4x₁ + 2x₂ ≥ 20
The feasible region is the region above the line 4x₁ + 2x₂ = 20.
b. −6x₁ + 4x₂ ≤ 12
The feasible region is the region below the line −6x₁ + 4x₂ = 12.c. x₁ + x₂ ≥ 6
The feasible region is the region above the line x₁ + x₂ = 6.d. x₁ + x₂ ≥ 0
The feasible region is the region above the x-axis.
Now, check the point of intersection of the lines.
They are:(10,0),(2,4),(6,0)The point (2,4) is not in the feasible region as it lies outside it.
Therefore, we reject this point.
The other two points, (10,0) and (6,0) are in the feasible region.
Now, check the values of the objective function at these two points.
Objective function value at (10,0): 80
Objective function value at (6,0): 48
Therefore, the minimum value of the objective function subject to the given constraints is 48 and it occurs at (6,0).
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how in the world do you do this problem
(-1,0)
y+__= 4(x+2)
Answers
Is this correct?
8EF625DF
Answers
The missing angles of the given complementary and supplementary angles above would be listed below as follows:
Angle1= 12°
Angle2= 145°
Angle3= 15°
Angle 4= 77°
Angle 5= 110°
What are complementary and supplementary angles?A complementary angle is the type of angle that is made up of two angles that adds up to 90°, while a supplementary angle is the type of angle that that is made up of two angles that adds up to 180°.
For Angle1:
X = 90-78 = 12°
Angle2:
X = 180-35 = 145°
Angle3:
X = 90-75 = 15°
Angle 4:
X = 90-13 = 77°
Angle 5:
X = 180-70 = 110°
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What is 8640 minutes, in days? (remember, there are 60 minutes in an hour and 24 hours in a day. ).
Answers
As there are 60 minutes in an hour and 24 hours in a day, there are 6 days as well as 144 days in 8640 minutes.
What is division?A number is split in division, which is a straightforward procedure. The simplest way to conceptualize it is as a set of things being distributed among a set of individuals, as in the example given above. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
Here,
There are 60 minutes in an hour,
=8640/60
=144 hours
There are 24 hours in a day,
=144/24
= 6 days
There is 6 days as well as 144 days in 8640 minutes as there are 60 minutes in an hour and 24 hours in a day.
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it takes 202020 drops of rain to make 111 milliliter. how many drops would it take to fill a 50-gallon rain barrel?
Answers
It would take a total of, 3,461,934 drops of rain to fill a 50-gallon rain barrel.
To determine how many drops of rain it would take to fill a 50-gallon rain barrel, we need to first convert the volume of the rain barrel to milliliters. One gallon is equal to approximately 3785 milliliters, so a 50-gallon rain barrel is,
3785 * 50 = 189,250 milliliters.
If it takes 202020 drops of rain to make 111 milliliters, then it would take approximately 189,250 / 111 = 1,697 sets of 202020 drops to fill a 50-gallon rain barrel.
Thus, it would take a total of 1,697 x 202020 = 3,461,934 drops of rain to fill a 50-gallon rain barrel.
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Which expression uses the associative property to make it easier to evaluate 14(1/7x2/5)?
A. (14x1/7)2/5
B.7(1/14x2/5)
C.(14x5/2)1/7.
D.14(2/5x1/7)
Answers
Answer:
A
Step-by-step explanation:
Associative property:
(a+b)+c=a+(b+c)
(a*b)*c=a*(b*c)
Quinn is playing in a trivia competition. He earns 50 points for each correct response, . He loses 25 points for each wrong response, . Which expression represents Quinn's total points in the trivia competition? A
Answers
Answer:
T = 50x - 25y
Step-by-step explanation:
The expression that would best represent this scenario would be the following
T = 50x - 25y
In this expression the variable T represents the total number of points, the variable x represents the total number of correct responses, and the variable y represents the total number of wrong responses which is subtracted from the product of the correct responses since Quinn is losing points for every wrong response.
A ship is at a distance of 200 m from a tall tower. What is the angle of depression (to the nearest degree) of the ship found by a man after climbing 50 m up the tower?
Answers
Answer:
14degrees
Step-by-step explanation:
Given the following
Distance of ship from the tower = 200m
Height of the tower = 50m
Required
Angle of depression theta
USing the SOH CAH TOA identity
Tan theta = opposite/adj
Tan theta = 50/200
Tan theta = 1/4
theta = arctan(0.25)
theta = 14.03degrees
Hence the angle of depression is 14degrees
Please help:)))))))))))
Answers
Answer:
good evening good evening good evening good evening
A pyramid has a square base of 8cm height of the pyramid is half the side of pyramid find the slant height
Answers
The slant height of the pyramid is approximately 5.657 cm.
Let's denote the side length of the square base of the pyramid as 's'.
According to the given information, the height of the pyramid is half the side length of the pyramid's base. This means the height (h) is equal to (1/2) * s.
To find the slant height (l) of the pyramid, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (in this case, the slant height) is equal to the sum of the squares of the other two sides.
In our case, the slant height (l) is the hypotenuse, and the height (h) and half the side length of the base (s/2) are the other two sides.
Using the Pythagorean theorem:
l^2 = h^2 + (s/2)^2
l^2 = [(1/2) * s]^2 + (s/2)^2
l^2 = (1/4) * s^2 + (1/4) * s^2
l^2 = (1/2) * s^2
Taking the square root of both sides:
l = √[(1/2) * s^2]
l = (1/√2) * s
Substituting the value of s = 8cm into the equation:
l = (1/√2) * 8
l ≈ 5.657 cm
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Can anyone help me with this?
Answers
Answer:
59.7%
Step-by-step explanation:
A of Circle = 50.24 sq. inches
A of Rectangle = 30 sq. inches
30 ÷ 50.24 × 100 = 59.71%
Not so sure though
hey can someone please help me with this question - its about solving 3 variable equations and you get 15 points!
Answers
The value of the variable x, y, and z will be negative 7, 2, and negative 1, respectively.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
The equations are given below.
x + y + z = -6 ...1
2x + (1/2)y - 7z = -6 ...2
-3x - 4y + 5z = 8 ....3
Multiply equation 2 by -2 and add with equation 1, then we have
-3x + 15z = 6 ...4
Multiply equation 1 by 4 and add with equation 3, then we have
x + 9z = - 16
x = - 9z - 16
Put the value of y in equation 4, then we have
- 3 (-9z - 16) + 15z = 6
27z + 15z + 48 = 6
42z = -42
z = -1
Then the value of x will be
x = - 9 (-1) - 16
x = 9 - 16
x = -7
Then the value of y will be
- 7 + y - 1 = -6
y = 8 - 6
y = 2
The value of the variable x, y, and z will be negative 7, 2, and negative 1, respectively.
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7. Where is most of the Earth’s supply of water found?
A. in rivers
B. in lakes
C. in glaciers and icecaps
D. in the ground
Answers
Ocean water: 97.2 percent
Glaciers and other ice: 2.15 percent
Groundwater,: 0.61 percent
Fresh water lakes: 0.009 percent
Inland seas: 0.008 percent
Soil Moisture: 0.005 percent
Atmosphere: 0.001 percent
Rivers: 0.0001 percent.
The approximate circumference of a circle is 7,459 miles. What is the diameter rounded to the nearest hundredths place? Use 3.14 for π. fill in the blank
___miles
Answers
We know that the circumference C of a circle is related to its diameter d by the formula:
C = πd
We are given that the circumference of the circle is approximately 7,459 miles. Substituting this into the formula above and solving for the diameter d, we get:
d = C/π
d = 7,459/3.14
d ≈ 2375.477707
Rounding to the nearest hundredths place, the diameter is approximately 2375.48 miles.
Therefore, the answer to fill in the blank is 2375.48miles.
Answer:
2374,27 miles
Step-by-step explanation:
diameter of circle = circumference/3.14
d = 7359 / 3.14 = 2374.27 miles
How many keys are required to fully implement a symmetric algorithm with 10 participants?
Answers
The number of keys required to fully implement a symmetric algorithm with 10 participants is: 45 (Option C)
What is a Symmetric Algorithm?Symmetric encryption or Algorithm is a kind of encryption that uses a single key (a secret key) to encrypt and decode electronic data.
The key must be exchanged between the organizations communicating using symmetric encryption so that it may be utilized in the decryption process.
What is the computation justifying the above result?The formula that determines the number of keys necessary for a symmetric algorithm is given as;
(n*(n-1))/2,
which is 45 in this situation, when n = 10.
That is
(10 * (10-1))/2
= 45.
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Full Question:
How many keys are required to fully implement a symmetric algorithm with 10 participants?
A. 10
B. 20
C. 45
D. 100
Rory is staying in a cabin on a hill 300 feet above sea level. She walks down the hill to the water’s edge. The equation of her average change in elevation over time is e = 300 – 10t, where t is the time in minutes since she left the cabin, and e is her elevation with regard to sea level. Which values are viable points, and what are their values in the table relating t and e?
Answers
Answer and Step-by-step explanation:
As per the given situation we have following equation
e = 300 - 10t
The elevation and the time can not be in the minus
= t ≥ 0
and
e ≥ 0
As per the provided equation, beginning at the time which is
t = 0
while
elevation which represents e = 300
whereas at the top,
when elevation = 0
So time will be
t = 30 minutes
Therefore, The viable points will be
(0 , 30) and (300 , 0)
Answer:
a = ✔ not viable
b = ✔ 265
c = ✔ 0
Step-by-step explanation:
Write an equation for the line that passes through (1,-9) and (1,12)
Answers
Equation of the line passing through (1, -9) and (1, 12) is y = -9
How to find equation of the lineThe equation to the line in slope intercept form
y = mx + c
where
m = slope
c = intercept
x = input variables
y = output variables
calculation of slope, m for (1, -9) and (1, 12)
(y - y₁) / (x - x₁) = m
m = (-9 - 12) / (1 - 1)
m = 1 / 0
m = undefined slope (this is the slope of vertical line)
equation of the line (1, -9)
(y - -9) = 0
y + 9 = 0
y = -9
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A plant is already 12.00 meters tall, and it will grow 15 centimeters every month. The plant's height, H (in meters), after x months is given by the following. H= 12.00 +0.15x What is the plant's height after 40 months?
Answers
Answer:
495cm
Step-by-step explanation:
so for a second forget about the already 12 meters. Multiply 15 by the amount of months, in this case 40 so 12x40= 480. Then add the 15, so its 495cm tall