The acceleration function is a(t) = 6(t - 3).
Acceleration is the rate at which an object changes its velocity. The acceleration function is a mathematical function that gives the acceleration of an object at any given time
To find the acceleration function, we need to take the second derivative of the given velocity function f(t).
f(t) = (t - 3)^3 + t
First, let's find the first derivative of f(t)
f'(t) = 3 × (t - 3)^2 + 1
Now, let's find the second derivative of f(t) ( the acceleration function )
a(t) = f''( t )
= d/dt [3 × (t - 3)^2 + 1]
Do the derivation
= 6(t - 3)
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The given question is incomplete, the complete question is:
The velocity (in meters per second) with which a roller coaster moves can be given by the function f(t) = (t - 3)^3 + t. find the acceleration function a(t).
The diameter,D , of a sphere is 19 mm. Calculate the sphere's volume , V.
I NEED THE ANSWER QUICKKKK
I remember doing this but I don’t seem to remember sorry
Select the expression that makes the equation true.
one half x (3 x 5 + 1) – 2 = ___
4 x (2 + 3)
(4 x 3) ÷ 2
6 ÷ 3 + 2
6 + 8 ÷ 4
The expression that makes the equation true is: (4 x 3) ÷ 2.
option 1 is the correct answer.
What is expression ?In mathematics, an expression is a combination of symbols and/or values that represents a quantity or a relationship between quantities. It can include variables, constants, mathematical operations, and functions.
According to the given information:first, let's simplify the expression within the parentheses:
3 x 5 + 1 = 15 + 1 = 16
Now, we can simplify the entire expression:
1/2 x (3 x 5 + 1) - 2 = 1/2 x 16 - 2 = 8 - 2 = 6
So, we need to select the expression that equals 6:
6 ÷ 3 + 2 = 4
6 + 8 ÷ 4 = 8
(4 x 3) ÷ 2 = 6
Therefore, the expression that makes the equation true is: (4 x 3) ÷ 2.
option 1 is the correct answer.
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Answer:
.
(4x3)---- 2
.
B
Step-by-step explanation:
hope this help!
>Y. Write exponential functions: word problems LZW
Dr. Powell is a veterinarian. He gave Ruby, one of the cats he is treating, 40 micrograms of
medication. Based on Ruby's size, Dr. Powell expects there will be about 32 micrograms of
medication remaining in her body after one hour. Dr. Powell knows that the amount of
medication remaining in Ruby's body will continue decreasing each hour.
Write an exponential equation in the form y = a(b)* that can model the amount of medication
in Ruby's body, y, x hours after it was administered.
Use whole numbers, decimals, or simplified fractions for the values of a and b.
y
DO
(0)
To the nearest whole number, how many micrograms of medication can Dr. Powell expect to
be remaining in Ruby's body after 4 hours?
micrograms
Rounding to the nearest whole number, Dr. Powell can expect about 16 micrograms of medication to be remaining in Ruby's body after 4 hours.
What is equation?In mathematics, an equation is a statement that two expressions are equal. It typically consists of two sides, a left-hand side and a right-hand side, separated by an equal sign (=). Equations are used to represent relationships between variables or to solve for unknown values. They are an important tool in algebra, calculus, and other areas of mathematics and science.
Here,
The exponential equation in the form y = a(b)^x that can model the amount of medication in Ruby's body, y, x hours after it was administered is:
y = 40(0.8)ˣ
where:
a = 40, the initial amount of medication given to Ruby
b = 0.8, the factor by which the medication decreases each hour
To find the amount of medication remaining in Ruby's body after 4 hours, we can substitute x = 4 into the equation and evaluate:
y = 40(0.8)⁴
y = 40(0.4096)
y = 16.384
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Triangle proofs level 2 please help!!!
numbers that are both positive and less then -3
Real number that is greater than or equal to zero. The only number that is both positive and negative is the number 0.
A designer enlarges an image with a length of 6 cm and a width of 9 cm by a scale factor of 3. The designer decides that the enlarged image is too large and reduces it by a scale factor of 0.5. Will the final image fit into a rectangular space that has an area of 121 square centimeters Search instead for A designer enlarges an image with a length of 6 cm and a widht of 9 cm by a scale factor of 3. The designer decides that the enlarged image is too large and reduces it by a scale factor of 0.5. Will the final image fit into a rectangular space that has an area of 121 square centimeters
The area of the final image is greater than 121 square centimeters, so the final image will not fit into a rectangular space that has an area of 121 square centimeters.
What is the scale factor?
A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The original image has a length of 6 cm and a width of 9 cm, and when it's enlarged by a scale factor of 3, its new length becomes 6 cm x 3 = 18 cm, and its new width becomes 9 cm x 3 = 27 cm.
Then, the designer reduces the enlarged image by a scale factor of 0.5, which means the new length becomes 18 cm x 0.5 = 9 cm, and the new width becomes 27 cm x 0.5 = 13.5 cm.
So, the final image has a length of 9 cm and a width of 13.5 cm.
To check if the final image will fit into a rectangular space that has an area of 121 square centimeters, we need to calculate its area:
Area of the final image = length x width
Area of the final image = 9 cm x 13.5 cm
Area of the final image = 121.5 square centimeters
Therefore, the area of the final image is greater than 121 square centimeters, so the final image will not fit into a rectangular space that has an area of 121 square centimeters.
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What is 16 + 2x = 2 + 4x
Answer:
x=7
Step-by-step explanation:
Check the attachment below:
Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. x²+6-9x
Answer:
x² - 9x + 6
Step-by-step explanation:
The polynomial in standard form is:
x² - 9x + 6
This is a quadratic polynomial because it has a degree of 2, and it has three terms.
What is the equation in vertex form of a parabola with a vertex of (–3, 4) that passes through the point (1, –4)
Answer:
y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
here (h, k ) = (- 3, 4 ) , then
y = a(x - (- 3) )² + 4 , that is
y = a(x + 3)² + 4
to ind a substitute the point (1, - 4 ) into the equation
- 4 = a(1 + 3)² + 4
- 4 = a(4)² + 4 ( subtract 4 from both sides )
- 8 = 16a ( divide both sides by 16 )
- [tex]\frac{8}{16}[/tex] = a , that is
a = - [tex]\frac{1}{2}[/tex]
y = - [tex]\frac{1}{2}[/tex] (x + 3)² + 4 ← equation of parabola
express x squared minus 5x + 8 in the form (x-a) squared + b
Answer:
(x-2.5)^2 + 1.75
Step-by-step explanation:
To write that as an equation, we get x^2 - 5x + 8.
now, we need to complete the square:
x^2 - 5x + 6.25 + 1.75 =
(x-2.5)^2 + 1.75.
50 points! Find the value of < Z O X:
< Z O X =
Answer:
64°
Step-by-step explanation:
You want the measure of angle ZOX, the smaller of a linear pair marked (3x -2)° and (5x +6)°.
Linear pairThe angles of a linear pair are supplementary—they total 180°.
(5x +6) +(3x -2) = 180
8x +4 = 180 . . . . . simplify
8x = 176 . . . . . . subtract 4
x = 22 . . . . . . divide by 8
The measure of angle ZOX is ...
∠ZOX = (3x -2)° = (3·22 -2)°
∠ZOX = 64°
__
Additional comment
Angle ZOY is ...
∠ZOY = (5·22 +6)° = 116°, the supplement of 64°.
Jason knows that za + 2d + g = 180°. Which of the following observations will allow him to complete his proof?
The equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.
given that za + 2d + g = 180°, some observations that could potentially be useful to Jason include:
Identifying any relationships or constraints between the variables za, d, and g that might help him simplify or solve the equation. For example, if he knows that za and g are complementary angles (i.e., they add up to 90°), he could substitute 90 - za for g in the equation to get a new expression in terms of za and d.
Using additional information about the angles or the situation to derive new equations or constraints that could help him solve for one or more variables. For example, if he knows that za and d are equal (i.e., za = d), he could substitute za for d in the equation to get a new expression in terms of za and g.
Identifying any patterns or structures in the equation that might suggest a particular approach or technique for solving it. For example, if he notices that the equation is a linear combination of three angles that add up to 180°, he might consider using systems of linear equations or other algebraic methods to solve for the variables.
Ultimately, the most effective observations for completing the proof will depend on the specific details of the problem and the approach that Jason is taking.
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The complete question:Jason knows that za + 2d + g = 180°. Which of the following observations, if true, would allow him to prove a statement or theorem related to the angles za, d, and g?
HELP ITS URGENT PLEASE
The total area of the given composite geometric figure is: 27 cm²
How to find the area of the composite figure?The formula for the area of a parallelogram is:
Area = base * height
The formula for the area of a square is:
Area = ¹/₂ * base * height
The area of the square is:
Area = 3 * 3
= 9 cm²
Area of parallelogram = 3 * 6
Area of parallelogram = 18 cm²
Total area of composite figure = 18 + 9
= 27 cm²
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Gary bought n notebooks for $3 each. he spent a total of $15. How many notebooks did he buy?
Answer:
Gary bought 5 notebooks
Step-by-step explanation:
the equation used for this would be 3n = 15
meaning you divide both sides by 3 which gets you n = 5
Data were recorded for the temperature of a cup of coffee over a 30 minute period. It is known that the temperature of
hot coffee will cool to room temperature following an exponential model.
Which of the following would linearize the data for temperature and minutes?
Minutes, Temperature
O Minutes, In(Temperature)
O In(Minutes), Temperature
In(Minutes), In(Temperature)
As it is known that the temperature of hot coffee will cool to room temperature following an exponential mode, the option which would linearize the data for temperature and minutes is "Minutes, ln(Temperature)". The Option B is correct.
What will linearize the data for temperature and minutes?Using logarithmic transformation, we can convert the exponential relationship between temperature and time into a linear relationship. By taking the natural logarithm of the temperature, we can rewrite the exponential model as:
ln(Temperature) = -kt + ln(T0)
In this model, ln(Temperature) is the natural logarithm of the temperature, k is a constant representing the rate of cooling, t is the time elapsed, and T0 is the initial temperature of the coffee.
This equation is in the form of a linear equation, y = mx + b, where ln(Temperature) is the y variable, -k is the slope, t is the x variable, and ln(T0) is the y-intercept. Therefore, plotting Minutes versus In(Temperature) will give a linear relationship.
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It would be very much appreciated if you helped me with this one problem...
Answer:Exact Form:
g=10/3
Decimal Form:
g=3. ¯3
Mixed Number Form:
g=3 1/3
Step-by-step explanation:
in which of the following ways are binomial distributions and hypergeometric distributions similar? multiple select question. they are both discrete distributions. they both have two possible outcomes: success or failure. the probability of success is constant in each trial. they both assume each trial is independent of each other.
Binomial distributions and hypergeometric distributions are similar in that they both have two possible outcomes (success or failure) and the probability of success is constant in each trial. They also both assume that each trial is independent of each other.
Both binomial distributions and hypergeometric distributions are similar in the following ways: they are both discrete distributions, they both have two possible outcomes (success or failure), the probability of success is constant in each trial, and they both assume that each trial is independent of each other.
A binomial distribution is a probability distribution that models the number of successes in a given number of independent trials with the same probability of success for each trial. In a binomial distribution, the random variable X is the number of successes in the given number of trials.
The probability of a success for each trial remains constant. The mean and variance of the binomial distribution are given by the formula: μ = np and σ2 = npq, respectively.
A hypergeometric distribution is a probability distribution that models the probability of selecting a certain number of successes in a given number of draws from a finite population without replacement. In a hypergeometric distribution, the random variable X is the number of successes in the given number of draws.
The probability of a success for each draw remains constant.
The mean and variance of the hypergeometric distribution are given by the formula: μ = nx/N and σ2 = nx(N-n)(N-x)/N2(N-1), respectively.
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Gareth won the lottery and invested it all into a savings account at the start of 2014.
There was £4 862 025 in the account at the start of 2017.
If compound interest is added to his account at a rate of 5% per annum, how much did he have in his account at the start of 2015?
Gareth had £4,199,999.94 in his account at the start of 2015 at rate 5%.
What is compound interest and simple interest?Compound interest is computed as a percentage of the principle plus the accrued interest, whereas simple interest is determined as a fixed percentage of the original amount. In other words, whereas compound interest is calculated on the principle amount plus any interest that has previously been earned, simple interest is computed on the initial principal amount. So, over time, compound interest often produces larger returns than simple interest, particularly for long-term investments.
The compound interest is given by:
[tex]A = P(1 + r/n)^{(n*t)}[/tex]
Substituting the given values, we get:
[tex]P = 4,862,025 / (1 + 0.05/1)^{(1*3)}\\P = 4,862,025 / 1.157625\\P = 4,199,999.94[/tex]
Gareth had £4,199,999.94 in his account at the start of 2015.
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Whats the answer to this question?
The triangles are necessarily congruent by the ASA congruence rule.
What is the ASA congruence rule?The ASA, which is an acronym for Angle-Side-Angle, congruence rule states that if two angles and an included side of one triangle are congruent to two angles and an included side of another triangle, then the two triangles are congruent.
The angle markings on the triangles ΔJLK and ΔZXY indicates;
∠J ≅ ∠Z, ∠K ≅ ∠Y
The side markings on the triangles indicates
Side JK in triangle ΔJLK is congruent to side ZY in triangle ΔZXY
Therefore, two angles and an included side in triangle ΔJLK are congruent to two angles and an included side in triangle ΔZXY, therefore, triangle ΔJLK is congruent to triangle ΔZXY by Angle-Side-Angle, ASA congruence rule.
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ABCD is a rectangle AD = 3x-12 AB=x+4
Perimeter of rectangle is 38 cm work out length AD
The length of AD is 23.5 cm.
The perimeter of a rectangle is the sum of the lengths of all four of its sides. So,
Perimeter = AD + AB + BC + CD
38 cm = AD + (x + 4) + (3x - 12) + (x + 4)
38 cm = 4x + 4
34 cm = 4x
x = 8.5 cm
Therefore, AD = 3x - 12 = 3(8.5) - 12 = 23.5 cm
The formula used to calculate the perimeter of a rectangle is P = 2(l + w) where P is the perimeter, l is the length and w is the width. The length of AD can be calculated by solving the equation 38 cm = 2(l + w). We know that AB = x + 4 and BC = 3x - 12, so l + w = x + 4 + 3x - 12 = 4x - 8. This means that 38 cm = 2(4x - 8), which can be rearranged to 34 cm = 4x. Therefore, x = 8.5 cm, so l = 8.5 cm + 4 cm = 12.5 cm and AD = 12.5 cm - 8.5 cm = 23.5 cm.
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Help asap first answer will get brainliest
Answer:
C. 13,200 mm²
Step-by-step explanation:
Split the irregular shape.2 triangles and a rectangleFind the areas of each shape.Triangle = A = 1/2 bhWe figured that, 60 is the height of a rectangle and 90 is the length that is connected to the triangles. Which is 90 - 60 = 30. And then the width is 200 that was not disrupted by the irregular shape. The we found that 120 + 2x = 200 because there are 2 triangles that are disrupting the straight line of the width of a rectangle. As a result, it is x = 40 so 40 are the base of the triangle.We plug it in, A = 1/2 40(30), 1/2 (1200), and A = 600.We multiply this by 2 because we have 2 triangles so 600 x 2 = 1200.Rectangle = A = bhWe found the A = bh so we have base which is 200 and we have height which is 60.We multiply 60 and 200. A = 60 x 200 = 12000Overall, we have area of a rectangle which is 12000 and the area of the two triangles are 1200.
We both add them to get the area of the irregular shape.
12000 + 1200 = 13,200 mm²
Factor the following polynomial completely 6x^2+12x+6 the correct answer is 6(x+1)^2 explain in full detail how this answer is achieved you must show every step to receive full credit
please
Answer: 6(x+1)^2
Step-by-step explanation:
1. Find the GCF. Because you know the equation is 6x^2+12x+6, you can see that the coefficients, 6 and 12, are all factors of 6. To make factoring easier, factor out 6 from all the coefficients, which leaves you with 6(x^2+2x+1)
2. Factor the equation in the parentheses. If you have learned your perfect squares, then you know that x^2+2x+1 is (x+1)^2 because x^2+2x+1 = (x+1)(x+1) (you can foil that out if you want to check). Once finished with this, it leaves you with 6(x+1)^2
I need help!
Given the points Q(-8, -8) and R(2, 7), find the coordinates of the point P on directed line segment QR that partitions segment QR in the ratio 2:3.
Answer:
(-2/5, 11/5)
Step-by-step explanation:
We can use the formula for finding a point that divides a line segment into a given ratio. Let P be the point on the line segment QR that partitions it in the ratio 2:3. Then we have:
P = ( (3x2 + 2x1)/(3+2), (3y2 + 2y1)/(3+2) )
where (x1, y1) = (-8, -8) is the coordinates of Q and (x2, y2) = (2, 7) is the coordinates of R.
Substituting the values, we get:
P = ( (32 + 2(-8))/(3+2), (37 + 2(-8))/(3+2) )
P = ( (-2/5), (11/5) )
Therefore, the coordinates of the point P on the directed line segment QR that partitions it in the ratio 2:3 are (-2/5, 11/5).
The total cost of a vacation rental depends on when it is being rented: during the week, on the weekend, or over a holiday. The total cost for three different groups to stay at the rental is shown in the table.
The correct statement regarding the solution of the system of equations is given as follows:
A. The solution to the system is viable.
How to model the situation?The situation is modeled by a system of equations, for which the variables are given as follows:
Variable x: cost of a weeknight.Variable y: cost of a weekend night.Variable z: cost of a holiday.From each row of the table, the equations are given as follows:
4x + 2y = 614.3x + y + z = 555.5x + y + z = 733.Subtracting the third equation by the second, the value of x is given as follows:
2x = 178
x = 178/2
x = 89.
From the first equation, the value of y is given as follows:
y = [614 - 4 x 89]/2
y = 129.
From the second equation, the value of z is given as follows:
z = 555 - 3 x 89 - 129
z = 159.
Hence the system has a viable solution.
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Determine if the following table is linear, exponential or quadratic. Then write the equation that represents the function.
This table is an example of exponential growth.
The equation that represents this exponential growth is y = 2ˣ.
What is the equation of Exponential growth?Exponential growth is characterized by an equation of the form y = bˣ, where b is a positive constant.
This table is an example of exponential growth.
This is because the y-values are increasing exponentially as the x-values increase.
The equation that represents this exponential growth is y = 2ˣ.
This can be seen by the fact that the y-values are equal to 2ˣ, where x is the corresponding x-value.
When x = 0, y = 2⁰ = 2.
When x = 1, y = 2¹ = 6.
When x = 2, y = 2² = 18.
When x = 3, y = 2³ = 54.
And finally, when x = 4, y = 2⁴ = 162.
Here, b = 2.
Exponential growth is different from linear and quadratic growth in that the rate of increase is not constant; instead, it increases as the x-values increase.
This is because the exponent in the equation increases as the x-values increase. This is why the y-values increase exponentially as the x-values increase.
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An airplane traveling from Chicago to Los Angeles travels 15 miles every 2 minutes. On the return trip, the plane travels 25 miles every 3 minutes. Graph each ratio relationship in the coordinate plane.
Answer:
(6,45)
Step-by-step explanation:
To graph each ratio relationship in the coordinate plane, we can plot the ordered pairs (time, distance) for each leg of the trip. For the first leg from Chicago to Los Angeles, the plane travels 15 miles every 2 minutes. So we can plot the following points:
(0, 0) - starting point
(2, 15) - after 2 minutes, the plane has traveled 15 miles
(4, 30) - after 4 minutes, the plane has traveled 30 miles
(6, 45) - after 6 minutes, the plane has traveled 45 miles
(8, 60) - after 8 minutes, the plane has traveled 60 miles
We can plot these points on a coordinate plane, with time on the x-axis and distance on the y-axis. The resulting graph would show a straight line with a slope of 7.5 (rise of 15/2 and run of 1).
For the second leg from Los Angeles to Chicago, the plane travels 25 miles every 3 minutes. So we can plot the following points:
(0, 0) - starting point
(3, 25) - after 3 minutes, the plane has traveled 25 miles
(6, 50) - after 6 minutes, the plane has traveled 50 miles
(9, 75) - after 9 minutes, the plane has traveled 75 miles
(12, 100) - after 12 minutes, the plane has traveled 100 miles
We can plot these points on the same coordinate plane as the first leg. The resulting graph would also show a straight line with a slope of 8.33 (rise of 25/3 and run of 1).
The two graphs would intersect at the point (6, 45), which represents the halfway point of the round trip.
a number m, rounded to 1 dp is 48.2
another number, n, rounded to 1 dp is 6.7
what are the lower and upper bound of m-n???
Answer:
I just had to say those numbers because of so I can send it like I'm about
To find the lower bound and upper bound of the difference m-n, we need to first find the possible range of values for m and n.
• For m rounded to 1 decimal place, the actual value could be anywhere between 48.15 and 48.25 (since the digit in the second decimal place could be anything from 0 to 9, and we round to the nearest 0.1).
• For n rounded to 1 decimal place, the actual value could be anywhere between 6.65 and 6.75.
Now, we can calculate the lower bound and upper bound of m-n:
Lower bound of m-n = (48.15 - 6.75) = 41.4
Upper bound of m-n = (48.25 - 6.65) = 41.6
Therefore, the lower and upper bounds of m-n are 41.4 and 41.6, respectively.
Describe the range of the relationship shown here
Expand this equation 5(y+3)
5y+15
I think this is correct. Hope this helps:)
Answer: 5y + 15
Step-by-step explanation: 5(y+3)
= 5(y) + 5(3)
= 5y + 15
The graph shows the depth, y, in meters, of a shark from the surface of an ocean for a certain amount of time, x, in minutes.
Part A: Describe how you can use similar triangles to explain why the slope of the graph between points A and B is the same as the slope of the graph between points A and C. (4 points)
Part B: What are the initial value and slope of the graph and what do they represent? (6 points)
The slope of the graph would give us the speed of the motion and that is 40 m/min.
How would the principle of similar triangles be used to show that slopes are equal?We can use this principle to show that the slopes of two lines are equal if they are parallel and intersected by a transversal line. Here's how:
Draw two parallel lines, labeled as line A and line B.
Draw a transversal line that intersects both lines A and B at two points.
Draw a perpendicular line segment from one of the intersection points on line A to the transversal line, and label it as segment 1.
Draw a perpendicular line segment from the corresponding intersection point on line B to the transversal line, and label it as segment 2.
The triangles formed by segment 1, the transversal line, and a segment on line A, and by segment 2, the transversal line, and a segment on line B, are similar triangles.
Since the corresponding sides of similar triangles are proportional, we can set up the following proportion: segment 1 / segment on line A = segment 2 / segment on line B.
Simplifying the proportion, we get segment 1 / segment 2 = segment on line A / segment on line B.
Since segment 1 and segment 2 are both perpendicular to the transversal line, they represent the rise of the lines A and B, respectively. The segments on lines A and B represent the run of the lines A and B, respectively. Therefore, we can rewrite the proportion as rise of line A / run of line A = rise of line B / run of line B.
This shows that the slopes of the two parallel lines, line A and line B, are equal.
The slope of the graph is;
m = 140 - 60/2 - 0
m = 40 m/min
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