what pattern of growth are we currently exhibiting? exponential growth intrinsic growth logistic growth none of the other answer options is correct. geometric growth

Answer:

Since the equation of the circle is:

[tex](x-3)^2 +(y-1)^2 = 100[/tex]

we can conclude that:

1. The center has coordinates (3, 1)

2. The new circle has a center with coordinates (3,5)

3. The new circle has an equation of:

[tex](x -3)^2 +(y - 5)^2 = 100[/tex]

The base οf the triangle is 5 centimeters and the height οf the triangle is 20 centimeters.

In geοmetry, a triangle is a three-sided pοlygοn that cοnsists οf three line segments οr sides and three angles.

Let's denοte the base οf the triangle by "b" and the height by "h". We knοw that the area οf the triangle is 50 square centimetres, sο we can use the fοrmula fοr the area οf a triangle tο set up an equatiοn:

[tex]Area = (1/2) * base * height[/tex]

Substituting the given values, we get:

[tex]50 = (1/2) * b * h[/tex]

We also know that the height of the triangle is four times the base:

h = 4b

We can substitute this expression for "h" into the equation for the area:

[tex]50 = (1/2) * b * (4b)[/tex]

[tex]50 = 2b^2[/tex]

Dividing both sides by 2, we get:

[tex]25 = b^2[/tex]

Taking the square rοοt οf bοth sides, we get:

b = 5

Sο the base οf the triangIe is 5 centimeters. Using the expressiοn fοr the height in terms οf the base, we can find the height:

h = 4b = 4(5) = 20

Sο the height οf the triangIe is 20 centimeters.

Hence, the base οf the triangIe is 5 centimeters and the height οf the triangIe is 20 centimeters.

To learn more about triangles, Visit

https://brainly.com/question/1058720

#SPJ1

The reasons that completes the proof to show that WX ≅ ZY are:

2. Given; 3. Alternate Interior Angles Theorem 4. Reflexive Property of Congruence 5. AAS 6. CPCTC.

Given that WX║ZY and <X ≅ <Z, we can prove that WX ≅ ZY as shown below in the proof.

Statements                        Reasons                                          

1. WX║ZY                          1. Given

2. <X ≅ <Z                         2. Given

3. <XWY ≅ <ZYW              3.  Alternate Interior Angles Theorem

4. WY ≅ WY                      4. Reflexive Property of Congruence

5. ΔWZY ≅ ΔYXW            5. AAS

6. WX ≅ ZY                       6. CPCTC

Learn more about congruency proof on:

https://brainly.com/question/29394252

#SPJ1

The rectangle ABCD have measures of angle a and b derived to be 69° and 138° respectively to the nearest degree.

Considering the right triangle ADC,

tan ACD = 6/16 {opposite/adjacent}

ACD = tan⁻¹(6/16)

ACD = 20.5560

ACD = 21° to the nearest degree

Angle ACD = Angle ABD, and ABD and a are complementary angles, so;

a + ABD = 90°

a + 21 = 90°

a = 90 - 21

a = 69

The angle b forms an isosceles triangle with the angles C and D, so;

b = 180 - 2(21) {sum of interior angles of a triangle}

b = 180 - 42

b = 138°

Therefore, the rectangle ABCD have measures of angle a and b derived to be 69° and 138° respectively to the nearest degree.

Read more about rectangle here:https://brainly.com/question/23008020

#SPJ1

so, they are not equally likely. Thus, P(spade) = 13/52 or 1/4, and P(heart) = 13/52 or 1/4, but P(spade) ≠ P(heart).

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that an event is impossible and 1 indicating that an event is certain to occur. The probability of an event is calculated by dividing the number of ways an event can occur by the total number of possible outcomes.

The true statements are:

P(ace) = 4/52 or 1/13

P(jack) = 4/13

P(ace) > P(king)

The false statements are:

P (numbered card) > P (face card) - this is not true since there are 12 face cards (4 jacks, 4 queens, 4 kings) and 40 numbered cards (2-10), so P(face card) = 12/52 or 3/13, and P (numbered card) = 40/52 or 10/13, which means that P (numbered card) > P (face card).

P(spade) = P(heart) - this is not true either, since there are 13 cards of each suit, but the spades and hearts are different suits, so they are not equally likely. Thus, P(spade) = 13/52 or 1/4, and P(heart) = 13/52 or 1/4, but P(spade) ≠ P(heart).

To know more about Probability, visit:

https://brainly.com/question/30034780

#SPJ1

The direct variation equation that shows the relationship between x and y, where y = 20 when x = 5, is y = 4x.

In a direct variation, the relationship between two variables can be described by the equation y = kx, where y and x are the variables and k is the constant of variation. This equation indicates that y varies directly with x, which means that as x increases or decreases, y also increases or decreases proportionally.

To find the constant of variation, we need to use the given information about the values of y and x. In this case, we are told that when x = 5, y = 20. We can substitute these values into the direct variation equation:

y = kx

20 = k(5)

To solve for k, we divide both sides by 5:

k = 20/5

Simplifying this expression, we get:

k = 4

Therefore, the direct variation equation that shows the relationship between x and y is:

y = 4x

This equation means that for any value of x, if we multiply it by 4, we will get the corresponding value of y. For example, if x = 2, then y = 4(2) = 8. If x = 10, then y = 4(10) = 40. In other words, y is always four times the value of x in a direct variation relationship.

Learn more about direct variation equation here:

https://brainly.com/question/28107529

#SPJ4

The solution to each of these recurrence relations with the given initial conditions are a) an = 1+1+2+3+4+5.....+n and b) an = n.n-1.n-2 = 2.5 = (n!)5

In the field of mathematics, a recurrent equation is a formula that determines the nth value of a sequence of numbers based on a combination of previous values. Typically, the equation only involves k past values of the sequence, where k is a constant parameter independent of n; this k is known as the recurrence order. These equations, also known as difference equations, describe a sequence or array in terms of itself through recursion. They establish a relationship between the dependent variable and the differences of various orders of the variable. Recurrent equations can be utilized to model the runtime of recursive programs by distinguishing between recursive and non-recursive operations.

a) an = an-1 + n, ao = 1

a1 = a0 +1 = 1+1

a2 = a1+2 = 1+1+2

a3= a2+3 = 1+1+2+3

an = 1+1+2+3+4+5.....+n

1+n(n+1)/2 = n2+n+2/2

e) an = n an-1, ao = 5

a1 = ao = 5

a2 = 2 a1 = 2.5

a3 = 3 a2 = 3.2.5

an = n.n-1.n-2 = 2.5 = (n!)5

To learn more about recurrence, click here:

brainly.com/question/16931362

#SPJ4

The measure of abd is (0.3x+67) and the measure of cbd is (0.1x+41), the value of x is 130.

Abd is an abbreviation for the term "abdomen." It is used to describe the part of the body located between the chest and the pelvis, and contains many vital organs including the stomach, intestines, pancreas, and liver. Abd is often used in medical terminology, particularly when referring to conditions that affect the abdomen such as appendicitis or diverticulitis.

The measure of ABD is (0.3x+67) and the measure of CBD is (0.1x+41). Since the two angles are supplementary (they add up to 180 degrees), we can set the two equations equal to each other and solve for x.
0.3x + 67 = 0.1x + 41
Subtracting 0.1x from both sides of the equation, we get:
0.2x = 26
Dividing both sides of the equation by 0.2, we get:
x = 130
Therefore, the value of x is 130.

To learn more about abd
https://brainly.com/question/29170861
#SPJ1

If The measure of abd is (0.3x+67) and the measure of cbd is (0.1x+41) then the value of x is 180.

What is an algebraic expression?

An algebraic expression is a mathematical phrase that contains variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division.

To find the value of x, we need to use the fact that the sum of the angles in a triangle is 180 degrees.

We know that the sum of angles ABD and CBD is equal to angle ABC, which is 180 degrees.

So we can set up the following equation:

ABD + CBD = ABC

(0.3x + 67) + (0.1x + 41) = 180

Simplifying the equation, we get:

0.4x + 108 = 180

Subtracting 108 from both sides, we get:

0.4x = 72

Dividing both sides by 0.4, we get:

x = 180

Therefore, the value of x is 180.

To know more about algebraic expressions and given link below -

https://brainly.com/question/953809

#SPJ1

Step-by-step explanation:

100 - 9 = 91   seats for seven student groups

91 / 7 = 13  seats in each student group

   each student group receives   13 - 9 = 4 more seats than the roped off section

The insurance company will pay a total of  $70,000 in damages as insurance.

What exactly is insurance?

Insurance is a contract between an individual or entity (the insured) and an insurance company (the insurer) in which the insurer agrees to provide financial protection or compensation to the insured in any loss or damage. The insured typically pays a premium to the insurer in exchange for this protection. Insurance policies can provide coverage for various risks, such as accidents, illness, property damage, and liability.

Now,

Theresa's insurance policy covers up to $25,000 for bodily injury per person, up to $50,000 total for bodily injury per accident, and up to $25,000 for property damage per accident.

For bodily injury, the insurance will cover $25,000 for the first passenger, $10,000 for the second passenger, and $10,000 for Theresa's son, which adds up to $45,000. Since this is below the $50,000 total for bodily injury per accident, the insurance will cover all the bodily injury damages.

For property damage, the insurance will cover up to $25,000 per accident. Since the total property damage is $18,000 + $7,500 = $25,500, which is above the $25,000 coverage limit, the insurance will only pay out $25,000.

Therefore, the insurance company will pay a total of $45,000 + $25,000 = $70,000 in damages.

To know more about Insurance visit the link

https://brainly.com/question/15094642

#SPJ1

Answer: x = 1 In4

Step-by-step explanation:

Sorry if I’m wrong

Answer:

a) 183.75

b) 386.25

i believe thats right, i am very sorry if i am wrong

Thus, the equation of line  parallel to given line and with passing points (-6, -4) is: y = -1/6 x - 10.

The slopes for perpendicular lines are the opposite reciprocals of the slopes of parallel lines, which are equal. It's a worked example of identifying the parallel or perpendicular nature of given lines.

The standard slope intercept form:

y = mx + c  ..eq 1

slope m and y intercept is c.

Given equation:

y = -1/6 x + 2 ..eq 2 on comparing eq 2 with eq 1

m = -1/6 and c is 2

Now, slope of two parallel lines are same.

Passing point = (-6, -4)

Equation of line:

y - y1 = m (x - x1)

y + 4 = -1/6( x + 6)

y = -1/6 x - 10

Thus, the equation of line  parallel to given line and with passing points (-6, -4) is: y = -1/6 x - 10.

Know more about the slopes for parallel lines

https://brainly.com/question/28427398

#SPJ1

Answer:

apples - $0,55 per pound

oranges - $0,45 per pound

Step-by-step explanation:

Let's assume, that apples cost x dollars per pound and oranges cost y dollars per pound.

Let's write 2 equations according to the given information and put them in a system:

{3x + 4y = 3,45,

{4x + 2y = 3,10;

Let's make x the subject from the 1st equation:

3x = 3,45 - 4y / : 3

x = 1,15 - 1 1/3y

Let's replace x in the 2nd equation:

[tex]4 \times(1.15 - 1 \frac{1}{3} y) + 2y = 3.10[/tex]

[tex]4.6 - \frac{16}{3} y + 2y = 3.10[/tex]

[tex] - \frac{10}{3} y = 3.10- 4.6[/tex]

[tex] - \frac{10}{3} y = - 1.5[/tex]

[tex]y = 0.45[/tex]

[tex]x = 1.15 - 1 \frac{1}{3} \times 0.45 = 0.55[/tex]

If a shoe size of 8 is added to the data, the IQR is affected in the following way: C. the IQR remains a 2.

In Mathematics, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):

IQR = Q₃ - Q₁

Based on the given data set, we can logically deduce the following interquartile ranges:

Quartile 3 (Q₃) = 8

Quartile 1 (Q₁) = 6

Now, the interquartile range (IQR) can be calculated as follows:

Interquartile range (IQR) = Q₃ - Q₁

Interquartile range (IQR) = 8 - 2

Interquartile range (IQR) = 2

Based on the 1.5 × IQR rule for outliers, we have:

1.5 × IQR = 1.5 × 2 = 3

Therefore, the shoe size will be 3 points below Q₁ and 3 points above Q₃:

Lower shoe size = 6 - 3 = 3

Upper shoe size = 8 + 3 = 11.

In conclusion, we can reasonably infer and logically deduce that the interquartile range (IQR) would remain at 2.

Read more on outliers here: https://brainly.com/question/30816160

#SPJ1

The inequality that models the story is n ≥ 8

An inequality is a mathematical statement that compares two values or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to)

The number of charms Aaliyah might add to the necklace is represented by n. Since she plans to put at least as many charms on the necklace as the bracelet, we can use the inequality symbol "≥" to indicate this relationship.

So, the inequality that models the story is

n ≥ 8

This inequality states that the number of charms added to the necklace (n) must be greater than or equal to 8, which is the number of charms Aaliyah added to the bracelet.

Learn more about inequality here

brainly.com/question/30228778

#SPJ4

The percentage of students who do not wear glasses is 30%.

Thirty-five out of 50 students in a class wear glasses. The percentage of students in the class who do not wear glasses is: 30%.Explanation:Given data: The total number of students in the class = 50Number of students who wear glasses = 35. We have to calculate the percentage of students who do not wear glasses.Total students = 50Number of students who wear glasses = 35.

So, the number of students who do not wear glasses = Total students - Number of students who wear glasses= 50 - 35 = 15Percentage of students who do not wear glasses = (Number of students who do not wear glasses / Total students) x 100= (15 / 50) x 100= 0.3 x 100= 30%.

Learn more about Percentage

brainly.com/question/29306119

#SPJ11

The length of the edge of the square is increasing at a rate of 12/13 cm/min when the area is 169 cm^2, given that the area of the square is increasing at a rate of 24 cm^2/min.

Let's assume that the side length of the square is represented by "x" and the area of square is represented by "A". Then we have:

A = x^2

Differentiating both sides with respect to time "t", we get:

dA/dt = 2x(dx/dt)

Given that dA/dt = 24 cm^2/min, we can find dx/dt when A = 169 cm^2 (which is the area of a square with side length of 13 cm):

24 = 2(13)(dx/dt)

Simplifying this expression, we get:

dx/dt = 24/(26) = 12/13

Therefore, the length of the edge of the square is increasing at a rate of 12/13 cm/min when the area is 169 cm^2.

To know more about area of a square:

https://brainly.com/question/1658516

#SPJ4

_____The given question is incomplete, the complete question is given below:

The area of a square is increasing at a rate of 24 cm^2/min

How fast is the length of the edge increasing when the area = 64 cm^2

The new location of Point A is (3, 5). This is because the x-coordinate remains unchanged, while the y-coordinate is inverted, making it positive.

Point A is located at (3, -5). To reflect this point over the x-axis, we need to calculate the new coordinates. First, we will note that the x-coordinate remains unchanged. This means that the new x-coordinate is 3. Secondly, we will note that the y-coordinate needs to be flipped, meaning it will become positive. To do this, we will take the opposite of the original y-coordinate. Since the original y-coordinate is -5, the new y-coordinate will be 5. Therefore, the new location of Point A is (3, 5).

Learn more about y-coordinate here

https://brainly.com/question/3641550

#SPJ4

Answer: $21.15

Step-by-step explanation:

Answer:

height ≈ 17.0 m

Step-by-step explanation:

consider the right triangle with angle 29° , opposite side x and adjacent side of 28 m

using the tangent ratio in the right triangle

tan29° =[tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{28}[/tex] ( multiply both sides by 28 )

28 × tan29° = x , then

x ≈ 15.5 m ( to the nearest tenth )

now add on the 1.5 m

height of tree = 15.5 + 1.5 = 17.0 m

The 55 in the expression represents the speed of the family’s car in miles per hour.

What is called distance?

The complete length of the path between any two points is called distance.

The expression 245-55t represents the distance, in miles, the family still needs to drive after t hours.

A camp counselor starts from home and drives to a campground.

The expression 245-55t represents the distance, in miles, the counselor still needs to drive after t hours.

Now, in expression 245 is the distance in miles between his home to the campground.

And 55 is the rate at which the distance 245 miles is reducing per hour.

The 55 in the expression represents the speed of the family’s car in miles per hour.

If the speed of the camp counselor is 55 miles per hour, then we can use the formula distance = speed × time

 Find out  long it will take for the counselor to reach the campground?

Let’s set distance = 0 and solve for t:

245-5t = 0

55t = 245

t =  4.45hours

Therefore, it will take approximately 4.45 hours for the camp counselor to reach the campground.

To know more about distance visit:

brainly.com/question/15172156

#SPJ1

The probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative is 0.9989, or approximately 99.89%.

What is binomial distribution?

A binomial distribution is a type of distribution distinct from a continuous distribution in which every trial has an equal chance of reaching a given value and is independent of every other trial. The binary distribution has only two possible outcomes.

This is a binomial distribution problem with n = 100 (sample size) and p = 0.4278 (the probability of not identifying as conservative, which is 1 - 0.572).

The probability of at least 50 respondents not identifying themselves as conservative can be calculated using the cumulative distribution function (CDF) of the binomial distribution:

P(X ≥ 50) = 1 - P(X < 50)

Using a binomial calculator or software, we can find that P(X < 50) = 0.0011.

Therefore,

P(X ≥ 50) = 1 - P(X < 50) = 1 - 0.0011 = 0.9989

So, the probability that at least 50 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative is 0.9989, or approximately 99.89%.

Learn more about binomial distribution on:

https://brainly.com/question/29137961

#SPJ1

a.  the equation showing the relationship between s and r:

6s + 2r = 21

b.  the equation that shows the rearrangement of r as a function of s:

r = (21/2) - 3s

c. If it takes Diego 1.2 seconds to spin around each time, the total time he spends spinning is r = 5.7 seconds

The equation showing the relationship between s and r: 6s + 2r = 21

The equation that shows the rearrangement of r as a function of s:

2r = 21 - 6s

r = (21/2) - 3s

c., the total time Diego spends spinning is:

6s = 6(1.2) = 7.2 seconds

Applying the equation in part (b), we can find the time he spends running:

r = (21/2) - 3s

r = (21/2) - 3(1.2)

r = 5.7 seconds

Learn more about function at: https://brainly.com/question/10439235

#SPJ1

The reflection's rule is described below. The right response is x-axis (x, y) = (x, -y).

When we gaze at our own reflection in a mirror, we naturally think of a reflection as a mirror image.

In maths, the concept of reflection and a mirror image are comparable.

The rules for reflection across the y-axis and x-axis are fundamental transformations in geometry. The rule for reflection across the y-axis is (x, y) → (-x, y), which means that every point's x-coordinate is negated while the y-coordinate remains the same. This transformation has the effect of reflecting the object or figure across the y-axis.    

Similarly, the rule for reflection across the x-axis is (x, y) → (x, -y), which means that every point's y-coordinate is negated while the x-coordinate remains the same. This transformation has the effect of reflecting the object or figure across the x-axis. These transformations are important in many areas of mathematics and science, including computer graphics and physics.

To learn more about reflection:

https://brainly.com/question/31157136

#SPJ4

A mathematical process called subtraction reflects the elimination of items from a collection. There are 14 pupils that enjoy pink polka dots.

A mathematical process called subtraction reflects the elimination of items from a collection.

Subtraction is symbolised by the negative sign.

Considering that there were 50 students in the sample as a whole, the number of pupils who enjoy pink polka dots is as follows:

50 students divided by (4+9+11+9+3) yields 14 students.

Thus, there are 14 students that enjoy pink polka dots.

To know more about subtraction, visit:

https://brainly.com/question/1927340

#SPJ1

The complete question is:

A sample of 50 11th graders was asked to select a favorite pattern out of 6 choices. the following display shows what their favorite color patterns were.

blue on grey 4

green 9

pink polka dots?

purple 11

red and orange stripes 9

yellow 3

The counts have been recorded in the accompanying table according to pattern and the number of students who selected the pattern. what is the missing value in the table?

Answer:

[tex]\frac{1}{35}=0.029[/tex]

Step-by-step explanation:

Each marble has a probability  [tex]\frac{1}{7}[/tex]  of being pulled out of the bag.

We need to pull out green, blue, red or yellow in the first pull.

That is mean we have a  [tex]\frac{4}{7}[/tex] probability to choose one of these. (Let it be green marble)

In secend pull we have 6 marbles in the bag and 3 of them we need to pull out. That is meean we have a probability [tex]\frac{3}{6}[/tex] to choose one of these (Let it be blue marble).

In third pull we have 5 marbles in the bag and 2 of them we need to pull out. That is meean we have a probability [tex]\frac{2}{5}[/tex] to choose one of these (Let it be red marble).

In last pull we have 4 marbles in the bag and we need to pull out last one (yellow). That is meean we have a probability  [tex]\frac{1}{4}[/tex].

[tex]\frac{4}{7} *\frac{3}{6} *\frac{2}{5}* \frac{1}{4} =\frac{4}{7} *\frac{1}{2} *\frac{2}{5} *\frac{1}{4} =\frac{1}{35}= 0.029[/tex]

Observational errors, Random errors, Systematic errors, Instrumental limitations and Personal factors are the causes for measurement error.

The difference between measured value and true value is known as error. Causes for measurement error are as follows:

Errors in the experiment can be due to various reasons like observational errors, random errors, systematic errors, errors due to instrumental limitations, and errors due to personal factors.

The difference between measured value and true value is known as error.

The following are the causes of measurement error:

Observational Errors

Observational errors are errors that occur during observation. These errors may occur due to factors such as lack of attention, inadequate experience, and poor eyesight.

Random Errors

Random errors are caused by factors that are unpredictable or random. These errors cannot be removed from the data because they are the result of random fluctuations. For example, when a thermometer is being used, the thermometer might display different temperatures for different readings.

Systematic Errors

Systematic errors are those errors that are caused by a defect in the measuring instrument or an improper calibration of the instrument. These errors can be removed by carefully calibrating the instrument and then performing the measurement.

Instrumental Limitations

Instrumental limitations are caused by the limitations of the measuring instrument. These errors can be minimized by selecting the appropriate instrument for the measurement task.

Personal Factors

Personal factors are errors that are caused by the individual performing the measurement. These errors can be minimized by providing proper training and ensuring that the individual is experienced in the field of measurement.

The above causes lead to the errors in the experiment. Hence, care must be taken to minimize these errors so that the results obtained are accurate.

For similar question on error

https://brainly.com/question/28771966

#SPJ11

Henry had 35/6 gallons of juice, which is equivalent to 5 and 5/6 gallons.

To convert quarts to gallons, we need to know that there are 4 quarts in 1 gallon. So, we divide the number of quarts by 4 to get the number of gallons.

In this problem, we're given that Henry had 23 1/3 quarts of juice. To convert this amount to gallons, we first need to convert the mixed number to an improper fraction. We can do this by multiplying the whole number by the denominator of the fraction and then adding the numerator. This gives us:

23 1/3 = (23 × 3 + 1) / 3 = 70 / 3

Now we can divide 70/3 by 4 to get the amount of juice in gallons:

70/3 ÷ 4 = 70/3 × 1/4 = 70/12

We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 2 in this case. This gives us:

70/12 ÷ 2/2 = 35/6

So, Henry had 35/6 gallons of juice in total.

To learn more about equivalent please click on below link        

https://brainly.com/question/14672772

#SPJ1

The height of the main cable 20 meters from the center is 16 meters above the road.

To find the equation of the parabola, we need to use the information given about the height of the cables at the towers and the center of the bridge. We know that the main cables are 20 meters above the road at the towers, so we can use this information to find the distance between the towers, which is

distance between towers = 80 meters - 2(20 meters) = 40 meters

We also know that the main cables are 4 meters above the road at the center, so we can use this information to find the height of the vertex of the parabola, which is

vertex height = 4 meters + 20 meters = 24 meters

We can now use the vertex form of a parabola to write the equation

y = a(x - h)^2 + k

where (h, k) is the vertex and a is a constant that determines the shape of the parabola.

Substituting the values we found for the vertex height and the distance between the towers, we get

y = a(x - 40)^2 + 24

We now need to find the value of a. To do this, we can use the fact that the vertical cables are spaced every 10 meters. This means that the distance between the vertex of the parabola and a point on the main cable 10 meters from the center of the bridge is

distance = 10 meters

Substituting x = 50 (since the center of the bridge is at x = 40 + 10 = 50) and y = 14 (since the cable is 4 meters above the road at this point), we get

14 = a(50 - 40)^2 + 24

-10 = 100a

a = -0.1

Substituting this value of a into the equation we found earlier, we get

y = -0.1(x - 40)^2 + 24

To find the height of the main cable 20 meters from the center, we can substitute x = 60 (since the center of the bridge is at x = 50 and we want to go 20 meters to the right) into the equation

y = -0.1(60 - 40)^2 + 24

y = -0.1(20)^2 + 24

y = -0.1(400) + 24

y = -40 + 24

y = -16

Learn more about parabola here

brainly.com/question/4074088

#SPJ4