The equation of motion for the mass attached to the spring
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
What is the equation of motion?Generally, The equation of motion for a mass on a spring is given by Hooke's law, which states that the force exerted by a spring is proportional to its displacement from equilibrium. The proportionality constant is known as the spring constant, which is denoted by the letter k.
In this case, the force exerted by the spring is 400 newtons, and the displacement from equilibrium is 2 meters. Therefore, the spring constant is given by:
k = F/x = 400 N/2 m = 200 N/m
The equation of motion for a mass on a spring is given by:
F = ma = -kx
where F is the force exerted by the spring, m is the mass of the object, a is the acceleration of the object, and x is the displacement of the object from equilibrium.
Substituting the values for the spring constant and the mass, we get:
-kx = -(200 N/m)(50 kg)(x'')
Solving for the acceleration, we get:
x'' = -k/m = -200 N/m / 50 kg = -4 m/s^2
This is the equation of motion for the mass attached to the spring. The negative sign indicates that the acceleration is in the opposite direction of the displacement, as is expected for a mass on a spring.
Finally, to find the equation of motion, we need to take into account the initial velocity of the mass. The equation of motion for an object with initial velocity is given by:
x = x_0 + v_0t + (1/2)at^2
where x is the displacement of the object, x_0 is the initial displacement (in this case, the equilibrium position of the spring), v_0 is the initial velocity, t is time, and a is the acceleration.
Substituting the values for the acceleration and the initial velocity, we get:
x = x_0 + 10 m/s t + (1/2)(-4 m/s^2)t^2
This is the equation of motion for the mass attached to the spring. The initial displacement, x_0, is the equilibrium position of the spring, which is assumed to be at x=0 in this case.
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12. Carly's family is going to buy cell phones for the entire family. After some research they have narrowed their choices
down to 2 companies. AT&T charges a monthly rate of $100 plus $15 for each phone on the account. Their competitor,
Sprint, charges a flat monthly fee of $200 and they will receive an unlimited number of phones on the account.
a. Write an equation for the cost of each cell phone provider and then graph the equations.
AT&T:
Sprint:
b. Use any method to determine which company would be cheaper if Carly's family consists of Carly, mom, dad, two brothers, and one sister. Explain your reasoning
Answer:
Step-by-step explanation:
a. The equation for the cost of AT&T would be $100 + $15n, where n is the number of phones on the account. The equation for the cost of Sprint would be $200.
We can graph these equations on a coordinate plane with the x-axis representing the number of phones on the account and the y-axis representing the monthly cost. The graph for the cost of AT&T would be a straight line starting at the point (0,100) and going through the point (1,115), (2,130), etc. The graph for the cost of Sprint would be a horizontal line at the y-coordinate of 200.
b. In order to determine which company would be cheaper for Carly's family, we can simply plug in the number of phones they have (5) into each of the equations we derived in part a. This would give us a cost of $200 for AT&T and $200 for Sprint. In this case, both companies would be equally cheap for Carly's family.
Alternatively, we could graph the equations and see which company's line is lower on the y-axis for the given number of phones (5). This would also show that both companies would be equally cheap for Carly's family in this case.
A taste test asks people from Texas and California which pasta they prefer, brand A or brand B. This table shows the results,
Answer:
D. 0.53
Step-by-step explanation:
California = 90
Total of those who prefer Brand A = 170
To find the percentage, you do:
90/170 × 100 = 52.941...
However you have to round it to two decimal points, hence you do:
52.941 ≈ 53%
53% = 0.53
This is due to 53% representing 53/100 = 0.53
Therefore, the probability that the person that likes brand A is from California is 0.53
:)
There are two investment options: Option 1: An initial investment of $5 that increases by 50% every year. Option 2: An initial investment of $0.01 that doubles every year. Write an equation for each option to model the value A of the account after x years
Equation for each option to model the value A of the account after x years is 5+ 5/nⁿ and 2ˣ 0.01.
What is an equation?
In arithmetic,an equation may be a formula that expresses the equality of 2 expressions, by connecting them with the sign =.
Main body:
for option 1
initial investment is $5 after 1 year investment is
5+5/2
after 2 year 5+5/2+(5+5/2)/2=5+5/2+5/2²
continuing this way we get the formula
5+ 5/nⁿ
for option 2
after 1 year money becomes 2*0.01
after 2 year money becomes 2²*0.01
after x year money becomes 2ˣ 0.01
Hence the forumla for each option is as provided.
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A small cube has the volume shown. Its side length is 3.5 in. less than a second, larger cube. What is the volume of the larger cube?
Volume:85 in^3
Answer:
not possible
Step-by-step explanation:
Answer:
[tex]493.039 \;in^3[/tex]
Step-by-step explanation:
If each side of the cube is [tex]a[/tex] then the volume of the cube is given by [tex]a^3[/tex]
If Volume is [tex]V[/tex] then each side [tex]a = \sqrt[3]{V}[/tex]
Here we are given the volume of the smaller cube as [tex]85\; in^3[/tex]
So each side of this cube = [tex]\sqrt[3]{85} = 4.396 \approx 4.4 \;in[/tex]
and each side of the larger cube [tex]= 4.4 + 3.5 = 7.9\;in[/tex]
Volume of larger cube [tex]= 7.9^3 = 493.039 \; in^3[/tex]
△ABC has vertices at A(-2, 4), B(-1, 1), and C(2, 2). The slope of AB¯¯¯¯¯¯¯¯ is , the slope of BC¯¯¯¯¯¯¯¯ is , and the slope of AC¯¯¯¯¯¯¯¯ is . △ABC a right triangle because
The slope of AB -3
The slope of BC 1/3
The slope of AC -1/2
△ABC a right triangle because two lines are perpendicular shown by a negative reciprocal slope -3 and 1/3
How to determine the slopesThe slope is represented as m, The slope by definition is the ratio change of the output values to the input values
The slope, m using the points A(-2, 4), and B(-1, 1)
m = (y₀ - y₁) / (x₀ - x₁)
m = (4 - 1) / (-2 - -1)
m = (3) / (-1)
m = -3
The slope, m using the points B(-1, 1), and C(2, 2)
m = (1 - 2) / (-1 - 2)
m = (-1) / (-3)
m = 1/3
The slope, m using the points A(-2, 4), and C(2, 2)
m = (4 - 2) / (-2 - 2)
m = (2) / (-4)
m = -1/2
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Could someone help me solve this?
Determine the equation that represents the proportional relationship shown in each table below.
Drag an equation into the box beside each table.
k=4/5h k=5/4h h=1/5 k h=5/1 k
The equations of the proportional relationships from the table are k = 5h, k = 5/4h and k = 1/5h
How to determine the equations of the proportional relationships?From the question, we have the following parameters that can be used in our computation:
Table 1Table 2Table 3The equation of a proportional relationship is represented as
k = Y/X * h
Where
(X, Y) is the coordinate of any ordered pair from the function or table
Using the above as a guide, we have the following:
Table 1
k = 10/2 * h
Evaluate the products and the quotient
k = 5h
Table 2
k = 5/4 * h
Evaluate the products and the quotient
k = 5/4h
Table 3
k = 5/25 * h
Evaluate the products and the quotient
k = 1/5h
Hence, the equations are k = 5h, k = 5/4h and k = 1/5h
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Willka can cover 13.5 m^2 with 3L of paint
Complete the table using equivalent ratios.
Willka covers 4.5 m² in 1L paint and 45 m² in 10L in paint according to the table.
What are equivalent ratios?
We know that the equivalent ratio is defined as the ratio which is having the same proportion as given ratio.
Now, using the division property of the ratio, we will divide the given ratio with the same number both sides.
According to the given question:
If Willka covers 13.5 m² with 3L paint, to cover x m² she will need 1L paint
By equivalent ratios
13.5 : 3 = x : 1
x = 13.5 / 3
x = 4.5
Similarly to cover y m² she needs 10L paint
13.5 : 3 = y : 10
y = 13.5 x 10/3
y = 45
Therefore the answer for the blanks is 4.5 and 45.
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Tricia got a 56% on her math test.
If she answered 14 questions
correctly, how many were on the
test?
Answer:
25 Questions
Step-by-step explanation:
RationingThis Question tests on the concept of Rationing using percentages.
Eg. 45% of 100 = 45, therefore 100% of 100 = 100.
SolutionGiven information from the question:
56% = 14 Questions
1% = (14 ÷ 56) Questions
Total number of questions in the test = 100%
100% = (14 ÷ 56) × 100 Questions = 25
Answer:
[tex]\huge\boxed{\sf 25\ questions}[/tex]
Step-by-step explanation:
Let the total questions be x.
Given that,
56% of total questions = 14
Key: "of" means "to multiply", % means out of hundred.
[tex]\displaystyle \frac{56}{100} \times x = 14\\\\0.56 \times x = 14\\\\Divide\ 0.56\ to\ both\ sides\\\\x = 14/0.56\\\\x = 25[/tex]
So, there were 25 questions on the test.
[tex]\rule[225]{225}{2}[/tex]
Ava’s runs at a rate of 15 kilometers per hour. What is Ava’s speed in meters per minute?
Answer:
250 meters per minute.
Step-by-step explanation:
1 km = 1000 m
15 km = 15*1000 = 15000 m
1 hour = 60 min
Then:
15km/h = 15000km/60minutes
= 250 meter per minute
Answer:250 meters / minute
Step-by-step explanation:1 km/h = 16.66667 m/min
Which of the following statement(s) is/are NOT TRUE for binary search algorithm? (select all that apply] * Binary search algorithm can be used for any arrays. Binary search algorithm can be implement using either iterative or recursive solutions. The worst-case time complexity of binary search is greater than sequential search Binary search algorithm uses the divide and conquer strategy. None of the above
are NOT true for binary search algorithm.
Now, According to the question:
Options 1, 3 are NOT true for binary search algorithm
Hence, Binary search algorithm can be used for any arrays.
and, The worst-case time complexity of binary search is greater than sequential search
are NOT true for binary search algorithm.
In the question:
Which of the following statement(s) is/are NOT TRUE for binary search algorithm? (select all that apply]
Binary search algorithm can be used for any arrays. Binary search algorithm can be implement using either iterative or recursive solutions. The worst-case time complexity of binary search is greater than sequential search Binary search algorithm uses the divide and conquer strategy. None of the aboveLearn more about Algorithm at:
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The number of miles driven by Harper is directly proportional to the number of gallons she used.
How many miles would she drive on } 50 gallons?
Answer:
Below
Step-by-step explanation:
From the data , the miles per gallon is
199.2 mi / 6 gal or 265.6 mi / 8 gal or 863.2 / 26
= 33.2 mi/gal
for 50 gallons this would be
33.2 mi / gal * 50 gal = 1660 mi
HELP What is the solution to this inequality? 6.9 < x−3 1/2
Answer:
Solve for x
by simplifying both sides of the inequality, then isolating the variable.
Inequality Form: x>10.4
Interval Notation: (10.4,∞)
Step-by-step explanation:
(2,5) and (-4,2) in standard form
The standard form is y= 1/2x+ 4.
What is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
(2,5) and (-4,2)
So, slope
= (2- 5)/ ( -4 - 2)
= -3 / (-6)
= 1/2
and, using slope- intercept form
y- 5 = 1/2( x - 2)
y-5 = 1/2x -1
y= 1/2x + 4
Hence, the standard form is y= 1/2x+ 4.
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8x-4=36
Solve for x please
Answer: x=5
Step-by-step explanation:
isolate x
8x-4+4=36+4
8x=40
x=5
Answer:
x=5
Step-by-step explanation:
You would first want to add 4 to both sides. Then divide 40 and 8 by 8 and you get x=5.
equations c= 5/9(F-32
When the temperature is 30° in Celsius, the temperature in Fahrenheit is 86.
What is an equation?An equation is a combination of different variables, in which two mathematical expressions are equal to each other.
The given equation to find the temperature,
C= 5/9(F-32) (1)
Here, C represents the temperature in Celsius,
And F represents the temperature in Fahrenheit.
To find the temperature in Fahrenheit, when C = 30°,
Substitute C = 30° in equation (1),
30 = 5/9(F - 32)
6 x 9 = F - 32
54 = F - 32
F = 86
The temperature in Fahrenheit is 86.
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Look at photo for problem
Just need chart filled out
5. y=(x+4)(x-1)
On solving the given equation y=(x+4)(x-1) the point on the graph are as follows:
(-4,0), (-1,0), (2,6), (-3,-4) &(0,-4)
What is a graph?
A relation is a specific instance of a function graph. A function is truly equivalent to its graph in set theory and the current mathematical underpinnings.
It is frequently more helpful to think about functions as mappings, which include the sets that constitute the domain and the codomain in addition to the relationship between input and output. For instance, the codomain should be considered while determining if a function is onto (surjective) or not. The codomain of a function is not determined by the graph alone.
It is typical to use the phrases function and graph of a function interchangeably since, although referring to the same thing, they suggest distinct ways of looking at it.
1)
let y=0
0=(x+4)(x-1)
i.e. x = -4 and -1
2)
Let x =0
y=(0+4)(0-1)
y=-4
3)
Let x = 2
y=(2+4)(2-1)
y=6
4)
Let x = -3
y=(-3+4)(-3-1)
y=-4
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You take a vacation with your family to Cancun, Mexico. One day you decide to rent a jet ski while at the beach. The equation T=
0.55m 5 gives the total cost in dollars T for renting a jet ski for m minutes. What is the cost for renting a jet ski for 35
minutes?
Answer:
19.25
Step-by-step explanation:
t = .55m
t = .55(35)
t = 19.25
I am not sure what you mean by 5 give the total cost in dollars T. I am not sure where the comes from.
Answer:
$24.25
Step-by-step explanation:
Given equation:
[tex]T=0.55m+5[/tex]
where:
T = total cost of renting a jet ski (in dollars)m = number of minutesTo find the total cost of renting a jet ski for 35 minutes, substitute m = 35 into the given equation and solve for T:
[tex]\implies T=0.55(35)+5[/tex]
[tex]\implies T=19.25+5[/tex]
[tex]\implies T=24.25[/tex]
Therefore, the total cost of renting a jet ski for 35 minutes is $24.25.
what values make the inequality b≤-6b≤−6 true
The values which are less than -7 on the number line makes the value true.
b≤-6
-7≤-6
-9≤-6
-256≤-6
only in the case where b = -6 satisfy only equality condition not less than condition. Other than this remaining other values which are less than -7 on the number line including rational numbers , decimal numbers, all negative numbers which are less than -6 satisfy.
The values which are less than -7 on the number line makes the value true
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Question what makes the value Inequality b≤-6 is true for what values of b?
A computer costs £ 964. A tax of 18.5% is then added to the cost of the computer.
Work out the amount of tax that is added to the cost of the computer.
Answer:
£ 178.34 tax amount
Step-by-step explanation:
A computer costs £ 964. A tax of 18.5% is then added to the cost of the computer. Work out the amount of tax that is added to the cost of the computer.
18.5% tax = 0.185 tax rate
0.185 tax rate * £ 964 = £ 178.34 tax amount
Lauren was given a gift card for a coffee shop. Each morning, Lauren uses the card to buy one cup of coffee. The original amount of money on the gift card was $10 each cup of coffee costs $2. Make a table of values and then write an equation in terms of x, representing the amount money remaining on the card after buying x cups of coffee.
The amount of money left on the gift card, in term of the number of cups, a Lauren has bought is represented by the equation would be A = 10 - 2a.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We are given that from the task content that the total amount of money Lauren has initially is $10.
Hence, each cup of coffee costs $2.
Since the amount of money Lauren has left each time,
That is related to the number of coffee cups bought by the equation;
A = 10 -2a.
where a ranges be between 0 and 5.
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rhonda's cell phone plan cost 50$ per month plus 0.25 for each text she sends, how many text messages can she send and still pay less than a total of 70$
The text messages that Rhonda can send and still pay less than a total of $70 is less than 80 messages.
How many text messages can she send?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
Let the number of tests be represented by t.
The inequality will then be:
50 + 0.25t < 70
0.25t < 70 - 50
0.25t < 20
Divide
t < 20/0.25
t < 80
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What is the net force if the forces are balanced? 0N,-5N,100J, 5N
When forces are balanced the sum of the net force is 0 N
What is net force?The total of all forces exerted on an object is known as the net force.
A mass can accelerate due to net force. A body is subject to another force whether it is at rest or in motion.
When there are a lot of forces acting on a system, the term "net force" is employed.
When the net force is summed to zero then the forces are said to be balanced
Hence a zero net force is a balanced force and will result to 0 N
N is the short form of Newton which is the unit of force
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Which of the following expressions are equivalent to - (8/3)
The solution is, the following expressions are equivalent to 4⁻³ / 4⁻⁸
A. 4^8/4^3
D. 4⁵
What is an exponent in math?An exponent refers to the number of times a number is multiplied by itself. For example, 2 to the 3rd (written like this: 23) means: 2 x 2 x 2 = 8. 23 is not the same as 2 x 3 = 6. Remember that a number raised to the power of 1 is itself.
here, we have,
We have to calculate to find the result -
The expression is = 4^(-3)/4^(-8)
According to the indices rule, the power will be deducted if it is a division.
Therefore, a^m/a^n = a^(m-n)
Using that formula,
4⁻³ / 4⁻⁸
= 4⁸ / 4³
= 4⁽⁸⁻³⁾
=4⁵
Therefore, the answer choice D is the option, and the answer is 4^5.
Option A is also correct.
Because we can find 4^5 with the help of that option.
Alternative way,
4^(-3)/4^(-8)
= 4^(-3+8)
= 4^(8-3)
= 4^8/4^3
In the is way, we can also find option A is correct.
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complete question:
Which of the following expressions are equivalent to 4^-3/4^-8?
If a fair coin is tossed 5 times, what is the probability, rounded to the nearest thousandth, of getting at most 2 heads?
Probability to get at most 2 heads after flipping coin for 5 times is 1/2.
What is probability?Probability is the ratio of good outcomes to all possible outcomes of an event is known as the probability.
The number of positive results for an experiment with n outcomes can be represented by the symbol x.
The probability of an event can be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
With a fair coin, there are [tex]2^{5}[/tex] = 32 possible combinations of heads and tails after 5 flips.With 0 heads,5C0 = 5!/0!5! = 1 ways
get one head 5C1 = 5!/ 4!1! = 5 ways
To obtain precisely 2 heads,5C2 = 5!/ 2!3! = 10 ways
Obtain 3 heads,5C3 = 5!/ 3!2! = 10 ways
Total methods to gain at most 2 heads are 1+5+10 = 16.
Probability to get at most 2 heads is = ( total methods to gain at most 2 heads)/(total ways)
P(total methods to gain at most 2 heads) = 16/32 =1/2.
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Precious is twice as old as Mika 2 years ago. The difference of their present age is 7. What is Precious' present age?
the answer is 14
simply multiply mika age by 2
since the difference is 7
meaning that mika is seven
and twice is 14
30 points !! Please help now math
The given 4th degree polynomial is ,[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex] zeroes of the equation are -5,-1,2
How to write equation of 4th degree polynomial from given graph?A fourth-degree polynomial, or quartic function, is one that has a variable raised to the fourth power as its highest order term.
If the highest order term is positive or negative, a fourth-degree polynomial's graph will frequently resemble a M or a W.
The function will reach infinity on both sides if the leading term's coefficient, a, is positive.
The function will extend to minus infinity on both sides if the coefficient an is negative.
The function's y-intercept, or the point at which the function crosses the y-axis, is indicated by the word a0. The x-intercepts are revealed by the function's roots.
Inflection Points are roots of double derivate equation.
Calculation:Given;
From the graph, x-intercepts are -5,-1,2.
That gives us (x+5),(x+1),(x-2) are factors of the function;
As at [tex]x=-1[/tex] graph touches x axis (x+1) is a double factor of f(x)
That leaves us with [tex](x+5),(x+1)^2,(x-2)[/tex] as factors of f(x);
[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex];
From graph inflections points are -2.686,0.186;
That gives [tex]f^|^|(x)=(x+2.686)(x-0.186)[/tex]
The given 4th degree polynomial is ,[tex]f(x)=(x+5)(x+1)^2(x-2)[/tex] zeroes of the equation are -5,-1,2
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Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
A has the larger standard devlation.
What is standard devlation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
We are given two plots of normal distributions A and B.
The mean of a normal distribution is located at the center of the plot.
Since the centers of both of the normal distributions A and B seems to be aligned, therefore, they both seems to have equal means.
The standard deviation basically determines the shape of the distribution.
As you can see, the normal distribution A is more spread out and thus has a larger standard deviation than normal distribution B.
Therefore, the two correct options are
• The means of A and B are equal.
• A has larger standard deviation.
Complete question: Given the plot of normal distributions A and B below, which of the following statements is true? Select all correct answers.
Select all that apply:
A has the larger mean.
B has the larger mean.
The means of A and. Q jual.
A has the larger standard devlation.
B has the larger standard deviation.
The standard deviations of A and B are equal.
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The bar graph below shows the regions in which all the passenger cars were produced during a recent year. What is the
difference between the number of passenger cars produced in Asia and the number produced
in Eastern Europe/Russia?
Latin America
North America
Eastem Europe/Russia
Asia
Westem Europe
0 2
4 6 8 10 12 14 16
Cars produced (in millions)
The difference between the number of passenger cars produced in Asia and the number produced in Eastern Europe/Russia is given as follows:
3 million.
What is shown by the bar graph?The bar graph given by the image at the end of the answer shows the number of passenger cars produced in each of the regions.
From the graph, the numbers for each region are given as follows:
Latin America: 2 million.North America: 3 million.Eastern Europe/Russia: 8 million.Asia: 11 million.Western Europe: 15 million.Then the difference between the number of passenger cars produced in Asia and the number produced in Eastern Europe/Russia is calculated as follows:
11 - 8 = 3 million.
Missing InformationThe bar graph is given by the image shown at the end of the answer.
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A parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. Let G be the dollar cost of parking for t hours. Is t a function of G? Explain your reasoning. (pleaseeee help I will mark you brainliest.)
T is not a function of G as they don't have a constant of proportionality.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It should be noted that the constant of proportionality simply means the ratio that relates two given values in what is known as a proportional relationship. In this case, other names for the constant of proportionality are the constant ratio, constant rate, unit rate, constant of variation, or the rate of change
Since the parking garage charges $5 for the first hour, $10 for up to two hours, and $12 for the entire day. This implies that they don't have a constant of proportionality.
In this case, the time doesn't have an effect on amount paid.
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