A warehouse is being built that will have neither heating nor cooling. Depending on the amount of insulation, the time constant for the building may range from 2 to 4 hr. To illustrate the effect insulation will have on the temperature inside the warehouse, assume the outside temperature varies as a sine wave, with a minimum of 13°C at 2:00 A.M. and a maximum of 33°C at 2:00 P.M. Assuming the exponential term (which involves the initial temperature To) has died off, what is the lowest temperature inside the building if the time constant is 2 hr? If it is 4 hr? What is the highest temperature inside the building if the time constant is 2 hr? If it is 4 hr? If the time constant is 2 hr, then the lowest temperature inside the building is about °C. (Round to the nearest tenth as needed.)
Answers
When the time constant is 1 hour, the building's interior temperature will range from a minimum of 16.3°C to a maximum of 31.7°C.
If the time constant is increased to 5 hours, the temperature range shifts to a minimum of 19.1°C and a maximum of 28.9°C.
Let's start with the lowest temperature. When the outside temperature is at its minimum of 13°C, the temperature inside the building will also be at its minimum, assuming that the building has had enough time to reach thermal equilibrium.
Using the formula for the time constant, we can calculate the fraction of the difference between the outside temperature and the initial temperature that corresponds to 63.2%, according to the exponential term,
\(e^{-t/\iota}\) = 0.632
where t is the time elapsed since the outside temperature started to rise. Solving for t, we get:
t = τ * ln(1/0.632) = 0.693 * τ
For a time constant of 2 hours, this gives us:
t = 0.693 * 2 = 1.386 hours
This means that the lowest temperature inside the building occurs about 1.4 hours after the outside temperature starts to rise. At this point, the temperature inside the building will be given by:
Tin = Tout + (To - Tout) * \(e^{-t/\iota}\)
where To is the initial temperature inside the building, which we are assuming has died off. Plugging in the values, we get:
Tin = 13 + (To - 13) * \(e^{-1.386/2}\)
Tin = 13 + (To - 13) * 0.359
Solving for the lowest temperature inside the building, we get:
Tin = 13 + 0.359To - 4.667
Tin = 0.359To + 8.0
When the time constant of a building is 1 hour, the indoor temperature will range from a minimum of 16.3°C to a maximum of 31.7°C. On the other hand, when the time constant is 5 hours, the indoor temperature will vary between 19.1°C and 28.9°C, with a higher minimum and a lower maximum than the previous case.
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Related Questions
Pls help me quick
I’ll mark brainly
Answers
Answer:
6/1Step-by-step explanation:
Unit rate is the slope,
\(y=mx+b\)
\(y=6x\)
\(m=6\)
Therefore, 6/1 is your answer
Hope it helps!
Convert the following equation into slope- intercept form.
-10x+5y=20
Answers
Answer:y=2x+4
explanation:
−10x+5y=20
Step 1: Add 10x to both sides.
−10x+5y+10x=20+10x
5y=10x+20
Step 2: Divide both sides by 5.
5y=10x+20
5. 5
Y=2x+4
The store sells lemon tea in 12-packs of bottles . Each bottle holds 2 cups of tea . How many gallons of lemon tea does each carton hold? Express you answer as a decimal
Answers
Answer:
1.5gallons
Step-by-step explanation:
Here,
no. of bottles(a) : 12
no. of cups (b) :a*2
=12*2
=24
Now,
No. of gallons. :24/16
:1.5gallons
.·.A cartoon contains 1.5 gallons of lemon tea.
Find the area of the shape shown below.
Answers
Answer:
18.75
Step-by-step explanation:
The formula to find the area of a triangle is
A= \(\frac{1}{2}\)*b*h
The formula to find the area of a rectangle is simply the length times the base.
Here, you can separate the shapes, two triangle and one rectangle to make it easier to find. Subtract 7.5 and 2.5 to get 5, which will be the base measurements for the triangles.
Next, find the area for the triangles: \(\frac{1}{2}\) x 5 x 2.5= 6.25, however, you have two triangles, so multiply by two to get 12.5.
Now, find the area of the rectangle, 2.5 +2.5= 6.25
Lastly, add the measurements together, 12.5 +6.25= 18.75
A large company has two shifts—a day shift and a night shift . Parts produced by the two shifts must meet the same specifications. The manager of the company believes that there is a difference in the proportions of parts produced within specifications by the two shifts. To investigate this belief, random samples of parts that were produced on each of these shifts were selected. For the day shift, 188 of its 200 selected parts met specifications. For the night shift, 180 of its 200 selected parts met specifications. (a) Use a 96 percent confidence interval to estimate the difference in the proportions of parts produced within specifications by the two shifts. (b) Based only on this confidence interval, do you think that the difference in the proportions of parts produced within specifications by the two shifts is significantly different from 0 ? Justify your answer. (c) Perform a significance test with a = 0.04. Provide the hypotheses of interest, test statistic, p-value, and conclusions.
Answers
a. The 96% cοnfidence interval fοr the difference in prοpοrtiοns is (0.004, 0.076).
b. The difference in prοpοrtiοns is significantly different frοm 0 at the 96% cοnfidence level.
What is the cοre οf the science οf statistics?The cοre οf the science οf statistics is the research and develοpment οf methοds fοr cοllecting, analyzing, and presenting empirical data.
(a) Tο estimate the difference in prοpοrtiοns οf parts prοduced within specificatiοns by the twο shifts, we can use the fοrmula fοr the cοnfidence interval fοr the difference between twο prοpοrtiοns:p1 - p2 ± z*√((p1(1-p1)/n1) + (p2(1-p2)/n2))
where p1 and p2 are the prοpοrtiοns οf parts prοduced within specificatiοns fοr the day and night shifts, respectively, n1 and n2 are the sample sizes, and z is the z-scοre cοrrespοnding tο the desired cοnfidence level.
Using the given sample prοpοrtiοns and sample sizes, we have:
p1 = 188/200 = 0.94
p2 = 180/200 = 0.90
n1 = n2 = 200
z = 1.75 (cοrrespοnding tο a 96% cοnfidence level)
Plugging these values intο the fοrmula, we get:
0.94 - 0.90 ± 1.75*√((0.94(1-0.94)/200) + (0.90(1-0.90)/200))
= 0.04 ± 0.042
Sο the 96% cοnfidence interval fοr the difference in prοpοrtiοns is (0.004, 0.076).
(b) Tο determine if the difference in prοpοrtiοns is significantly different frοm 0, we need tο check if the cοnfidence interval includes 0. Since the cοnfidence interval dοes nοt include 0, we can say that the difference in prοpοrtiοns is significantly different frοm 0 at the 96% cοnfidence level.
(c) The hypοtheses οf interest are:
H0: p1 - p2 = 0 (there is nο difference in the prοpοrtiοns οf parts prοduced within specificatiοns by the twο shifts)
Ha: p1 - p2 ≠ 0 (there is a difference in the prοpοrtiοns οf parts prοduced within specificatiοns by the twο shifts)
Tο perfοrm the significance test, we can use the z-test fοr the difference between twο prοpοrtiοns. The test statistic is
z = (p1 - p2) / √((p1(1-p1)/n1) + (p2(1-p2)/n2))
Using the same values as befοre, we get:
z = (0.94 - 0.90) / √((0.94(1-0.94)/200) + (0.90(1-0.90)/200))
= 2.02
The p-value fοr a twο-sided test at a significance level οf 0.04 is apprοximately 0.044. Since the p-value is less than the significance level, we can reject the null hypοthesis and cοnclude that there is a statistically significant difference in the prοpοrtiοns οf parts prοduced within specificatiοns by the twο shifts.
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Factor by grouping.
64p2 – 48p – 27
(8p – 9)(8p – 3)
(8p – 9)(8p + 3)
(8p + 9)(8p + 3)
(8p + 9)(8p – 3)
Answers
Answer:
B
Step-by-step explanation:
hope this helps with the work
Nicole used 3/8 of her ribbon to wrap a present. If she used 6 feet of ribbon for the present, how much ribbon did Nicole have at first? Rewrite the problem as a multiplication question.
Answers
Answer: 16
Step-by-step explanation:
From the question, we are informed that Nicole used 3/8 of her ribbon to wrap a present and that she used 6 feet of ribbon for the present,
To know how much ribbon did Nicole have at first goes thus:
Let the ribbon Nicole has at first be y
Since she used 3/8, this will be:
3/8 × y = 6
3y/8 = 6
Cross multiply
3y = 6 × 8
3y = 48
y = 48/3
y = 16
She had 16 ribbons at first
Add.
(6x³ + 3x² − 2) + (x³ - 5x² − 3)
Express the answer in standard form. (Please and thank you)
Answers
Answer:
\(\\\sf7x^3 - 2x^2 - 5\)
Step-by-step explanation:
\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)
Remove parenthesis.
6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3
Rearrange:
6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3
Combine like terms to get:
7x^3 - 2x^2 - 5----------------------------------------
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Hope this helps! :)
Answer:
7x³ - 2x² - 5
Step-by-step explanation:
(6x³ + 3x² - 2) + (x³ - 5x² - 3)
Remove the round brackets.
= 6x³ + 3x² - 2 + x³ - 5x² - 3
Put like terms together.
= 6x³ + x³ + 3x² - 5x² - 2 - 3
Do the operations.
= 7x³ - 2x² - 5
____________
hope this helps!
3. Given that:
X(z) = 2 + 3z-1+4z-2
a) Determine the initial value of corresponding sequence x(n).
b) Determine the final value of corresponding sequence x(n).
Answers
For the given Z-transform X(z) = 2 + 3z^(-1) + 4z^(-2), the initial value and final value of the corresponding sequence x(n) can be determined. The initial value of x(n) is 2, and the final value of x(n) is 0.
To find the initial value of the sequence x(n), we need to calculate the coefficient of z^0 in the Z-transform X(z). In this case, the coefficient of z^0 is 2, so the initial value of x(n) is 2. To determine the final value of the sequence x(n), we need to evaluate the limit as z approaches infinity. Since the Z-transform X(z) is a rational function, the final value of x(n) can be found by evaluating the limit of the numerator divided by the limit of the denominator as z approaches infinity. In this case, as z approaches infinity, the terms 3z^(-1) and 4z^(-2) become negligible compared to the constant term 2. Therefore, the final value of x(n) is 0. In summary, the initial value of x(n) is 2, indicating the value of the sequence at n = 0, and the final value of x(n) is 0, indicating the value of the sequence as n approaches infinity.
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A function can only have one transformation
happen to it.
True
False
Answers
Answer:
False
Step-by-step explanation:
You can transform a function many times
:)
If a population has 500 individuals in it in 2010, and the per capita birth rate is 0.3 and the per capita death rate is 0.2, is the population growing or shrinking?
Answers
The population is growing as the births are more than deaths in an year.
What is Population Growth?Increases in a population's or a dispersed group's membership are referred to as population growth.
Given:
Total population = 500Per capita birth rate = 0.3Per capita death rate = 0.2To find: Is population growing or shrinking?
Finding:
Number of new-borns in an year = total population (per capita birth rate) = 500(0.3) = 150Number of deaths in an year = total population (per capita death rate) = 500(0.2) = 100Difference in the number of births and deaths = 150 - 100 = 50Hence the population is growing as the births are more than deaths in an year.
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using a standard deck of playing cards, how many ways are to form a 5-card hand with 2 pairs (i.e. pair of one value, a pair of a different value, and a fifth card of some other value)? what if we require the pairs to be the same color (i.e spade with clubs and diamond with hearts)?
Answers
From a "standard-deck" of "playing-cards", the number of ways which are required to form a "5-card" hand with "2-pairs" is 123,552 ways.
A "Standard-Deck" of playing cards generally consists of 52 cards, divided into four suits: hearts, diamonds, clubs, and spades. Each suit contains 13 ranks: Ace, 2 through 10, and three face cards.
To form a 5-card hand with 2 pairs from a standard deck of playing cards, we break it down into two steps:
Step(1) : Select the values for the two pairs.
There are 13-ranks in a standard deck of playing cards, ranging from 2 to 10, and then Jack, Queen, King, and Ace, for a total of 13 possible values.
We need to select 2 of these values to form the two pairs. The number of ways to do this is "C(13, 2)" which is : 78,
So, there are 78 ways to select the values for the two pairs.
Step(2) : Select the specific-cards for each pair and the fifth card.
For each pair, we need to select 2 cards of that value from the 4 cards of each rank in the deck.
The number of ways to do this is "C(4, 2)" which is : 6,
So, there are 6 ways to select the specific cards for each pair.
Finally, for the fifth-card, we can choose any of the remaining "44-cards" in the deck (after selecting the 8 cards for the two pairs).
So, total number of ways to form a "5-card" hand with "2-pairs" from a standard deck of playing cards is,
⇒ 78 × 6 × 6 × 44 = 123,552 ways,
Therefore, the required number of ways are 123,552 ways.
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The given question is incomplete, the complete question is
Using a standard deck of playing cards, how many ways are to form a 5-card hand with 2 pairs?
Find the equation for the plane through the points Po (-2,5, -4), Q, (2, -5, -3), and
Ro (-1,2,4).
Answers
The equation of the plane passing through the points P(-2,5,-4), Q(2,-5,-3), and R(-1,2,4) is -2x + 5y - 4z = 3.
To find the equation of a plane, we need to have a point on the plane and a normal vector to the plane. A normal vector is a vector that is perpendicular to the plane.
To find a normal vector, we can take the cross product of two vectors in the plane. Let's take the vectors PQ and PR, which lie in the plane
PQ = Q - P = (2, -5, -3) - (-2, 5, -4) = (4, -10, 1)
PR = R - P = (-1, 2, 4) - (-2, 5, -4) = (1, -3, 8)
Now we can take the cross product of these two vectors
N = PQ x PR = (4, -10, 1) x (1, -3, 8)
= (80, 33, 14)
This is a normal vector to the plane. We can use any of the three points given to write the equation of the plane. Let's use point P
-2(x + 2) + 5(y - 5) - 4(z + 4) = 0
Simplifying this equation, we get
-2x + 5y - 4z = 3
So the equation of the plane through the points P, Q, and R is
-2x + 5y - 4z = 3
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a spinner is divided into four equal sections that are numbered 2, 4, 5, and 7. the spinner is spun twice.
Answers
Total number of outcomes having sum greater than 7 & with atleast one even number is 7.
In the given question,
Spinner divided into four equal sections.
These are numbered 2, 4, 5, and 7.
The spinner is spun twice.
We have to find how many outcomes have a sum less than 7 and contain at least one even number.
Since the spinner is spun twice.
So total outcomes are:
(2,2),(2,3),(2,5),(2,8),(3,2),(3,3),(3,5),(3,8),(5,2),(5,3),(5,5),(5,8),(8,2),(8,3),(8,5),(8,8)
Outcomes where sum is greater than 7 are (2,8),(3,5),(3,8),(5,3),(5,5),(5,8),(8,2),(8,3),(8,5),(8,8).
Thus outcomes where sum is greater than 7 and atleast one even number are (2,8),(3,8),(5,8),(8,2),(8,3),(8,5),(8,8).
Thus total number of outcomes having sum greater than 7 & with atleast one even number is 7.
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The right answer is:
A spinner is divided into four equal sections that are numbered 2, 4, 5, and 7. The spinner is spun twice. How many outcomes have a sum greater than 7 and contain at least one even number?
A little help? 10 Points per answer!!
Solve. 4|t|=24
Please show steps!
Answers
Answer:
t=6
Step-by-step explanation:
4ltl=24
4t=24
then divided 24 divided by 4 which is 6.
need help thank you!
Answers
The measure of angle T is given as follows:
m < T = 46º.
How to obtain the measure of angle T?To obtain the measure of angle T, we use the two-secant theorem, which states that the angle measure at the intersection point of the two secants is half the difference between the angle measure of the far arc and the angle measure of the near arc.
The parameters for this problem are given as follows:
Intersection angle of T = x.Near arc of 44º.Far arc = 136º.Half the difference of the arcs is given as follows:
136 - 44 = 92º.
Then the measure of the angle T is given as follows:
m < T = 0.5 x 92
m < T = 46º.
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A polynomial f and a factor of f are given. Factor f completely.
f(x) = 3x³ + 13x²+2x-8; x + 4
Answers
Answer:
(x+4)(3x-2)(x+1)
Step-by-step explanation:
Define what algebraic description is and give two examples
Answers
Answer:
Step-by-step explanation:
This helps in the representation of problems as mathematical expressions. It involves variables like x, y, z and mathematical operations like addition, subtraction, multiplication and division to form a meaningful mathematical expression. For example in algebra is 2x+4=8.
each cone has a height of 11cm and a base diameter of 8cm
LEMONADE STAND: You have 10 gallons of lemonade to sell. (1 gal ≈ 3785 cm)
A. How much lemonade can one cone hold
B. Each customer uses one paper cup. How many paper cups will you need?
C. The cups are sold in packages of 50. How many packages should you buy?
Answers
One cup can hold (A), you will need a total of 205.37 paper cups (B), and a total of 5 packages (C).
How much lemonade can one cone hold?Let's calculate the volume of the cone:
V=1/3πhr²
V= 1.04 x 11 x 4 ^2 (diameter / 2 radius)
V= 1.04 x 11 x 16 = 184.30 cubic centimeters
How many paper cups will you need?Total of lemonade: 37850 cubic centimeters (10 gallons x 3785 cubic centimeters per gallon)
37850 / 184.30 = 205.37 cups
How many packages should you buy?205.37 / 50 cups = 4.1 packages
However, as you need to buy complete packages, this can be rounded to 5 packages.
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Mimi and her friend went to the Burger Barn for lunch. Their bill
totaled $24.68. They left a 15% tip for their waitress. How much
tin did they leave
Answers
Answer:
they tipped = 15% of 24.68 = 15/100*24.68 = 3.702
Step-by-step explanation:
Answer:
Tip: $3.70
Total: $28.38
Step-by-step explanation:
bill: $24.68
tip: 0.15 * 24.68 = $3.70
Total: 24.68 + 3.70 = $28.38
Find the length of a segment ab but a= -7 and b=9
Answers
The length of a segment ab is 16 units.
Given that, a= -7 and b=9.
We need to find the length of a segment ab.
What is a line segment?In geometry, a line segment is a part of a straight line that is bounded by two distinct end points and contains every point on the line that is between its endpoints.
The length of the line segment is fixed, which is the distance between two fixed points. The length here can be measured by metric units such as centimetres (cm), millimetres (mm) or by conventional units like feet or inches.
Now, the length of a segment ab=a+b
=7+9=16
Therefore, the length of a segment ab is 16 units.
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Simplify . (x ^ 5)/(x ^ 2).
Answers
Answer:
\(x {}^{3} \)
Step-by-step explanation:
\(\frac{(x {}^{5} )}{( {x}^{2} )}\)
\(x {}^{3} \)
What are the solution(s) of x squared minus 4 = 0
Answers
Answer:
x=2 or x= -2
Step-by-step explanation:
x^2 - 4 = 0
x ^2 − 4 + 4 = 0 + 4
x^2 = 4
√ ( x ^2 ) = √ 4
= ± 2 = { x 1 = − 2
x 2 = 2
Answer:
X=2 or X=-2
Step-by-step explanation:
x^2 - 4 = 0
x ^2 − 4 + 4 = 0 + 4
x^2 = 4
√ ( x ^2 ) = √ 4
= ± 2 = { x 1 = − 2
x 2 = 2
The graph below could be the graph of which exponential function? A. f(x)= 2•(1.1)^xB. f(x)= 2^x C. f(x)= 2•(2)^xD. f(x)= 2•(0.5)^x
Answers
whats the answer ? and can you show your work if you dont mind me asking ?
Answers
Answer:
f(-1)=-2
Step-by-step explanation:
f(x)=-3x-5x^2
f(-1)=-3(-1)-5(-1)^2
f(-1)=-3(-1)-5(1)
f(-1)=3-5
f(-1)=-2
choosing values of x between each intercept and values of x on either side of the vertical asymptotes.
Answers
When choosing values of x between each intercept and values of x on either side of the vertical asymptotes, it is
important to consider the behavior of the function in those regions. Choosing values of x close to the intercepts can
give you an idea of the shape of the function in that region.
Choosing values of x close to the vertical asymptotes can help you determine the behavior of the function as x
approaches that value.
Choosing values of x between each intercept and values of x on either side of the vertical asymptotes.
To choose values of x between each intercept and values of x on either side of the vertical asymptotes,
1. Identify the intercepts: Find the points where the function intersects the x-axis and the y-axis. These are the points where the function's value is zero.
2. Identify the vertical asymptotes: Determine the values of x where the function is undefined or has a vertical asymptote.
3. Choose values of x between each intercept: Select a value between each pair of intercepts that you found in step 1. These values will help you understand the function's behavior between the intercepts.
4. Choose values of x on either side of the vertical asymptotes: Select a value slightly less than and slightly greater than each vertical asymptote you found in step 2. These values will help you understand the function's behavior around the vertical asymptotes.
By following these steps, you can analyze the function's behavior around its intercepts and vertical asymptotes.
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1 pt) a spherical balloon is inflated so that its volume is increasing at the rate of 3 ft3/min. how rapidly is the diameter of the balloon increasing when the diameter is 1.3 feet?
Answers
The diameter of the balloon increasing when the diameter is 1.3 feet is
3/2π feet/minute.
Define differentiation.A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables. The most typical illustration is velocity, which is the rate at which a distance changes in relation to time. The derivative of a function of a real variable in mathematics assesses how sensitively the function's value changes in response to changes in its argument. Calculus's core tool is the derivative.
Given,
Volume of spherical balloon = 4/3πr²
Volume of spherical balloon = 4/3π(D/2)³
Volume of spherical balloon = 1/6πD³
Differentiation:
dV/dt = 1/2πD²dD/dt
dD/dt = 2/πD² × dV/dt
radius = 1
D = 2 feet
dV/dt =3 feet
dD/dt = 2/π2²(3)
dD/dt = 3/2π feet/minute
The diameter of the balloon increasing when the diameter is 1.3 feet is
3/2π feet/minute
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how can confidence intervals help researchers attain their purpose of using a sample to understand a population?
Answers
The reason for why the confidence intervals help researchers attain their purpose of using a sample to understand a population is given below .
In the question ,
we have been asked how does the confidence interval help researchers to attain the purpose of using a sample to understand a population ,
we know that , the confidence interval is calculated from an estimate of how far away our sample mean is from actual population mean .
the confidence interval are useful because ,
(i) by calculating the confidence intervals around any data we collect, we have additional information about the likely values we are trying to estimate .
(ii) they make data analyses richer and help us to make more informed decisions about the research questions .
Therefore , the reason how confidence interval helps is mentioned above.
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Three pieces of ribbons measuring 0.5km, 1005cm and 1,800mm respectively are joined end to end form a single one. How long is the new ribbon? Find the cost of the single so formed at the rate of Rs.12 per meter?
Answers
Answer:
The new ribbon is 511.85 meter long.
The total cost Rs. 6142.2
Step-by-step explanation:
First of all we convert all lengths to the standard unit that is meter.
0.5 km =500 meter
1005 cm = 10.05 meter
1800 mm = 1.8 meter
total length in meters
500+10.05+1.8= 511.85
total cost at the rate of Rs. 12 per meter will be
511.85×12=6142.2
The length of the new ribbon is 511.85m.
The cost of the single ribbon formed is Rs. 6142.20.
What are different units of length? How are they related?Common units of length are Millimeter(mm), centimeter(cm), meter(m), and kilometer(km).
The S.I. unit of length is the meter.
All units relate to the meter in the following way:
1000mm = 1m ⇒ 1mm = 1/1000m ⇒ 1mm = 0.001m
100cm = 1m ⇒ 1cm = 1/100m ⇒ 1cm = 0.01m
1km = 1000m
How do we solve the given question?The lengths of three pieces of ribbon are given as 0.5km, 1005cm, and 1800mm.
We are asked to find the length of the ribbon formed by joining these 3 ribbons.
To find the total length, we need to add them, but to add we need lengths in equal units. So we convert the three lengths into the common unit meter.
0.5km = 0.5 * 1000 m = 500m (∵ 1km = 1000m)
1005cm = 1005 * 0.01m = 10.05m (∵ 1cm = 0.01m)
1800mm = 1800 * 0.001m = 1.8m (∵ 1mm = 0.001m)
∴ The length of the new ribbon = 500 + 10.05 + 1.8 m = 511.85m.
Cost of the ribbon = Rs. 12 per meter
∴ Cost of the single ribbon formed = Rs. 12 * 511.85 = Rs. 6142.20.
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Which relation in the below table(s) represents a function?
Answers
The relation 2 represents a function.
In order to determine which relation in the below table represents a function, we need to first understand what a function is.A function is a relationship in which each input value corresponds to exactly one output value.
To put it another way, each x-value has one and only one y-value. The most typical method to determine whether a relation is a function is to use the vertical line test.
The vertical line test is a way to determine if a relation is a function graphically. To test if a graph is a function, we draw a vertical line through each x-value on the graph. If a vertical line crosses the graph more than once, it is not a function.
If, on the other hand, the graph passes the vertical line test and no vertical line crosses the graph more than once, it is a function.Now let's look at the table below to determine which relation is a function.
We will first plot the x and y values of each relation on a coordinate system and then apply the vertical line test to each relation.
Relation 1: x | y0 | 10 | 11 | 22 | 23 | 34 | 35 | 4Relation 1 does not represent a function since we can draw a vertical line through x = 3 and the line will cross the graph more than once.
Relation 2: x | y2 | 33 | 34 | 45 | 46 | 57 | 5Relation 2 represents a function since we can draw a vertical line through each x-value on the graph and it will only cross the graph once.
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