an oil prospector will drill a succession of holes in a given area to find a productive well. the probability that he is successful on a given trial is .2. a what is the probability that the third hole drilled is the first to yield a productive well? b if the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?

So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.

In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.

Here,

We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.

In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:

(x, y) → (x', y')

To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:

x' = x + 8

y' = y + 4

To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:

x' = x - 4

y' = y - 4

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The probability of getting a straight in a five-card poker hand is 0.0019, which is calculated by dividing the total number of possible straights by the total number of possible five-card hands.

To calculate the probability of getting a straight in a five-card poker hand, we need to first understand the concept of a straight. A straight is a combination of five cards that are in consecutive ranks, such as 6-7-8-9-10 or 10-J-Q-K-A.

The total number of possible five-card hands is given by the mathematical formula 52 choose 5, which is equal to 2,598,960. To calculate the number of possible straights, we need to consider the number of ways that we can choose five consecutive ranks out of the thirteen ranks available in a standard deck of cards. There are 10 ways to do this, since we can start with each of the 10 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) and have one unique straight for each.

However, there are different ways to arrange the cards in a straight. For example, the straight 10-J-Q-K-A can be arranged in five different ways (10-J-Q-K-A, A-10-J-Q-K, K-A-10-J-Q, Q-K-A-10-J, J-Q-K-A-10). Therefore, the total number of possible straights is 10 * 5 = 50.

To calculate the probability of getting a straight, we divide the number of possible straights by the total number of possible five-card hands. Thus, the probability of getting a straight in a five-card poker hand is 50/2,598,960, or approximately 0.0019. Therefore, the chances of getting a straight are relatively low, but not impossible.

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To determine the sample size needed to have a % confidence that our sample mean will be within hours of the true mean, we would need to use a formula. Specifically, we would use the formula: n = (Z^2 * s^2) / E^2

Where n is the sample size needed, Z is the z-score associated with the desired confidence level, s is the standard deviation of the population, and E is the margin of error (in this case, the specified difference of hours between the sample mean and true mean).

Assuming we have information about the population standard deviation (s), we can plug in the values for Z, s, and E to find the necessary sample size. For example, if we wanted to be 95% confident that our sample mean would be within 2 hours of the true mean, we would use a Z-score of 1.96 (which corresponds to a 95% confidence level). Let's say the population standard deviation is 5 hours. Plugging in these values, we would get:

n = (1.96^2 * 5^2) / 2^2
n = 96.04

So we would need a sample size of at least 97 in order to be 95% confident that our sample mean would be within 2 hours of the true mean.
To determine the sample size needed to be confident that our sample mean will be within a specific number of hours of the true mean, we need to know the confidence level, standard deviation, and margin of error (in hours). The formula for calculating the sample size is:

n = (Z^2 * σ^2) / E^2

where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = population standard deviation
E = margin of error (in hours)

Once you provide the confidence level, standard deviation, and margin of error (hours), we can plug in the values and calculate the required

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Answer:

17.2 hours, or 17 hours and 12 minutes

Step-by-step explanation:

If she reads 50 pages per hour, then 860/50 = 17.2

The exponential function for the new participants is f(x) = 3 * 4^x

Let's start with the initial number of participants who sent selfies on Day 0.

We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.

On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.

We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.

Therefore, we can write an exponential function of the form:

f(x)=a * 4^x

Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.

We know that a = 12 from our earlier calculations.

So, we have

f(x) = 3 * 4^x

Hence, the function is f(x) = 3 * 4^x

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The given statement about developing quantitative and measurable usability tests is true.

Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.

By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.

This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.

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a) 80 hours after 11:00 on a 12-hour clock would be 7:00.

b) 40 hours before 12:00 on a 12-hour clock would be 4:00.

c) 100 hours after 6:00 on a 12-hour clock would be 10:00.

a, To find this, we need to divide 80 by 12 (the number of hours on the clock), which gives us a quotient of 6 and a remainder of 8. We then add the remainder to the starting time of 11:00, giving us 7:00.

b, To find this, we need to subtract 40 from 12 (the number of hours on the clock), which gives us 8. We then subtract 8 from the starting time of 12:00, giving us 4:00.

c, To find this, we need to divide 100 by 12 (the number of hours on the clock), which gives us a quotient of 8 and a remainder of 4. We then add the quotient (which represents a full cycle of 12 hours) to the starting time of 6:00, giving us 6+8=14:00, which is equivalent to 2:00 on a 12-hour clock. Finally, we add the remainder of 4 to 2:00, giving us 10:00.

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The actual height of the statue is option C 231.2 feet.

A scale factor is a number used in mathematics to scale or multiply a quantity or measurement by another factor in order to establish a proportional relationship between two identical figures or objects.

In other terms, the scale factor is the ratio of the corresponding lengths, widths, or heights of the two figures or objects if they are similar, that is, they have the same shape but may range in size. This implies that you may determine the dimension of the second object by multiplying one dimension of one object by the scale factor.

Given that the scale factor is 230:1.

Thus,

actual height of statue / 230 = height of drawing / 1.2 feet

Now,

actual height of statue = (1.2 feet / 1.2 feet) * 230

actual height of statue = 230 feet

Hence, the actual height of the statue is option C 231.2 feet.

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The substance's half-life in days is 3 days.

What is exponential decay?

If a quantity declines at a pace proportionate to its current value, exponential decay may be present. The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time.

Here, we have

Given: An 18-gram sample of a substance that's a by-product of fireworks has a k-value of 0.215.

We have to find the substance's half-life in days.

Using the formula for the exponential decay that is N = N₀e⁻ⁿˣ,

we have N = 18/2, N₀ = 18, and n = 0.215.

N = N₀e⁻ⁿˣ

9 = 18e⁻⁰°²¹⁵ˣ

9/18 = e⁻⁰°²¹⁵ˣ

1/2 = e⁻⁰°²¹⁵ˣ

Taking logs on both sides, we get

㏑(1/2) = -0.215x

x = ㏑(1/2)/(-0.215)

x = -0.6931/(-0.215)

x = 3.22

Hence, the substance's half-life in days is 3 days.

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x=47°

The degree of a triangle is equal to 180°.

Since a triange=180°, you would subtract 180 by 102+31 because the other two angles are 102° and 31°.

180-102-31=47°

Therefore the answer would be x=47°

Answer:

6.8 ounces

To set up a hypothesis test for this production process, we need to define the null and alternative hypotheses. The null hypothesis (H0) is that the average amount of soda in each can is equal to 6.8 ounces, while the alternative hypothesis (Ha) is that the average amount of soda in each can is not equal to 6.8 ounces.

We can then collect data by taking regular random samples from the production process and calculate the sample mean and standard deviation. We can then perform a statistical test such as a t-test or z-test to determine whether we can reject or fail to reject the null hypothesis.

If we reject the null hypothesis, we can conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces. If we fail to reject the null hypothesis, we cannot conclude that there is evidence that the average amount of soda in each can is different from 6.8 ounces.

I hope this helps! Let me know if you have any other questions.

Answer: Beth and Jose should leave a $6.15 tip.

Step-by-step explanation: We need to find 20% of $30.75 so you need to multiply 30.75 by 0.20 to find 6.15 to be 20% of 30.75.

Answer:

A) $6.15

Step-by-step explanation:

20%= 0.2
30.75 x 0.2 = 6.15

Answer:

[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]

"Gov" refers to "Student  Government".

==================================================

Explanation:

The rows are labeled "7th grade", "8th grade" and "Total".

The columns are labeled "Music", "Student  Government", "Theater", "Sports", and "Total".

I'll abbreviate "Student  Government" to "Gov" so that the table doesn't get too wide.

There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.

----------

We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.

Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.

----------

There are 21 students in student government. This value goes at the bottom of the "student government" column.

9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.

----------

There are 65 students in theater. This value goes at the bottom of the "theater" column.

There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).

----------

There are 88 students in sports.

30 are in 8th grade, so 88-30 = 58 must be in 7th.

----------

At this point, you should have these values along the bottom row:

80, 21, 65, 88, 254

The first four values (80, 21, 65, 88) should add to the grand total 254.

Along each row, add up the values to get the row total.

7th grade: 42 + 12 + 20 + 58 = 132

8th grade:  38 + 9 + 45 + 30 = 122

There are 132 seventh graders and 122 eighth graders.

Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.

Step-by-step explanation:

7 + x = 2x, so x = 7

The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.

Answer:1

1. is 2/7

2. is .5

3 is 1.94 repeating and

4 is 7/11

Step-by-step explanation:

The opportunity of drawing a chocolate from the bag is 0.4, therefore, the answer is A. 0.4.

Steven has a bag of 20 pieces of candy, out of which 8 are chocolates. If he draws one piece of sweet at random, the opportunity of it being a chocolate may be calculated through dividing the wide variety of chocolates in the bag with the aid of the full quantity of chocolates inside the bag. In this situation, there are 8 chocolates out of 20 total candies.

The formulation to calculate the opportunity is:

P(chocolate) = number of candies / total range of candies

Substituting the given values, we get:

P(chocolate) = 8 / 20

Simplifying this fraction, we get:

P(chocolate) = 0.4

Consequently, the opportunity of drawing a chocolate from the bag is 0.4  

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The power series method can be used to solve a nonhomogeneous differential equation about an ordinary point by finding both a homogeneous and particular solution using a series expansion and the method of undetermined coefficients.

The power series method is a technique used to find a series solution of a differential equation. When applied to a nonhomogeneous differential equation, the method involves finding both a homogeneous solution and a particular solution.

Assuming that the nonhomogeneous differential equation has the form

y''(x) + p(x)y'(x) + q(x)y(x) = f(x)

where p(x), q(x), and f(x) are functions of x, we can begin by finding the solution to the associated homogeneous equation

y''(x) + p(x)y'(x) + q(x)y(x) = 0

Using the power series method, we can assume a solution of the form:

y(x) = a0 + a1(x - x0) + a2(x - x0)^2 + ...

where a0, a1, a2, ... are constants to be determined, and x0 is the ordinary point of the differential equation.

Next, we can find the coefficients of the power series by substituting the series solution into the differential equation and equating coefficients of like powers of (x-x0). This leads to a system of equations for the coefficients, which can be solved iteratively.

After finding the homogeneous solution, we can find a particular solution using a similar method. Assuming a particular solution of the form:

y(x) = u(x) + v(x)

where u(x) is a solution to the associated homogeneous equation, and v(x) is a particular solution to the nonhomogeneous equation, we can use the method of undetermined coefficients to find v(x). This involves assuming a form for v(x) based on the form of f(x), and then solving for its coefficients using the same technique as before.

Once we have found both the homogeneous and particular solutions, we can combine them to obtain the general solution to the nonhomogeneous differential equation.

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When we look across each row of the table the pattern we observe is that the multiplication of the table leads to 12.

The quantity of space a three-dimensional item occupies is measured by its volume. Usually, it is expressed in cubic units like cubic metres or cubic feet. If an object has irregular or curved shapes, the volume can be determined by using its measurements, such as length, breadth, and height, or by employing more difficult mathematical calculations. In several disciplines, such as physics, engineering, and architecture, volume is a crucial notion.

From the table we see that the arrangement of the 12 cubes is made in different length and width, such that the multiplication of the three is 12.

Here we have,

Long    wide       tall

2            3             2

2             6            1

3             1             4

3             2            2

3             4            1

4              1            3

6              2            1

Hence, when we look across each row of the table the pattern we observe is that the multiplication of the table leads to 12.

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The complete question is:

Answer:

x = 8, y = 3

Step-by-step explanation:

Assuming the figure is a parallelogram, opposite sides on a parallelogram are equal.

This means that 3x-2 = 2x+6 and 3y-5 = y+1.

To solve these equations:

3x-2 = 2x+6 (collect like terms)

3x-2x = 6+2

x = 8

3y-5 = y+1 (collect like terms)

3y-y = 1+5

2y = 6 (divide both sides by 2)

y = 3

∴ x = 8, y = 3

The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

The explicit formula for a geometric sequence is:

an = a1 * [tex]r^{(n-1)}[/tex]

What is arithmetic sequence?

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a fixed constant number, called the common difference, to the preceding term.

To write the explicit formula for both an arithmetic and geometric sequence, the following values must be known:

For an Arithmetic Sequence:

The first term (a1) of the sequence.

The common difference (d) between consecutive terms in the sequence.

The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

Where:

an is the nth term of the sequence.

a1 is the first term of the sequence.

d is the common difference between consecutive terms.

n is the position of the term in the sequence.

For a Geometric Sequence:

The first term (a1) of the sequence.

The common ratio (r) between consecutive terms in the sequence.

The explicit formula for a geometric sequence is:

an = a1 * r^(n-1)

Where:

an is the nth term of the sequence.

a1 is the first term of the sequence.

r is the common ratio between consecutive terms.

n is the position of the term in the sequence.

Therefore, The explicit formula for an arithmetic sequence is:

an = a1 + (n-1)d

The explicit formula for a geometric sequence is:

an = a1 * [tex]r^{(n-1)}[/tex]

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The distance from A to B is  724.64 ft

Consider the following figure.

In right triangle CDA, the sine of angle DAC would be,

sin(∠DAC) = CD/CA

sin(32°) = CD/1540

CD = 816.1 ft

Consider the tangent of angle DAC.

tan(∠DAC ) = CD/AD

tan(32°) = 816.1 / AD

AD = 816.1/ 0.63

AD = 1295.4

Let us assume that distance AB = x feet

In right triangle CDB, the tangent of angle CBD would be,

tan(∠CBD) = CD/DB

tan(∠CBD) = CD/(DA + AB)

tan(22°) = 816.1 / (1295.4+ x)

1295.4 + x = 816.1 / 0.4040

1295.4 + x = 2020.04

x = 2020.04 -  1295.4

x = 724.64 ft

Therefore, the required distance is  724.64 ft

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Find the complete question below.

Chad drinks  389.28  fluid ounces of water in 6 days.

A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.

An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.

given that,

chad drinks 64.88 fluid ounces of water per day,

so in 6 days

he will drink = 6 x water drink per day

= 6 x 64.88

= 389.28

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Answer: x=23±√609/10

Step-by-step explanation:

Using the substitution method we know that the value of y in the given situation is 2 respectively.

The substitution method is typically used in mathematics to solve an equation system.

In this approach, you solve the equation for one variable first, then you enter its value into the other equation.

A false statement is produced if the variables x = 3 and y = 2 are substituted into the first equation: 2(2) = 3 + 9.

Try changing the first equation as x = 2y 8 to solve this system.

Next, change x in the second equation to 2y 8, and then solve for y.

The right response is x = 2, y = 3.

So, get the value of y as follows:

3x - 9y =8 ...(1)

-2x + 2y= 8 ...(2)

Now, take equation (1):

3x - 9y =8

3x = 8 + 9y

x = (8 + 9y)/3

Now, substitute x = (8 + 9y)/3 in equation (2):

-2x + 2y= 8

-2[(8 + 9y)/3] + 2y= 8
-2[(8 + 9y)] + 2y= 8*3
-16 + 18y + 2y = 24

20y = 24 + 16

20y = 40

y = 40/20

y = 2

Therefore, using the substitution method we know that the value of y in the given situation is 2 respectively.

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The probability of the weekend being dry for the school picnic is approximately 23.4%.

First, let's define some terms:

1. Probability: The likelihood of a specific event happening
2. Picnic: The school event that is scheduled for a two-day weekend in May
3. Rainy: Refers to days with rain

Now, let's calculate the probability that the weekend will be dry:

There are 16 rainy days in May, and May has 31 days. So, there are (31 - 16) = 15 dry days in May.

Each weekend has two days. Since May has 31 days, there are (31 / 7) = approximately 4.43 weeks in May. To account for the remaining days, we round down to 4 weeks and add the remaining 2 days as another weekend, resulting in 5 weekends.

Now, we'll determine the probability of having a dry day on any given day in May:

Dry day probability = (number of dry days) / (total days in May) = 15 / 31 ≈ 0.484

Since we want the probability of having two consecutive dry days (the whole weekend), we'll multiply the probabilities of each day being dry:

Weekend probability of being dry = (dry day probability) * (dry day probability) ≈ 0.484 * 0.484 ≈ 0.234

So, the probability of the weekend being dry for the school picnic is approximately 23.4%.

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The best center is the mean because there are no outliers

To determine the best center, we need to examing the ages of the player withing the range of age.

The ages of the players are: 11, 10, 11, 11, 8, 11, 12, 11, 9, 10, 11, 12

In the above list of age, we can seee that there are no outliers are

When there are no outliers in a dataset, the best center to use is the mean

Hence, the best center is the mean

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The top of the ladder is dropping at a rate of -5/24 ft/s (approximately -0.208 ft/s) when the base is 5 feet from the wall.To answer your question, we'll use the Pythagorean theorem for the right triangle formed by the ladder, wall, and ground.

Let x be the distance from the base of the ladder to the wall, and y be the distance from the top of the ladder to the ground. The ladder's length (13 ft) is the hypotenuse of the triangle.
According to the Pythagorean theorem:
x² + y² = 13²
When the base is 5 feet from the wall:
5² + y² = 13²
y² = 144
y = 12 ft
Now, we'll differentiate the equation with respect to time (t):
2x(dx/dt) + 2y(dy/dt) = 0
Given that the base is being pulled away at 0.5 ft/s (dx/dt = 0.5 ft/s), we can find the rate at which the top of the ladder is dropping (dy/dt) when x = 5 ft and y = 12 ft:
2(5)(0.5) + 2(12)(dy/dt) = 0
5 + 24(dy/dt) = 0
dy/dt = -5/24

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The top of the ladder is dropping at a rate of [tex]5/\sqrt(119)[/tex]feet per second.

Let's begin by drawing a diagram of the situation:

           |\

           | \

           |  \   <-- ladder

           |   \

           |    \

           |     \

           |         \

           |______\

              wall

A right triangle formed by the ladder, the wall, and the ground.

Let's call the distance from the foot of the ladder to the wall "x" and the height of the ladder "y".

The ladder is 13 feet long and that the foot of the ladder is being pulled away from the wall at a rate of 0.5 feet per second.

The height of the ladder is changing when the foot of the ladder is 5 feet from the wall.

Using the Pythagorean theorem,

the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation

[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

[tex]x^2 + y^2 = 13^2[/tex]

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

[tex]2x dx/dt + 2y dy/dt = 0[/tex]

We want to find. [tex]dy/dt[/tex] when [tex]x = 5[/tex], so, we need to substitute. [tex]x = 5[/tex] and [tex]dx/dt = 0.5[/tex] into the equation above:

[tex]2(5)(0.5) + 2y dy/dt = 0[/tex]

[tex]y dy/dt = -5[/tex]

[tex]dy/dt = -5/y[/tex]

Pythagorean theorem to solve for y when. [tex]x = 5[/tex]:

[tex]5^2 + y^2 = 13^2[/tex]

[tex]y^2 = 144 - 25[/tex]

[tex]y^2 = 119[/tex]

[tex]y = \sqrt(119)[/tex]

The foot of the ladder is 5 feet from the wall, the height of the ladder is:

[tex]y = \sqrt(119) feet[/tex]

And the rate of change of the height of the ladder is:

[tex]dy/dt = -5/y = -5/\sqrt(119) feet per second[/tex]

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