No, a fluid obeying the clausius equation of state have a vapor-liquid transition
This is because a straight line does not exist between a liquid's temperature and its vapour pressure.
What is the Clausius equation of state?The Clausius Clapeyron equation is described as a way of describing a known discontinuous phase transformation that exists between two phases of matter of a single constituent.
This equation was named after Rudolf Clausius and Benoît Paul Émile Clapeyron.
It also states that a straight line does not exist between a liquid's temperature and its vapour pressure.
The equation also helps us to estimate the vapor pressure at another temperature.
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In the figure below, O is the center of the circle. Name a diameter of the circle.
The diameter of circle O in the image given is: AB.
What is the Diameter of a Circle?The diameter of a circle can be referred to as the largest chord in a circle which is the line segment that passes through the center of a circle with both ends on the circle.
In the image given, AB is the largest chord and also passes through the center of the circle, O.
Thus, the diameter is: AB.
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The ________ could be used to describe a data set by itself, while ___________ would almost never be used to describe a data set by itself.
The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.
Brief Description of Mean and Interquartile Range
While interquartile range only assesses the middle half of the data, mean and range deal with the entire set of data. The mean is significant in statistics because it helps us determine where a dataset's "center" is. The mean contains information from each observation in a dataset as a result of how it is calculated.
The interquartile range in descriptive statistics reveals the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The second and third quartiles, or the center half of your data set, are contained in the interquartile range (IQR).
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A rectangle room has a perimeter of 70m.what would be the length of the longest side of the room?
Answer:
The longest side of room is 24m
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For which interval(s) is the function increasing and decreasing? y=3x^3 -16x+2
Considering the critical points of the function, we have that:
The function is increasing for |x| > 1.63.The function is decreasing for |x| < 1.63.What are the critical points of a function?The critical points of a function are the values of x for which:
[tex]f^{\prime}(x) = 0[/tex]
In this problem, the function is:
[tex]f(x) = 3x^3 - 16x + 2[/tex]
The derivative is:
[tex]f^{\prime}{x} = 6x^2 - 16[/tex]
The critical points are given as follows:
[tex]6x^2 - 16 = 0[/tex]
[tex]x^2 = \frac{16}{6}[/tex]
[tex]x = \pm \sqrt{\frac{16}{6}}[/tex]
[tex]x = \pm 1.63[/tex]
For x < -1.63, one example of the derivative is:
[tex]f^{\prime}{-2} = 6(-2)^2 - 16 = 8[/tex]
Positive, hence increasing.
For -1.63 < x < 1.63, one example of the derivative is:
[tex]f^{\prime}{0} = 6(0)^2 - 16 = -16[/tex]
Negative, hence decreasing.
For x > 1.63, one example of the derivative is:
[tex]f^{\prime}{2} = 6(2)^2 - 16 = 8[/tex]
Positive, hence increasing.
Hence:
The function is increasing for |x| > 1.63.The function is decreasing for |x| < 1.63.More can be learned about critical points at https://brainly.com/question/2256078
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In a group of 55 people, 3x+5 people like banana and x+5 people like apple. If all the people who like apple also like banana and if 2x+15 people like at least one of fruit then find how many like
(i) bananas only,
(ii) none of the fruits
(iii) at most one fruit
also show subset
i. The number of people who like banana only is 20.
ii. The number of people who like none of the fruits is zero.
iii. The number of people who like at most one fruit is 30.
The question has to do with sets.
What is a set?A set a collection of well ordered items
i. How to find how many people like banana only.Since we have 55 people, 3x + 5 people like banana and x + 5 people like apple. If all the people who like apple also like banana and if 2x + 15 people like at least one of fruit then, we have that
3x + 5 + x + 5 + 2x + 15 = 55
3x + 2x + x + 5 + 5 + 15 = 55
6x + 30 = 55
6x = 55 - 25
6x = 30
x = 30/6
x = 5
Since the number of people who like banana only is 3x + 5.
So, number of people who like banana only is n = 3x + 5
= 3(5) + 5
= 15 + 5
= 20
So, the number of people who like banana only is 20.
ii. The number of people who none of the fruits.Since from the question, a person likes at least one fruit, either banana, apple or both. No one likes none of the fruits.
So, the number of people who like none of the fruits is zero.
iii. The number of people who like at most one fruit?To like at most one fruit, the person either likes apple or banana.
So, their sum is n = 3x + 5 + x + 5
= 4x + 10.
Since x = 5, we have n = 4x + 10.
= 4(5) + 10
= 20 + 10
= 30
So, the number of people who like at most one fruit is 30.
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Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
Answer:
Step-by-step explanation:
Evaluate 5 - 3(a3 – b2)2 when a = 3 and b = 5.
5 - 3 × (a³-b²)² a=3 and b=5
5 - 3 × (3³ - 5²)² =
5 - 3 × (27 - 25)² =
5 - 3 × (2)² =
5 - 3 × 4 =
5 - 12 =
-7
How many distinct triangles can be formed for which m∠E = 64°, g = 9, and e = 10?
triangle(s)
How many distinct triangles can be formed for which m∠J = 129°, k = 8, and j = 3?
triangle(s)
Answer:
10Step-by-step explanation:
1.For two side measures and one angle measure to form one distinct triangle, the given angle must be between the given sides, or opposite the longest side.
When the given measures are ...
E = 64°g = 9e = 10The given angle is opposite the longest side, so one distinct triangle can be formed.
2.No triangle can be formed if the given angle is opposite the shorter given side, and either of ...
the angle is right or obtusethe ratio of shorter to longer sides is less than the sine of the given angle.__
Additional comment
As we can see from the above, the only ambiguous cases arise when the given angle is opposite the shorter given side. When that happens, the ratio of the shorter to longer given side relative to the sine of the given angle determines the nature of the solution:
two distinct triangles if the ratio is greater than the sineone right triangle if the ratio is equal to the sine.Answer:
1
0
Step-by-step explanation:
A sphere of radius 222 inches is cut by three planes passing through its center. This partitions the solid into 888 equal parts, one of which is shown above. The volume of each part is t\pitπt, pi cubic inches. What is the value of ttt?
The value of t based on the information about the sphere is 1.3π.
How to calculate the value?It should be noted that the volume of a sphere is 4/3πr³. In this case, it's divided into 8 equal parts.
Volume of each part = 1/8 × 4/3πr³
= 1/8 × 4/3 × π × 8
= 4/3π
= 1.3πin³
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Of the last 16 people at a carnival booth, 6 won a prize. what is the experimental probability that the next person at the booth will win a prize? write your answer as a fraction or whole number. p(win)
The experimental probability that the subsequent booth competitor will receive a reward is 3/8.
Probability calculationThe possibility of an event occurring is determined by probability.
The probability of the occurrence ranges from 0 to 1.
If the event doesn't happen, it = 0;
otherwise, it = 1.
For instance, the likelihood that it will storm on Sunday ranges from 0 to 1. If it storms, the event is given a value of 1. If it doesn't, the event is given a value of zero.
Depending on the outcome of a study that has been run several times, the experimental probability is calculated.
The number of winners in the games divided by the total number of competitors in those games determines the probability that the following competitor will earn a reward.
So, here the probability = 6/16 = 3/8 (by dividing both the numerator and the denominator by 2).
Therefore, the final solution is P= 3/8 .
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Determine the missing digit (denoted with*) for the American Express Traveler's Check identification number 783920*814 a) 3
b) 2
c) 6
d) 9
The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.
In this question,
A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.
A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.
The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.
The American Express Traveler's Check identification number is 783920*814.
In Airline tickets, there are several digits plus a check digit.
Divide the ID number by 7. The check digit is the remainder.
Sum of digits = 7+8+3+9+2+0+8+1+4
⇒ 42
Now divide the sum by 7, the remainder is
⇒ 42 mod 7 = 42 - (5×7)
⇒ 42 mod 7 = 6
Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.
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What are the factors of 3x2 23x − 8? (3x − 4)(x 2) (3x − 2)(x 4) (3x − 8)(x 1) (3x − 1)(x 8)
Answer:
(3x − 1)(x 8)
Step-by-step explanation:
The table gives the populations of three countries in 2013.
United States Brazil Germany
3.16 × 108 1.96 × 108 8.0 × 107
1) Difference of the populations of Germany and Brazil = 1.16 X 10^8
2) Difference of the populations of Brazil and the United States = 1.2 X 10^8
3) Sum of the populations of Brazil and Germany = 2.76 X 10^8
4) Sum of the populations of the United States and Brazil = 5.12 X 10^8
According to the statement
we have given that the populations of three countries which are
United States is 3.16 × 10^8 and Brazil is 1.96 × 10^8 and Germany is 8.0 × 10^7
And we have to arrange the sums and differences in increasing order of their values.
so, we have to find the
a) the difference of the populations of Germany and Brazil
So,
Difference of the populations of Germany and Brazil = 1.96 X 10^8 - 8 X 10^7 = 116000000 = 1.16 X 10^8
And then we have to find the
b) the sum of the populations of the United States and Brazil
So,
Sum of the populations of the United States and Brazil = 3.16 X 10^8 + 1.96 X 10^8 = 512000000 = 5.12 X 10^8
And then we have to find the
c) the difference of the populations of Brazil and the United States
So,
Difference of the populations of Brazil and the United States = 3.16 X 10^8 - 1.96 X 10^8 = 120000000 = 1.2 X 10^8
And then we have to find the
d) the sum of the populations of Brazil and Germany
So,
Sum of the populations of Brazil and Germany: 1.96 X 10^8 + 8 X 10^7 = 276000000 = 2.76 X 10^8
NOW, we arrange the sum and difference in increasing order of their values.
So,
1) Difference of the populations of Germany and Brazil = 1.16 X 10^8
2) Difference of the populations of Brazil and the United States = 1.2 X 10^8
3) Sum of the populations of Brazil and Germany = 2.76 X 10^8
4) Sum of the populations of the United States and Brazil = 5.12 X 10^8
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Bill and jenna are solving the quadratic equation x 2 - x = 12. bill solved this way jenna solved this way x 2 - x = 12 x(x - 1) = 12 x = 12 or 13 x 2 - x = 12 x 2 - x - 12 = 0 (x - 4)(x 3) = 0 x = 4 or x = -3 which student is correct? what error did the other student make when solving?
Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
Form of quadratic equationThe form of quadratic equations is given as
ax2 + bx + c = 0
So, for the quadratic equation, we have
x² - x = 12
Let's make it into quadratic form
x² - x - 12 = 0
Bill solved it as
x(x - 1) = 12
This is wrong, because quadratic equations must be written in the form before solving for the variables
Jenna solved it as
x 2 - x - 12 = 0
Jenna is correct because she converted the equation to a quadratic form before solving for the variables.
Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.
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Please help!!!!!!!!!!
Answer: 18.7
Step-by-step explanation:
Find the lengths of AB, BC, and CA
AB = [tex]\sqrt{(4-(-1))^{2} + (-1-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1
BC = [tex]\sqrt{(0-(-1))^{2} + (-3-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1
CA = [tex]\sqrt{(0-4)^{2} + (-3-(-1))^{2} }[/tex] = 2[tex]\sqrt{5}[/tex] ≈ 4.5
7.1 + 7.1 + 4.5 = 18.7
Celia uses the steps below to solve the equation Negative StartFraction 3 over 8 EndFraction (negative 8 minus 16 d) + 2 d = 24.
Step 1 Distribute Negative StartFraction 3 over 8 EndFraction over the expression in parentheses.
3 minus 16 d + 2 d = 24
Step 2 Simplify like terms.
3 minus 14 d = 24
Step 3 Subtract 3 from both sides of the equation.
Negative 14 d = 21
Step 4 Divide both sides of the equation by –14.
d = StartFraction 21 over negative 14 EndFraction = Negative three-halves = negative 1 and one-half
Which corrects the error in the step in which Celia made the first error?
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over 2d, to get 3 minus 16 d + (negative three-fourths d) = 24.
In step 1, she should have also distributed Negative StartFraction 3 over 8 EndFraction over –16d, to get 3 + 6 d + 2 d = 24.
In step 3, she should have added 3 to both sides of the equation to get Negative 14 d = 27.
In step 3, she should have first divided both sides by –14 to get 3 + d = 24
The error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
Simplifying linear equationsGiven the following equation as shown below
-3/8(-8-16d)+2d = 24
Step 1 Distribute -3/8 over the expression in parentheses
3 + 6d + 2d = 24
Simply the like terms
3 + 8d = 24
Subtract 3 from both sides of the equation.
8d = 24 - 3
8d = 21
d = 21/8
Hence the error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
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the half life of an element in the periodic table measured over a period of time, t, is modeled by the function f(t)=16(1/2)^t. what is the initial amount of the element
The initial amount of the element is 16
How to determine the initial amount?The function is given as:
f(t) = 16(1/2)^t
Set t = 0, to determine the initial amount
f(0) = 16(1/2)^0
This gives
f(0) = 16 * 1
Evaluate
f(0) = 16
Hence, the initial amount of the element is 16
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write 158/4 as a mixed number in simplest terms. thank you :)
158/4 as a mixed number in the simplest term is [tex]39\frac{3}{4}[/tex]
Converting improper fractions to mixed numberThe given fraction is 158/4
The number of times that 158 can be divided by 4 = 39
4 x 39 = 156
The remainder = 159 - 156
The remainder = 3
The mixed number is of the form:
[tex]Quotient\frac{Remaider}{Divisor}[/tex]
Therefore, the mixed number is [tex]39\frac{3}{4}[/tex]
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kathy uses a 1/2 cup of milk with every bowl of her favorite cereal if there are only 3 3/5 cups of milk left, then how many bowls of cereal would kathy have?
Taking a quotient, we will see that she can make 7 bowls of cereal (and some leftover milk).
How many bowls of cereal would kathy have?We know that for each bowl, she needs 1/2 cups of milk.
And we also know that she has a total of (3 + 3/5) cups of milk.
To know how many bowls she can make, we need to take the quotient between the total that she has and the amount that she needs for each bowl:
(3 + 3/5)/(1/2)
We can rewrite the total as:
3 + 3/5 = 15/5 + 3/5 = 18/5
Then the quotient becomes:
(18/5)/(1/2) = (18/5)*2 = 36/5 = 35/5 + 1/5 = 7 + 1/5
So she can make 7 bowls of cereal (and some leftover milk).
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The width of a rectangle is 4 less than twice its length. if the area of the rectangle is 75 cm 2 , what is the length of the diagonal?
Answer:
Step-by-step explanation:
The square of y varies directly as the cube of x. when x = 4, y = 2. which equation can be used to find other combinations of x and y?
The equation can be used to find other combinations of x and y is y^2 = (1/16)x^3
How to determine the equation?The direct variation from the square of y to the cube of x is represented as:
y^2 = kx^3
Where k represents the variation constant.
When x = 4, y = 2.
So, we have:
2^2 = k * 4^3
This gives
4 = 64k
Divide both sides by 64
k = 1/16
Substitute k = 1/16 in y^2 = kx^3
y^2 = (1/16)x^3
Hence, the equation can be used to find other combinations of x and y is y^2 = (1/16)x^3
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There are 86,400, frames of animation in 1 hour of anime.
How many frames are there per second?
There are 3,600, seconds in 1 hour.
Answer:
There are 24 frames of animation in 1 second of anime. Step-by-step explanation: There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.
Solve for x:
[tex] \frak{2 ( 3x + 1 ) + 3 ( 5x + 2 ) = x - 1}[/tex]
[tex] \\ \\ \\ [/tex]
Thank uh -,-
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]
[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]
[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]
[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]
[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]
[tex]\qquad❖ \: \sf \:20x = - 9[/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]
[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]
x = –9/20Step-by-step explanation:
________________________________
→ 2(3x + 1) + 3(5x + 2) = x – 1
→ 6x + 2 + 15x + 6 = x – 1
→ 21x + 8 = x – 1
→ 21x – x = – 1 – 8
→ 20x = – 9
→ x = –9/20
________________________________
Hope it helps you :')Choose the correct simplification of the expression ( expression in photo! )
A. G^7h
B. G^3h
C. G^7h^7
D. G^3/h^7
Use the rules of exponents to simplify the expression.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]
To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{5-2}h^{4-3} \end{gathered}$}[/tex]Subtract 2 from 5.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{3 }h^{3-2} \end{gathered}$}[/tex]Subtract 3 from 4.
[tex]\large\displaystyle\text{$\begin{gathered}\sf g^{3 }h^{1} \end{gathered}$}[/tex]For any term t, t¹ =t.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf g^{3}h \end{gathered}$} }[/tex]Therefore, the correct option is "B".
Solve the quadratic equation numerically (using tables of x- and y- values). x(x + 6) = 0 a. x = -1 or x = 3 c. x = 0 or x = -3 b. x = 0 or x = 6 d. x =0 or x = -6
Answer:
d. x =0 or x = -6
Step-by-step explanation:
x(x + 6) = 0
This is telling us that either x is 0 or x is -6, because:
1) when x = 0, 0*(0+6)=0, and
2) when x = -6, -6*(-6+6) = 0; -6(0) = 0
What additional information is obtained by measuring two individuals on an ordinal scale compared to a nominal scale
The direction of the difference between the 2 measurements.
What is nominal and ordinal scale with example?Examples of data for a nominal scale include a person's gender, ethnicity, and hair color. On the other hand, an ordinal scale requires putting data in a certain order, or in relation to one another and "ranking" each parameter (variable).What is the difference nominal and ordinal?Ordinal data has a preset or natural order, whereas nominal data is categorized without a natural order or rank. A number that can be measured, however, will always be present in numerical or quantitative data.What is an example of a ordinal scale?First place would go to a student with a score of 99 out of 100; third place would go to a student with a score of 92 out of 100; and so on.Learn more about ordinal scale and nominal scale here:
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The length of a rectangle plus its width is 24 cm. The area is 135 cm. What are the length and width of the rectangle
Answer:
[tex]l = 5.63 \\ [/tex]
hope this helps
Last week salazar played 13 more tennis games than perry. if they played a combined total of 53 games. How many games did salazar play?
If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.
Let the total number of games played by Perry be x.
It is given that, Salazar played 13 more tennis games than Perry.
⇒ Total games played by Salazar = x + 13
Also, Salazar and Perry played a combined of 53 games.
Hence, total number of tennis games played by Salazar and Perry = 53
⇒ Games played by Salazar + Games played by Perry = 53
⇒ x + (x + 13) = 53
2x + 13 = 53
2x = 53 - 13
2x = 40
x = 40 / 2
x = 20
Therefore, total number of games played by Salazar = x+13
= 20 + 13
= 33
Thus, Salazar played total 33 games.
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Write an expression using fractions to show how to determine the amount that each person will pay. Then calculate each person's contributions showing all steps in long division.
Me: $14.89
Friend 1: $7.27
Friend 2: $25.67
Friend 3: $11.59
The fraction based on the information given illustrated for each person.
How to illustrate the information?Me: $14.89
Friend 1: $7.27
Friend 2: $25.67
Friend 3: $11.59
Total = $59.42
The fraction for each person will be:
Me: $14.89 = 14.89/59.42 = 0.25
Friend 1: $7.27 = 7.27/59.42 = 0.12
Friend 2: $25.67 = 25.67/59.42 = 0.32
Friend 3: $11.59 = 11.59/59.42 = 0.195
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Jim jogged from his house to the gym at 15 km/hr. On the trip home on the same route he walked at 10 km/hr. Together the two trips took him two hours. What is the distance from his home to to the gym
The distance from Jim's home to the gym is 12 km.
What is Speed?Speed is defined as the rate at which the position of object is changed.
Speed = Distance / Time
Here, there are two different speeds given for the same distance.
Average speed is the total distance travelled by the total time taken.
If distance is a constant,
Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.
Average speed = (2 × 15 × 10) / (15 + 10)
= 12 km/hr
So, Total distance travelled = Average speed × total time taken
= 12 × 2
= 24
Distance = 24 / 2 = 12
Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.
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Find a and k so that the given points lie on the parabola (An algebraic solution is required)
The value of a is -3 and the value of k is 10
A parabola is a U-shaped plane curve where any point is equidistant from a fixed point (known as the focus) and from a fixed line known as the directrix. The parabola is an integral part of the conic section topic
The section of a right circular cone by a plane parallel to the generator of the cone is a parabola. It is the location of a point that moves so that the distance from the fixed point (the focus) is equal to the distance from the fixed line (the directrix).
The fixed point is called the focus
A fixed line is called a directrix
Solving an algebraic equation is the process of finding a number or set of numbers that, when substituted for the variables in the equation, reduce them to an identity. Such a number is called the root of the equation
Here the equation y = a(x -2)^2 + k...........(1)
and two points A(1,7) and B(4, -2) is given
We need to find the value of a and k
Put A(1,7) in equation (1) , we get,
7 = a + k ,therefore k = 7 - a......(2)
Put B(4, -2) in equation (1), we get,
-2 = 4a + k........(3)
Put k= 7-a in (3)
-2 = 4a+7 -a
3a = -9
a= -3
From equation (2) , we get k = 7-(-3)= 10
Hence the value of k is 10 and the value of a is -3
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For the given points to lie on the parabola,
a = -3 and k = 10.
An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).
According to the question,
Equation of parabola : y = a[tex](x-2)^{2}[/tex] + k
Points A(1,7) and B(4,-2)
For the points to lie on the parabola,
7 = a[tex](1-2)^{2}[/tex]+k
7 = a + k
Similarly,
-2 = a[tex](4-2)^{2}[/tex] + k
-2 = 4a + k
On solving the two equations simultaneously, we get,
a = -3
k = 10
Learn more about parabolas here:
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