EXERCISES INTEGRALS
INTEGRALS EXERCISES PLEEASEEEE HELPPP I’LL GIVE U A CROWN PLEASEEE

The additive inverse of 3/7 is -3/7.

The additive inverse of any number is the opposite of that number. If a number is added to its additive inverse, the sum of both numbers becomes zero. In other words, the additive inverse is the number that is added to a given number to make the sum zero. That is what you add to a number to get zero is called its additive inverse.

That is, Number + Additive inverse = 0

OR

The negative of a number.

Now we are given the number

3/7

So, the additive inverse of 3/7:

⇒3/7 + Additive inverse = 0

⇒Additive inverse = -3/7

Thus the additive inverse of is 3/7 is -3/7.

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a) The equation would be 25 + 16x = 201.

b) Kallik was a member of the club for 11 years.

What is an equation?

An equation is a mathematical statement that shows the equality of two expressions. It consists of two expressions separated by an equal sign (=), and the goal is to find the values of the variables that make the equation true. Equations can be used to model real-world situations, to describe relationships between variables, or to solve problems.

a. Let's call the number of years that Kallik was a member of the club "x". The equation to model the membership fees can be written as follows:

25 + 16x = 201

b. To solve for the number of years, we can subtract 25 from both sides of the equation:

16x = 176

And then divide both sides by 16:

x = 11

So Kallik was a member of the club for 11 years.

Hence,

a) The equation would be 25 + 16x = 201.

b) Kallik was a member of the club for 11 years.

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Step-by-step explanation:

what happen if a body is projected at an angle of 75 to the horizontal then it is a projector Once More with the same initial speed as an angle of 15 so he wants me to calculate the horizontal Range and I don't know have

Answer:

y > -14

Step-by-step explanation:

4y < 5y + 14

Subtract 5y from both sides of the < sign:

4y - 5y < 5y - 5y + 14

-y < 14

Divide both sides by -1:

y > -14 is the answer.

Note, in the last step, the sign flips because we are dividing by a negative

There are 12 red counters and 18 blue counters in the bag.

We can use the formula for conditional probability to find the number of red and blue counters in the bag.

The probability of both counters being blue is:

P(blue and blue) = P(blue | blue) * P(blue) = (y/ (x+y)) * (y-1) / (x+y-1) = 57/100

We can then use this equation to find the value of y:

y = ((x+y) * 57/100) / ((x+y-1) * 100/57)

We can also use the equation:

P(red | blue) = P(red and blue) / P(blue) = P(red) * P(blue) / P(blue) = x * y / (x+y)

We can then use this equation to find the value of x:

x = (57 * (x+y)) / (100 - 57)

Now we have two equations with two variables:

y = ((x+y) * 57/100) / ((x+y-1) * 100/57)

x = (57 * (x+y)) / (100 - 57)

We can use the first equation to solve for y in terms of x and substitute into the second equation:

x = (57 * (x + (((x+y) * 57/100) / ((x+y-1) * 100/57)))) / (100 - 57)

Solving for x, we get x = 12 and y = 18

Therefore, there are 12 red counters and 18 blue counters in the bag.

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at a particular restaurant, each pizza roll has 65 and each chicken wing is 11 pizza rolls and 6 chicken wings.

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So,  the y-intercept of the equation 3x + y = -1 is the point (0, -1).

The y-intercept of a linear equation in the form of y = mx + b is the point at which the line crosses the y-axis, which is the point (0, b). In the equation 3x + y = -1, the y-intercept is the point at which y = -1 and x = 0, which can be found by solving for y when x = 0:

3(0) + y = -1

y = -1

So the y-intercept of the equation 3x + y = -1 is the point (0, -1). This means that the equation of the line passes through the point (0, -1) on the Cartesian plane.

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Using Pythagoras theorem, The height of the television is 56.65 inches.

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

Using Pythagoras theorem,

d² = (ax)² + (bx)²

= x² (a² + b²)

⇒ x = √(d²/a²+b²)

length = a . √(d²/a²+b²)

width = b. √(d²/a²+b²)

with an aspect of 16:9,

has an advertised size of 65 inches,

a = 16, b = 9, d = 65

length = 56.65 inches

width = 31.87 inches

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Step-by-step explanation:

always remember :

the sum of all angles in a triangle is always 180°.

so, in triangle EFD

180 = E + F + D = 37 + 105 + D

D = 38°

since we know that the combination (sum) of B and D is 90° (right angle),

B + D = 90

B + 38 = 90

B = 52°

and now we look at the triangle ABC and its angles to get A, which then in turn gets us I of the triangle A(BD)I.

180 = A + B + C = A + 52 + 83

A = 45°

and that means for A(BD)I

180 = A + (B + D) + I = 45 + 90 + I

I = 45°

FYI : that means that the total triangle is an isoceles triangle (both legs are equally long : AB = DI).

Answer:

Four folk love legends: "Cowhand and Weaver Girl", "Meng Jiangnu crying at the Great Wall" (cry Wan Xiliang), "Liang Shanbo and Zhu Yingtai", "The Legend of the White Snake", the author does not know

The development history of the Four ancient Chinese folk legends: China is a country with a vast territory and abundant resources and a long history, which contains extremely rich national cultural heritage. Among them, the four most Chinese ones are the famous "Cowhand and Weaver Girl", "Meng Jiangnu", "Liang Shanbo and Zhu Yingtai" and "The Legend of the White Snake". The most widespread, the most influential.

Brief introduction: the gigolo knit legend began in the book of songs, cable ":" Qi he vega ", "Huan he cow". "Nineteen Ancient Poems · Long Distance Star" has called the cowherd and weaver girl husband and wife. Ying Shao "custom" Yi wen: "Zhinv Tanabata when crossing the river, make magpie bridge, legend has it that the magpie head without reason all Kun, because beam (note: bridge) to cross Zhinv also. The story has been preliminarily formed and combined with the Qixi Festival custom.

The legend of Meng Jiangnu originated from the record of Qi Liang's wife refusing to hang herself in the area of the Marquis of Qi and adhering to the rules of etiquette in the Zhuan. Later, it was added in the Dangong that "Duke Zhuang of Qi attacked Ju and took away (tunnel) and Qi Liang died. The weeping wife who greeted his coffin on the road is the archetype of the story. Han Liu Xiang's Biography of Liannu (IV) : "Qi Liangzhu died in battle, his wife cried in the city, ten days the city collapsed." And Tang (anonymous) "carved jade collection" record "Qin when Yan Qi Liang, married Meng Chao female Zhongzi wife, because good was built the Great Wall officials killed, Zhongzi cry under the Great Wall, the city collapsed. It is known that this legend was popular in the Tang Dynasty, but Meng Zhongzi and Qiliang were renamed Meng Jiangnv and Fan Xiliang in the legend. The story of Butterfly lovers first appeared in Tang's "Ten Taoist and Four Tibetan Records", which recorded the story of Liang and Zhu "having a taste of schoolmates" and "sharing the tomb". There are more detailed records in Xuanbaozhi of late Tang Zhang Reading. To the Ming Dynasty Feng Menglong's "Ancient and modern novels", and added to the British Taiwan confused belt, Liang Shanbo doubts and butterflies.

The story of White Snake came into being the latest. The origin of the story is as follows. It originates from the Three Towers of West Lake. To the Ming Dynasty Feng Menglong's "Lady White Forever Town Leifeng Pagoda" (" Warning Word "), the story has been preliminarily finalized.

Answer: 7.5 cm; 1.6 cm

Step-by-step explanation:

If that is a right triangle, it is probably a 30 60 90 triangle and we can use this special property to say that the leg facing the 30 degree angle is half of the hypotenuse. The hypotenuse measures 15 cm, which means we can say that the leg facing the 30 degree angle is 7.5 cm. Next, since 21 cm is the sum of the 2 legs, we can add 21 cm to 15 cm to get 36 cm. Now that we know our hypotenuse, perimeter, and one of our legs, we can find the other leg by using basic algebra to get 1.6 cm. Hopefully this helps! I'm not sure tho.

Percentage of Phosphorus in Diphosphorus Trichloride is  36.8 %

A figure or ratio stated as a fraction of 100 is called a percentage. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.

The Latin phrase "per centum," which meaning "by the hundred," was the source of the English word "percentage." Fractions having a denominator of 100 are called percentages. In other words, it is a relationship where the value of the entire is always assumed to be 100.

Finding the percentage of a whole in terms of 100 is what percentage calculation refers to. A percentage can be found in one of two ways:

Formula of DiPhosphorus trichloride.

P₂Cl₃

Molar mass of the compound = 31 * 2 + 35.5* 3 = 168.5

Percentage of Phosphorus in the compound is = (62/168.5) *100 = 36.8 %

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When the discriminant b² - 4ac is greater than zero and also a perfect square, the nature of roots of the quadratic equation ax² + bx + c = 0 will be real and distinct.

A perfect square means that the discriminant can be written as a product of two equal factors, for example (x+y)^2 = x^2 + 2xy + y^2. In this case the roots can be easily calculated by using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

In this scenario, the square root of the discriminant will be a real number and not a complex number, and the equation will have two distinct solutions for x. This means that the graph of the equation will cross the x-axis twice.

It's important to notice that the values of a,b and c also play an important role in the nature of the roots.

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The equation's solution yields -4/3 for x. Rhoda is the wrong, for this reason.

When two expressions are connected with the equals sign (=) in a mathematical formula, it expresses the equality of the two expressions.

Equation given: 4(x-8)=7 (x-4).

Here is how to answer the given equation:

4x-32=7x-28

7x-4x=-32+28

3x=-4

x=-4/3

Kylie starts off with a first step that yields the result 4x-32=7x-28. Using a first step that yields 4x-8=7x-4, Rhoda uses.

The equation's solution yields -4/3 for x. Rhoda is the wrong, for this reason.

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The number from greatest to least in the given set of numbers are:

-14/5 < -2.25 < 1 ¼ < 3/2

A group of numbers is referred to as an element and makes up a set of numbers. The collection of numbers in the set may be infinite or finite. Roster notation is a method for indicating sets. For example, the set "2,31" contains the elements 2 and 31.

We need a way to say which numbers are included when a set has an infinite number of elements because it is impossible to list them all. Our number system is based on a few well-known infinite sets.

Given mixed fractions and decimals:

-14/5, -2.25, 1 ¼, 3/2

So,

-14/5 = −2.8

-2.25

1 ¼ = 1.25

3/2 = 1.5

As, −2.8 < -2.25 < 1.25 < 1.5, The numbers from greatest to least are:

-14/5 < -2.25 < 1 ¼ < 3/2.

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Complete question:

The sum of given polynomials (m + n + 3) + (m + n + 4) is 2m + 2n + 7

A polynomial is an equation composed of more than two algebraic terms, particularly the sum of numerous terms containing different powers of the same variable(s)

The polynomials can be added by first organising them in standard form, then grouping like terms together, and lastly simplifying them.

Given the expression:

(m + n + 3) + (m + n + 4)

Now, we have to combine the like terms.

(m + m) + (n + n) + (3 + 4)

Add the coefficients of the same variable:

2m + 2n + 7

The sum of polynomials is 2m + 2n + 7

Complete question:

What is the sum of the polynomials (m+n+3)(m+n+4)

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Answer:

Step-by-step explanation:

Therefore, the expression mR > 90°, mS + mT 90°, mR > mT and mR > mS comes out to be true for the solution to the right angle triangle problem.

Triangles are polygons with three sides and three vertices. The triangle's angles are created by joining its three sides from ends to ends at such a single point. Three angles in the triangle combine to form a 180-degree angle.

Here,

An RST is a triangle.

This means that m∠R+m∠S+m∠T = 180° and m∠S+m∠T = 180° - m∠R.

It is given that mvR > m∠S + m∠T.

'- m∠R' '- (m∠S + m∠T)' 

The formula is changed to 180°-(mS + mT) and 180°-(mR + mS) by appending 180 degrees to both sides.

(m∠S + m∠T) - 180 degrees

The angle becomes 180° by multiplying m∠S + m∠T on both sides.

=>2(m∠S+m∠T) < 180°

=> m∠S+m∠T < 90°

M R > 90° because M ∠R + M∠ S + M ∠T = 180°.

Yet again, mvR > m∠S + mT.

=> "m∠R > m∠T," "m∠R > mS," etc.

This means that the first, second, third, and fifth options are correct.

The fact that m∠S = m∠T can only happen when m∠R=90° should be highlighted

This is why m∠S = m∠T is inaccurate.

Furthermore, there is not enough proof to prove that m∠S > m∠T.

Because of this, mS > mT is likewise incorrect.

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The degree measure is which is equivalent to [tex]\frac{7 \pi}{11}[/tex] is 114.54°.

The size of an angle is measured in terms of a unit of measurement. 1 degree is equivalent in magnitude to 1/360 of a whole rotation.

A rotational angle is said to have a measure of one degree, denoted by the symbol 1°, if it is (1/360)th of a revolution from the initial side to the terminal side. Radian scale. A unit circle's unit arc's centrally subtended angle is said to have a measure of 1 radian.

The radius of an arc divided by its length is known as the radian measure (r). Radian measure is a pure number that doesn't require a unit symbol because it is the ratio of one length to another.

Convert radians to degrees, multiply by 180/π, since a full circle is 360° or 2π radians.

= [tex]$ \frac{7 \pi}{11} \times \frac{180}{\pi}[/tex]

= [tex]$ \frac{7 }{11} \times 180[/tex]

=[tex]$ \frac{1260}{11}[/tex]

= 114.54°

Therefore, the correct answer is 114.54°.

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Full question:

The equation of the directrix for the parabola y = 18 · x² - 4 · x + 41 is y = 2935 / 72.

In this question we find the case of the equation of a parabola in standard form:

y = a · x² + b · x + c

Where:

This equation must be changed into vertex form:

y - k = C · (x - h)²

Where:

Where the vertex constant is:

C = 1 / (4 · p)

Where p is the distance between focus and vertex.

And the equation of directrix is:

y = k - 1 / (4 · C)

First, write the quadratic equation in standard form:

y = 18 · x² - 4 · x + 41

Second, use algebra properties until vertex form is obtained:

y = 18 · [x² - (2 / 9) · x + 41 / 18]

y = 18 · [x² - (2 / 9) · x + 1 / 81] + 18 · (367 / 162)

y = 18 · (x - 1 / 9)² + 367 / 9

y - 367 / 9 = 18 · (x - 1 / 9)²

Third, find the equation of the directrix:

y = 367 / 9 - 1 / (4 · 18)

y = 2935 / 72

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Step-by-step explanation:

the volume of a cylinder (as any regular 3D object) is

base area × height

since the base area of a cylinder is the area of a circle, that means

pi×r² × height

in our case we have

4860 = pi×r²×180

27 = pi×r²

r² = 27/pi

r = sqrt(27/pi)

FYI :

sqrt(27/pi) = 2.931615071... cm

Emani will be able to purchase the subscription for a maximum of 5 months if she wants to spend $210 or less from her summer job.

The subscription has a one-time fee of $30 plus $9 per month, so the total cost per month is $9 + $30 = $39.

Emani plans to spend $210 or less from her summer job on this subscription, so we can write an inequality to represent this situation:

$39x <= $210

Where x is the number of months Emani will be able to purchase the subscription.

To solve for x, we need to divide both sides of the inequality by $39:

x <= (210/39)

x <= 5.38

So Emani will be able to purchase the subscription for a maximum of 5 months, if she wants to spend $210 or less from her summer job.

Note: This is an approximation, since x can't be a decimal. And if you round down to 5 months she will be able to spend $195.

Therefore, Emani will be able to purchase the subscription for a maximum of 5 months if she wants to spend $210 or less from her summer job.

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The subscription has a one-time charge of $30 and a monthly fee of $9, making the monthly cost total $9 + $30 = $39 for the subscription.

We can create an inequality to symbolize this circumstance since Emani intends to spend no more than $210 from her summer job on this subscription:

$39x <= $210

Emani will have the option to buy the subscription for x months.

Divide both parts of the inequality by $39 to find the value of x:

x <= (210/39)

x <= 5.38

Answer:

The values are calculated with the help of table.

Step-by-step explanation:

We are given the following information in the question:

A table is shown showing trees on two different plots of land which are tested for disease.

     Tree:        1           2           3           4          5           6          7        

      Plot:         A          A           B           B         B           A          B

Disease:        Y          N           Y           Y          Y          N         N

We have to find:

Calculating from the table, we can fill the values as:

                                              Plot A                Plot B

Disease Present                        1                          3

Disease not Present                2                          1

The degree of the polynomial is significant when writing it in its standard form since the terms are written in descending order of the power of x.

The formula for a polynomial in its standard form is [tex]f(x)=a_a x^n+a_{n-1} x^{n-1}+a_{n-2} x^{n-2}+\ldots . .+a_1 x+a_0[/tex]

A polynomial is written in the standard form when the term with the largest power of the variables comes first, followed by the subsequent terms in decreasing order of the variable power. Leading term and leading coefficient are terms used to describe the first term and its coefficient, respectively, in the polynomial's standard form.

According to the definition of a polynomial in standard form, exponents must be written in decreasing order. The standard form of polynomials is used to facilitate calculations. Exponents must be expressed in decreasing order in order to be considered a polynomial in standard form. To make calculations easier, polynomials are expressed in their standard form.

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The graph of the inequality x - 6y > 18 is plotted and attached

Inequality are graphed considering the table of values formed by assigning several values for x

x - 6y > 18

rearranging the equation will result to

x - 18 > 6y

y < x/6 - 3

for x = -6, y < -6 / 6 - 3 = -4

for x = 0, y < 0 / 6 - 3 = -3

for x = 6, y < 6 / 6 - 3 = -2

Table of value

x      y

-6    -4

0      -3

6      -2

the equation: y < x/6 - 3 will have a dashed line and shading is below the line because it has a less than sign

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The answer is the equation can have many solutions. the given equation is the linear equation that may have infinitely many  solutions.

The equation given in the question is  

2x + y – 5 = 0  

4x + 2y – 10 = 0  

For the given equation it can be written as:  

[tex]a_{1} x+ b_{1}y - c_{1} = 0[/tex]

[tex]a_{2} x+ b_{2}y - c_{2} = 0[/tex]

Here, [tex]a_{1}[/tex] = 2, [tex]b_{1}[/tex] = 1, [tex]c_{1}[/tex] = −5  

[tex]a_{2}[/tex]= 4, [tex]b_{2}[/tex]= 2,  [tex]c_{2}[/tex]= −10

So, according to the question given for the equation:

[tex]\frac{a_{1} }{a_{2}} = \frac{2}{4} = \frac{1}{2}[/tex]

[tex]\frac{b_{1} }{b_{2}} = \frac{1}{2}[/tex] and

[tex]\frac{c_{1} }{c_{2}} = \frac{-5}{10} = \frac{1}{2}[/tex]

⇒  [tex]\frac{c_{1} }{c_{2}} = \frac{b_{1} }{b_{2}} = \frac{c_{1} }{c_{2}}[/tex]

From the above solution, we see the end result for the equation given so, we can say that this given equation can have infinitely many solutions.

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Based on the unit rate, Brand X costs $0.10 per fluid ounce less than Brand Y.

The unit rate refers to the ratio of one value to the whole.

The unit rate is the average of the values of the data set.

We can compute the unit rate by dividing the total value by the number of units.

The total cost of Brand X for 5 fluid ounces = $3.25

The unit cost of Brand X per fluid ounce = $0.65 ($3.25/5)

The total cost of Brand Y for 8 fluid ounces = $6.00

The unit cost of Brand Y per fluid ounce = $0.75 ($6.00/8)

The difference in the unit cost of Brand X and Brand Y = $0.10 ($0.75 - $0.65)

Thus, we can state that Brand Y costs more than Brand X per unit.

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Answer:

[tex]6\frac{3}{4}[/tex] and [tex]3\frac{1}{8}[/tex]

Step-by-step explanation:

I don't know what benchmark fractions are but here's what I did

[tex]4\frac{7}{8} + 1 \frac{7}{8} = 5 \frac{14}{8} = 6 \frac{6}{8} or 6\frac{3}{4}\\5\frac{3}{8} - 2\frac{1}{4} = 5\frac{3}{8} - 2\frac{2}{8} = 3\frac{1}{8}[/tex]

The first question is straight forwards since the fractions have the same denominator, so its simply adding and simplification.

The second questions needs you to find a common denominator (8) and swap the fraction to that of 8 before subtracting

The partial sum is called  the sum of part of the sequence, they are also called as finite series.

Since adding all the terms does not yield the sums of these series, we can study their behaviour by looking for patterns in the partial sums. A partial sum is the total of a limited number of the series' terms. To see how the infinite sum behaves, we can examine a collection of these sums. The index of the final term in the sum is used to denote each of these partial sums. For instance, is the total of an infinite series' first six terms.

The first five partial sums are in the following order: 1, 4, 9, 16, and 25. This trend will persist, and the terms will keep expanding without limit. In other words, because the infinite total is infinitely huge, the partial sums keep increasing.

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The requried solution of the given system of equations is x = -9 and y = 2.

Simultaneous linear equations are two- or three-variable linear equations that can be solved together to arrive at a common solution.

Here,
1/3x + y = -1  - - - - - - -(1)

1/3x + 8y = 13 - - - -- - (2)

Subtract equation 1 from 2,
8y - y = 13 + 1
y = 2

Now,
1/3x + 2 = -1
x = -9

Thus, the requried solution of the given system of equations is x = -9 and y = 2.

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the of is .

The formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides

Given data ,

Let the be

Now , the value of k is determined by

The values of Time be x = { 2 , 4 , 6 , 8 }

The values of distances be y = { 8,16,24,32 }

Now , the constant of proportionality is given by

y = kx

Divide by x on both sides of the equation , we getk = y/x

Substituting the values in the equation , we get

k = 8/2

k = 4

And , k = 16/4

k = 4

Therefore , the value of is .

Hence , the constant of is

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The value of constant or K is found to be 4.

The formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides

Given data ,

Let the be

Now , the value of k is determined by

The values of Time be x = { 2 , 4 , 6 , 8 }

The values of distances be y = { 8,16,24,32 }

Now , the constant of proportionality is given by

y = kx

Divide by x on both sides of the equation , we getk = y/x

Substituting the values in the equation , we get

k = 8/2

k = 4

And , k = 16/4

k = 4

Hence , the constant of is 4.

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