Training neural networks requires two steps. In the forward pass we compute the output of the network and the loss given the input, and in the backward pass we compute the derivatives for all the parameters given the loss, and the values computed in the forward pass. Take the regression network of slide 10 of lecture 6 ("Beyond linear models") and assume you have some instance, some target value and, and that you are using squared error loss. Write pseudocode for the forward and backward pass. You may use a separate variable for each node in the network, or store all the values of one layer in a list or similar datastructure. You can use whatever form of pseudocode seems most appropriate, but the more detailed it is, the better. When in doubt, we suggest making it as close to runnable python code as you can.

The linear function that models the data is S = 3.8x - 14.506 and  the circumference of a finger with a ring size of 6 is 5.4 cm.

a. To find a linear function S that models the data, we need to find the slope and y-intercept of the line that best fits the data. The slope can be found by using the formula:

m = (y2 - y1) / (x2 - x1)

Using the first two data points, we can find the slope:

m = (7 - 4) / (5.66 - 4.87)

m = 3 / 0.79

m = 3.8

To find the y-intercept, we can use the formula:

y = mx + b

Substituting one of the data points and the slope into the formula and solving for b:

4 = (3.8)(4.87) + b

b = 4 - (3.8)(4.87)

b = -14.506

So the linear function that models the data is:

S = 3.8x - 14.506

b. To find the circumference of a finger with a ring size of 6, we can substitute S = 6 into the linear function and solve for x:

6 = 3.8x - 14.506

3.8x = 20.506

x = 5.4 cm

So the circumference of a finger with a ring size of 6 is 5.4 cm.

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The coordinates of the other endpoint, Q, are (3,-8).

The midpoint formula is used to find the coordinates of the midpoint of a line segment. The formula is as follows:
M = ((x1+x2)/2, (y1+y2)/2)

In this case, the midpoint M=(1,-2) and one endpoint P=(-1,4) are given. We can plug these values into the formula to find the coordinates of the other endpoint, Q:
(1,-2) = ((-1+x2)/2, (4+y2)/2)

Solving for x2 and y2, we get:
x2 = 2(1) + 1 = 3
y2 = 2(-2) - 4 = -8

Therefore, the coordinates of the other endpoint, Q, are (3,-8).

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-13 is the  value of b in linear equation.

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

                              Equations with variables of power 1 are referred to as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

y = 6x + 4

 y = mx + c

is a straight line  of gradient of c.

  m = 6

y = 6x + c

the line passes through points(x,y) where x = 3 and y = 5

      5 = 6 * 3 + c

        c = 5 - 18

         c = -13

         y = 6x - 13

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Answer:

1. 2430 feet

2. 1.8 m/s^2

Step-by-step explanation:

See the attached worksheet.

A time versus speed graph contains a small treasure of mathematical rewards. The area under the graph is equal to the distance travelled. The slope of the line segments represents acceleration.

For total distance: If we break the graph into three sections (2 triangles and a rectangle) we can calculate the areas for each. Each area is the distance travelled for that segment. As shown on the workseet, the total area is 2430 miles, the distance travelled by the train for this question.

The slope of the line in the first 10 seconds is 1.8 meters/sec^2, the acceleration of the train over that period.

The first 3 iterates of the function f(x) = 3x when x0=2 are,

⇒ 6, 18, 54

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The function is,

⇒ f (x) = 3x

At x₀ = 2

Now, We get;

The first iterate is,

⇒ f (x₁) = 3x₀ = 3 × 2 = 6

Second iterate is,

⇒ f (x₂) = 3x₁ = 3 x 6 = 18

Third iterate is,

⇒ f (x₃) = 3x₂ = 3 x 18 = 54

Thus, The first 3 iterates of the function f(x) = 3x when x0=2 are,

⇒ 6, 18, 54

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[tex](f+g)(x)= f(x) .g(x)[/tex][tex](f+g)(0) = f(0)+g(0) = 1+\frac{1}{2} = \frac{3}{2}[/tex][tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]Answer:

Step-by-step explanation:

We are given:

[tex]f(x) = x^{2} +1\ ;g(x) = \frac{1}{2-x}[/tex]

We need to find:

a) [tex](f+g)(0)[/tex]

b) [tex](f.g)(0)[/tex]

[tex]f(0) = 0^{2} +1 = 1[/tex]

[tex]g(0) = \frac{1}{2-0} =\frac{1}{2}[/tex]

a) we know that

[tex](f+g)(x)= f(x) +g(x)[/tex]

[tex](f+g)(0) = f(0)+g(0)[/tex]

Using the value of f(0) and g(0)

we get

b) we know that

[tex](f+g)(x)= f(x) .g(x)[/tex]

[tex](f+g)(x)= f(x) .g(x) = (1)(\frac{1}{2}) =\frac{1}{2}[/tex]

So we have answer for a) 3/2 and for b) 1/2

Using the expressions to evaluate each function we are left with the following:

To evaluate the expressions, we simply need to substitute the value of x with 0 in the given functions and then perform the indicated operations. For part a, we need to add the functions f and g, and for part b, we need to multiply them:

(f + g)(0) = f(0) + g(0) = (0² + 1) + (1 / (2 - 0)) = 1 + (1 / 2) = 1.5

(f · g)(0) = f(0) * g(0) = (0² + 1) * (1 / (2 - 0)) = 1 * (1 / 2) = 0.5

In conclusion, we have that (f + g)(0) = 1.5 and (f · g)(0) = 0.5.

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Answer:

4x + 14

Step-by-step explanation:

2 (3x2 - 4x + 7)

= 2 ( 6x - 4x + 7)

= 2 ( 2x + 7)

= 4x + 14

The factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]

To factor the given polynomial completely, we need to find the greatest common factor (GCF) of all the terms. The GCF of 60a^(3)b^(2), 10a^(2), and -50a^(4)b^(2) is 10a^(2).

So, we can factor out 10a^(2) from each term to get:

[tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}[/tex]

Now, we can check our answer by multiplying the factors back together:

[tex]10a^{(2)}(6ab^{(2)}+1-5a^{(2)}b^{(2))}=60a^{(3)}b^{(2)}+10a^{(2)}-50a^{(4)}b^{(2)}[/tex]

Therefore, the factored form of the given polynomial is [tex]10a^{(2)}(6ab)^{(2)}+1-5a^{(2)}b^{(2))}.[/tex]

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The division is one of the four basic arithmetic operations in mathematics, along with addition, subtraction, and multiplication. It involves breaking a number or quantity into equal parts, or groups, and determining how many groups or how many items are in each group.

In mathematics, a division sentence is a statement that represents the operation of division. It is typically written in the form of a fraction or using the division symbol, with a dividend (the number being divided) on top and a divisor (the number by which the dividend is being divided) on the bottom. For example, the division sentence 8 ÷ 2 = 4 can also be written as the fraction 8/2 = 4/1.

The result of a division operation is called the quotient.

Division is a fundamental concept in mathematics and is used in many areas of study, including algebra, geometry, and statistics. It is also an important tool in everyday life, such as in calculating the cost per unit of a product or dividing a recipe to adjust the serving size.

Without a specific drawing to refer to, it's difficult to provide a specific explanation of how Adrian used it to solve a division sentence. However, I can provide a general explanation of how a drawing might be used to illustrate or solve a division problem.

One common way to use a drawing to solve a division problem is through the use of equal groups. For example, consider the division problem 12 ÷ 3. To solve this problem, we can draw 12 circles and group them into equal groups of 3. We would then count the number of groups to determine the quotient, which is the answer to the division problem.

Another way to use a drawing to solve a division problem is through the use of a number line. For example, consider the division problem 15 ÷ 5. We can draw a number line and mark the starting point at 0, the ending point at 15, and the intervals at 5. We would then count the number of intervals to determine the quotient, which is the answer to the division problem.

Regardless of the specific method used, a drawing can help to illustrate the concept of division and make it more concrete and visual. It can also be a useful tool for students who are just learning about division or who struggle with more abstract or symbolic representations of mathematical concepts.

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The height in meters is 1.73 meters (rounded to two decimal places), the weight in other unit (kg) approximately 92.1 kg.The distance ran is approximately 546 meters

The distance you have run is 597 yards. To convert yards to meters, we can use the conversion factor 1 yard = 0.9144 meters. Therefore, the distance you have run in meters is approximately 546 meters (rounded to the nearest meter).

Your weight is currently expressed in pounds (lbs). To express your weight in other units, we can use conversion factors. For example, your weight in kilograms (kg) can be found by multiplying your weight in pounds by 0.453592. Using this conversion, your weight would be approximately 92.1 kg (rounded to one decimal place). Alternatively, your weight in stones (st) can be found by dividing your weight in pounds by 14. Using this conversion, your weight would be approximately 14.5 st (rounded to one decimal place).

Therefore, the hieght, weight and distance ran are 1.73 meters,  92.1 kg and 546 meters respectively.

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The question is :

What is the height in meters and how many meters has he run, and in what unit could you express his weight, for someone who is 5 ft 8 in tall and weighs 203 lbs and ran a distance of 597 yards ?

x1 = 5 and x2 = 0

The following LP problem in a spreadsheet MAX: 4x1 + 4x2 Subject to: 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.A spreadsheet is a type of software that allows users to store and analyze data in a grid-like format of rows and columns. Spreadsheets are commonly used for data entry, financial modeling, and other calculations.In the given problem, we are supposed to find the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0.The first two constraints are represented by inequalities. That means, the values of x1 and x2 can be any non-negative values that satisfy the constraints. Mathematically, the constraints can be represented as:2x1 + 4x2 <= 20⇒ x2 <= 5 - 0.5x1--------(1)3x1 + 5x2 <= 15⇒ x2 <= 3 - 0.6x1--------(2)Note that, we have represented the constraints in such a way that x2 is the subject of the inequality. This is done to make it easier to graph and find the feasible region.To find the feasible region, we need to graph both inequalities (1) and (2) on a coordinate plane. The feasible region is the shaded area that is common to both regions. It is given below:The feasible region is the triangular-shaped region. Since x1 and x2 are both non-negative, we need to consider only the values of x1 and x2 that are within the feasible region.Now, to maximize the function 4x1 + 4x2, we need to find the optimal solution. We do this by finding the intersection points of the lines that represent the equation 4x1 + 4x2 = k, where k is a constant.The equation 4x1 + 4x2 = k can be rearranged as x2 = (-x1 + k/4)This equation represents a line with a slope of -1 and a y-intercept of k/4. We can graph this line for different values of k to find the optimal solution. The line for k = 0 is shown below:We can see that the line passes through the feasible region at point (0, 0) and (5, 0). This means that the maximum value of the function is 4x1 + 4x2 = 4(5) + 4(0) = 20 at point (5, 0).Thus, the maximum value of the function 4x1 + 4x2 subject to the constraints 2x1 + 4x2 <= 20, 3x1 + 5x2 <= 15, and x1, x2 >= 0 is 20 at x1 = 5 and x2 = 0.

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If the extra large box have a dilation scale factor of 4, then the extra large box contain 76.8ounces.

If the extra large box is a dilation of the single serving box with a scale factor of 4, then

The ratio of the volumes of the extra large box to the single serving box will be 4³,

We know that, Volume is a three-dimensional measurement and is affected by the cube of the scale factor.

So, the volume of the extra large box will be;

⇒ 4³ × 1.2 ounces = 4×4×4×1.2 ounces = 76.8 ounces,

Therefore, the extra large box will contain 76.8 ounces of cereal.

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The x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

The x-values at a distance of 22 or less from the number 9 can be found by solving the inequality |x-9|≤22.

Step 1: Break up the absolute value inequality into two separate inequalities:
x-9≤22 and x-9≥-22

Step 2: Solve each inequality for x:
x≤31 and x≥-13

Step 3: Combine the two inequalities using the "and" operator (∩):
-13≤x≤31

Step 4: Write the solution in interval notation:
[-13, 31]

So, the x-values at a distance of 22 or less from the number 9 are all the numbers in the interval [-13, 31].

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a. The equation "(a) x2+3​=x+4" gives the solution as x = 1.

b. The equation "(b) 2x-1​-x-4=2" gives the solution as x = -1.

To solve these radical equations, we will need to isolate the radical on one side of the equation and then square both sides to get rid of the radical. After that, we can solve for x using standard algebraic methods.

(a) x2+3​=x+4

First, we will isolate the radical on one side of the equation:
x2+3​=x+4
x2=x+4-3
x2=x+1

Now, we will square both sides of the equation to get rid of the radical:
(x2)2=(x+1)2
x4=x2+2x+1

Next, we will rearrange the equation and set it equal to zero:
x4-x2-2x-1=0

Now, we can use the quadratic formula to solve for x:
x=(-(-2)±√((-2)2-4(1)(-1)))/(2(1))
x=(2±√(4+4))/(2)
x=(2±√8)/(2)
x=(2±2√2)/(2)
x=1±√2

So, the solutions for x are 1+√2 and 1-√2.

(b) 2x−1​−x−4​=2

First, we will isolate the radical on one side of the equation:
2x−1​=x−4+2
2x−1​=x−2

Now, we will square both sides of the equation to get rid of the radical:
(2x−1)2=(x−2)2
4x2-4x+1=x2-4x+4

Next, we will rearrange the equation and set it equal to zero:
3x2=3

Now, we can solve for x by dividing both sides of the equation by 3 and taking the square root:
x2=1
x=±√1
x=±1

So, the solutions for x are 1 and -1.

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Answer: ??

Step-by-step explanation:

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence.

A sequence in mathematics is an ordered collection of numbers that is typically defined by a formula or rule. Every number in the series is referred to as a term, and its location within the sequence is referred to as its index. Depending on whether the list of terms stops or continues indefinitely, sequences can either be finite or infinite. By their patterns or uniformity, sequences can be categorised, and the study of sequences is crucial to many areas of mathematics, such as calculus, number theory, and combinatorics. Mathematical, geometrical, and Fibonacci sequences are a few examples of popular sequence types.

given

The sequence's terms are all different by 7 (i.e., 12 - 5 = 19 - 12 = 26 - 19 =... = 7).

The following is a definition of a recursive formula for the nth element of the sequence:

a 1 = 5 (the first term of the series is 5) (the first term of the sequence is 5)

For n > 1, each term is derived by adding 7 to the preceding term, so a n = a n-1 + 7.

Thus, beginning with a 1 = 5, the formula a n = a n-1 + 7 can be used to recursively find the nth term of the sequence. For instance, we have

a_2 = a_1 + 7 = 5 + 7 = 12

a_3 = a_2 + 7 = 12 + 7 = 19

a_4 = a_3 + 7 = 19 + 7 = 26

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Answer:

0.68 inches

Step-by-step explanation:

The interior diameter of the old pipe is 0.63 inches, and the plumbing tape will fill 0.15 inches of the space between the old pipe and the new pipe. Therefore, the total diameter that the new pipe must fit inside is:

0.63 inches + 0.15 inches = 0.78 inches

The new pipe must be 0.1 inches smaller than this diameter to ensure a proper fit. Therefore, the diameter of the new pipe should be:

0.78 inches - 0.1 inches = 0.68 inches

So, the new pipe must have an interior diameter of 0.68 inches to fit correctly inside the old pipe with the plumbing tape.

This construction is also known as the "perpendicular bisector" construction.

To construct a line through a given point that is perpendicular to a given line using a ruler and compass, you will need to follow these steps:

By following these steps, you have used the ruler and compass to construct a line through a given point that is perpendicular to a given line. This construction is also known as the "perpendicular bisector" construction.

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Answer - The value of cos 2.240 degrees comes out to be 0.9992.

To determine the value of cos 2.240 degrees, we can use the following steps: Convert the angle from degrees to radians. To do this, we can use the formula: radians = degrees * π/180. Plugging in the given angle, we get: radians = 2.240 * π/180 = 0.0391 radians

Use the cosine function to find the value of cos 2.240 degrees.- The cosine function is defined as cos(x) = adjacent/hypotenuse, where x is the angle in radians.- Plugging in the angle in radians that we found in Step 1, we get: cos(0.0391) = adjacent/hypotenuse

Use a calculator to find the value of cos(0.0391).- Using a calculator, we find that cos(0.0391) = 0.9992. The value of cos 2.240 degrees is 0.9992.

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It will take the second skater 20 seconds to catch up to the first skater and pass him/her.

In physics, speed and motion are related concepts that describe the movement of objects in space.

Speed is a scalar quantity that measures how fast an object is moving. It is the rate at which an object covers distance, typically measured in meters per second (m/s), kilometers per hour (km/h), or some other unit of distance per unit of time.

Motion, on the other hand, is the change in position of an object over time, with respect to a reference point. In physics, motion can be described in terms of displacement, velocity, and acceleration. Displacement refers to the change in position of an object relative to a reference point, while velocity describes how fast an object is moving in a specific direction.

Acceleration refers to the rate at which an object's velocity changes over time, either by increasing or decreasing in speed or changing direction.

In summary, speed is a measure of how fast an object is moving, while motion is the change in position of an object over time.

We can start by setting up an equation to represent the distance each skater travels, with t representing the time it takes for the second skater to catch up to the first skater:

Distance traveled by the first skater = Distance traveled by the second skater + 40 meters

Using the formula distance = rate × time, we can plug in the given rates and the unknown time to get:

12t + 40 = 14t

Simplifying this equation, we get:

40 = 2t

t = 20 seconds

Therefore, it will take the second skater 20 seconds to catch up to the first skater and pass him/her.

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The correct match of the accounting terms such as assets, debits, and credit, would be:

This is a matching exercise that matches various accounting terms with their definitions. Here are the meanings of the terms:

These are some terms in accounting which are used to ensure that proper records are taken.

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The value of x is 3  and the sides of given rectangle are 3,3,9,9.

What is Area of rectangle ?

area of rectangle can be defined as product of length and breadth.

From the given figure ,

it is given that ,

perimeter of rectangle = 24 cm

and the sides are ,

x,x,x+6,x+6

so we know that perimeter of rectangle = 2 (l+b)

that is,

24 = x+x+x+6+x+6

24 = 4x + 12

4x = 12

x = 3

Therefore, The value of x is 3  and the sides of given rectangle are 3,3,9,9.

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a. since it provides the lowest regret value should the demand be high.

b. Expected Monetary Value for Gradual Introduction= $2.8 million. Expected Monetary Value for Concentrated Introduction= $1.5 million
c. EVPI = $1.3 million

a. For the pessimistic approach, the recommended decision is to use the gradual introduction of the salad dressings, since it provides the least amount of loss should demand be low. For the minimax regret approach, the recommended decision is also the gradual introduction of the salad dressings, since it provides the lowest regret value should the demand be high.

b. Using the expected monetary value approach, the optimal decision would be to use the gradual introduction of the salad dressings. This is because the expected monetary value for a gradual introduction is $2.8 million, which is higher than the expected monetary value of $1.5 million for a concentrated introduction.

Expected Monetary Value for Gradual Introduction: 0.7 * $1 million + 0.3 * $4 million = $2.8 million
Expected Monetary Value for Concentrated Introduction: 0.7 * -$5 million + 0.3 * $10 million = $1.5 million

c. The EVPI (Expected Value of Perfect Information) for this problem is $1.3 million, which is calculated by subtracting the expected monetary value from the best case outcome.

Best case outcome: $10 million
Expected Monetary Value: $2.8 million
EVPI: $10 million - $2.8 million = $1.3 million

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Simplifying the exponents gives us n^(30)p^(-120) and this is our final simplified answer, expressed using exponents.

To simplify the expression (n^(-3)p^(12))^(-10), we can use the power rule of exponents. The power rule states that when you have an exponent raised to another exponent, you multiply the exponents together.

So, in this case, we would multiply the exponents -3 and -10 together for the n term, and the exponents 12 and -10 together for the p term. This would give us:

n^((-3)*(-10))p^((12)*(-10))

Simplifying the exponents gives us:

n^(30)p^(-120)

And this is our final simplified answer, expressed using exponents.

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Answer:

57,600 if talking about hundreds. If talking about hundredths, 57.61

Answer:

57600

Step-by-step explanation:

nearest hundred (100)

614 is closer to 600

from 651 it becomes near 700 therefore the answer becomes 57600

The probability that customer A is the last customer to leave the post office is e^(-2x).

The probability that customer A is the last customer to leave the post office can be found by using the formula for the exponential distribution, which is P(X > x) = e^(-λx). In this case, λ = 1 and x is the serving time for customer A.

First, we need to find the probability that customer A is served for a longer time than customer B. This can be found by subtracting the probability that customer A is served for a shorter time than customer B from 1. That is, P(X > x) = 1 - P(X < x).

P(X > x) = 1 - P(X < x) = 1 - (1 - e^(-λx)) = e^(-λx)

Next, we need to find the probability that customer A is served for a longer time than customer C. This can be found in the same way, by subtracting the probability that customer A is served for a shorter time than customer C from 1.

P(X > x) = 1 - P(X < x) = 1 - (1 - e^(-λx)) = e^(-λx)

Finally, we need to multiply these two probabilities together to find the probability that customer A is the last customer to leave the post office. P(A is the last customer to leave) = P(A is served longer than B) * P(A is served longer than C) = e^(-λx) * e^(-λx) = e^(-2λx)

Since λ = 1 and x is the serving time for customer A, the probability that customer A is the last customer to leave the post office is e^(-2x). Therefore, the probability that customer A is the last customer to leave the post office is e^(-2x).

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The is no solution of the  equation  (1)/(x-1)-1=(x)/(x-1).

To solve for all values of x in the equation (1)/(x-1)-1=(x)/(x-1), we can follow these steps:

1. Multiply both sides of the equation by (x-1) to eliminate the denominators:
1 - (x-1) = x

2. Simplify the left side of the equation:
- x + 2 = x

3. Add x to both sides of the equation to isolate the variable on one side:
2 = 2x

4. Divide both sides of the equation by 2 to solve for x:
x = 1

Therefore, the solution for x is 1.

When we plug x = 1 back into the original equation, we get a denominator of 0, which is undefined. This means that there are actually no solutions for this equation.

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The mass of the gold bar of the trapezium shape and a density of 19.3g/cm³ is found to be 8.646 KG.

The volume of the trapezoidal prism will be determined first. V = BL, where B is the area of the trapezoidal face and L is the prism's length, is the formula for the volume of the prism.

We are aware that a trapezoid's area is equal to B = 1/2(6+10). (4)

B = 32 m²

When we enter the formula for volume, V = 32 x 14 V = 448 m³, we know that L is 14 cm.

Divide the mass by the volume to get the density, or D = M/V.

According to values,

19.3 = M/448

M = 8646.4 grams, which is equal to 8.646 grams.

The density is stated to be 19.3 kg/m³. Hence, the gold weighs 8.646 kilos.

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Complete question - The gold bar trapezium has cross-sectional area. Gold has a density of 19. 3 per cm3. Work out the mass of the gold bar. Give your answer in kilograms. The dimension of the trapezium are length = 14cm, parallel sides are 6cm and 10cm nd the height is 4cm.

Answer:

360 people pledged $25.

Step-by-step explanation:

You'll need to set up only one equation to solve this.

Let's use x for the number of people who pledged $50. Since twice as many people pledged $25, it would be 2x. Keep this in mind for later.

Multiply 2x by 25, and you should get 50x. Now, your equation is 50x + 50x = 18,000. Simplify this to 100x = 18,000.

Now, divide both sides by 100. After doing so, you should have x = 180. This is how many people pledged $50. To find how many pledged $25, plug the value of x into 2x. (In other words, multiply 180 by 2.) After doing so, you should get 360. This is how many people pledged $25.

Hope this helps!

If the stone dropped by Maria falls 2 meter in 1st second, then the stone would have fallen 30 meter after 10 seconds.

The distance that the stone falls in the first second is = 2 meters;

The distance that the stone falls in the 50th second is = 149 meters;

So, the rate of fall of the stone can be calculated as:

⇒ (149 - 2)/(50 - 1);

⇒ 147/49;

⇒ 3.

So , the stone is falling at the rate of 3 meter per second,

The distance fall by the stone after 10 second can be calculated as :

⇒ 10×3

⇒ 30 meter.

Therefore, After 10 seconds the stone would have fallen 30 meter.

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