On a hot summer day in Death Valley, the amount of water in a swimming pool is 4000 gallons. 30 Days later, the amount of water in the pool is 3500 gallons. If the evaporation follows a continuous exponential model for decay, find k, the constant of proportionality in the equation A=Av0e^kt. Round to 4 decimal places.

Write a function that models the amount of water in the pool A(t), t days after the original measurement

Answer:

Step-by-step explanation:

[tex]a[/tex] is the amount earned on the first day.

She earnt $[tex]$a[/tex] dollar on day 1, $55.50 on day 2, and $65.50 total in the 2 days.

So we get

                  [tex]a+55.50=65.50[/tex]

Answer: go look on yt there’s a good video on this one

Step-by-step explanation:

Conner worked 5 hours on Monday.

Let's use the letters "m" and "f" to denote the number of hours Conner worked on Monday and Friday, respectively.

Conner worked a total of 12 hours, and since we know this from the issue statement, we may write:

m + f = 12

Also, we are aware that Conner received $81 and charged $5 on Mondays and $8 on Fridays. Hence, we can write:

5m + 8f = 81

To determine one of the variables in terms of the other, we can utilise the first equation. To solve for "f," we obtain:

f = 12 - m

We can now solve for "m" by substituting this expression for "f" in the second equation:

5m + 8(12 - m) = 81

After simplifying and finding "m," we obtain:

5m + 96 - 8m = 81

-3m + 96 = 81

-3m = -15

m = 5

Conner spent 5 hours at work on Monday as a result.

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The length of the silver rod when heated to 500°C is approximately 48.47 cm.

To solve this problem, we can use the formula:

L₂ = L₁ (1 + αΔT)

where L₁ is the original length of the rod at temperature T₁, L₂ is the new length of the rod at temperature T₂, α is the coefficient of linear expansion of the material, and ΔT = T₂ - T₁ is the change in temperature.

We are given that the original length of the silver rod is L₁ = 48 cm at temperature T₁ = 13°C. The coefficient of linear expansion for silver is α = 2x10^(-5) °C^(-1). The change in temperature is ΔT = 500°C - 13°C = 487°C.

Substituting these values into the formula, we get:

L₂ = 48 cm (1 + 2x10^(-5) °C^(-1) x 487°C)

= 48 cm (1 + 0.00974)

= 48 cm (1.00974)

= 48.47 cm

Therefore, the length of the silver rod is approximately 48.47 cm.

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_____The given question is incorrect, the correct question is given below:

A silver rod measures 48 cm at 13°C. What is its length when heated to 500°C? (α=2x10^(-5) °C^(-1)).

The amount more that Alex earn per hour more than Sam is $2.

A linear equation is an equation that has a single variable that is raised to the power of one. The general form of a linear equation is

y = mx + c

Where:

The linear equation that represents the amount that Alex earns is y = 20x. This means that for every hour worked, Alex earns $20. Looking at the table, Sam earns $18 for every hour worked. This can be represented with the equation : y = 18x

The difference in the amount earned = 20 - 18 = $2

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Answer:

6/100=3/50

Step-by-step explanation:

The first bag contains the numbers 1 through 10, which is a total of 10 numbers. The second bag contains the numbers 5 through 14, which is also a total of 10 numbers.

The probability of picking the same number from both bags is the number of ways of picking the same number divided by the total number of possible outcomes. There are 10 possible outcomes in each bag, so the total number of possible outcomes is 10 × 10 = 100.

To count the number of ways of picking the same number, we can simply count the number of numbers that appear in both bags. There are six numbers that appear in both bags: 5, 6, 7, 8, 9, and 10.

Therefore, the probability of picking the same number from both bags is:

6/100

Simplifying this fraction by dividing both the numerator and denominator by 2 yields:

3/50

So the probability of picking the same number from both bags is 3/50.

The transformation as a whole is given by P → Q → R → S. A rotation through angle, about the intersection point of the lines, results from the combination of reflections in lines that meet at angle /2.

Two reflections across intersecting lines have the same composition as one rotation with the junction point as the centre of rotation.

By (0,-1/2), the initial translation is provided.

Given by is the reflection along the x-axis (x,-y)

By (0,1/2), the final translation is indicated. Hence, the transformation as a whole is provided by

(x,y) → (x,-y) → (x,-y+1/2) → (x,y+1)

This demonstrates that the resulting isometry moves the values of (x,y) by one unit in the positive y-direction to (x,y+1).

The whole transformation is provided by:

P → P + (0,d/2) → Q → Q - (0,d/2)

The total transformation is given by:

P → P + (d/2,0) → (x,-y) → (x,y) → Q

where Q is positioned (x,y). Adding the two transformations together, we obtain:

P → P + (0,d/2) → Q → Q - (0,d/2) = P + (d,0)

This demonstrates that a translation across distance d, in the direction perpendicular to the lines of reflection, results from the combination of reflections on parallel lines spaced d/2 apart.

The total transformation is given by:

P → Q → R → S

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Answer:

To rewrite a mixed number as an improper fraction, you need to multiply the whole number by the denominator of the fraction, then add the numerator. The resulting sum is the numerator of the improper fraction, while the denominator remains the same.

For example, to rewrite the mixed number 3 1/2 as an improper fraction, you would:

Multiply the whole number 3 by the denominator 2: 3 x 2 = 6

Add the numerator 1 to the product: 6 + 1 = 7

Write the sum 7 as the numerator of the improper fraction, with the denominator 2: 7/2

So, the improper fraction equivalent of the mixed number 3 1/2 is 7/2.

Step-by-step explanation:

sale price=$30

discount price=0.05

Taking it $30*0.05=600$

after applying 0.08

600*0.08=48$

, so 48$ is the final price of the wind chime.

We need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.

In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions arranged in rows and columns. Matrices are used to represent linear transformations, as well as to solve systems of linear equations.

A matrix with m rows and n columns is called an m x n matrix. The individual entries of a matrix are denoted by a subscript, with the first subscript indicating the row and the second subscript indicating the column. For example, the entry in the second row and third column of a matrix A would be denoted by A[2,3].

Matrices can be added, subtracted, multiplied, and divided (by a scalar). Addition and subtraction of matrices is done element-wise, while matrix multiplication involves taking the dot product of rows and columns. Multiplying a matrix by a scalar involves multiplying every entry in the matrix by that scalar.

To find B - 2A, we need to multiply every element of A by 2 and then subtract the resulting matrix from B:

2A = [(-4)*2 (-3)*2 ; (-2)*2 (-3)*2 ; (-3)2 32 ; (-2)2 42] = [-8 -6 ; -4 -6 ; -6 6 ; -4 8]

B - 2A = [6 -9 ; 7 12 ; -3 -3 ; 2 -7] - [-8 -6 ; -4 -6 ; -6 6 ; -4 8] = [14 -3 ; 11 18 ; 3 9 ; 6 -15]

So C = B - 2A = [14 -3 ; 11 18 ; 3 9 ; 6 -15]

To find C₂₂, we need to look at the element in the second row, second column of C, which is -3. Therefore, C₂₂ = -3.

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The percent of carbon remaining after 30642 years if, the half-life of carbon is 5730 years would be 3.1%

Total time is given: 30642 years

Half-Life of carbon-14 : 5730 years

After 1 half-life of the carbon-14 remaining carbon: 1/2

After 2 half-lives the carbon-14 remaining carbon : 1/4

After 3 half-lives the carbon-14 remaining carbon : 1/8

...

...

After n half-lives the carbon-14 remaining carbon : (1/2)^n

Number of half-lives in 30642 years: 30642 / 5730 ≈ 5 approx.

Amount of carbon remaining after 5 half-lives: 1/32

1/32 ≈ 0.031 = 3.1%

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The approximate change in cost corresponding to an increase in sales of one unit is 8.50. and actual change in cost is 8.25.

To answer this question, we need to use differentials to approximate the change in cost corresponding to an increase in sales (or production) of one unit. To do this, we need to calculate the derivative of the given cost function C = 0.075x^2 + 6x + 7.

The derivative of this function is dC/dx = 0.15x + 6. We can now use this derivative to approximate the change in cost when x is increased by one unit. This is given by dC/dx = 0.15(10) + 6 = 8.5.

To compare this with the actual change in cost, we can calculate the change in cost when x is increased from 10 to 11. This is given by C(11) - C(10) = (0.075x^2 + 6x + 7) | 11 - (0.075x^2 + 6x + 7) | 10 = 0.075(121) + 66 + 7 - 0.075(100) - 60 - 7 = 8.25.

Therefore, the approximate change in cost when x is increased by one unit (calculated by differentials) is 8.50 and the actual change in cost is 8.25. This shows that the approximate change in cost calculated by differentials is an accurate estimation of the actual change in cost.

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the slope goes by several names

• average rate of change

• rate of change

• deltaY over deltaX

• Δy over Δx

• rise over run

• gradient

• constant of proportionality

however, is the same cat wearing different costumes.

[tex]\stackrel{ y-intercept }{(\stackrel{x_1}{0}~,~\stackrel{y_1}{4})}\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{12}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{12}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{0}}} \implies \cfrac{ 8 }{ 4 } \implies 2[/tex]

Austin needs to cover 15 square inches of surface area with paint in order to finish the task.

The area of the pennant is the length times the width, which is 3 inches times 5 inches. This gives us 15 square inches of surface area to be covered. To calculate the amount of paint needed, we first need to calculate the area of the pennant. The formula for area is area = length x width. Plugging in the measurements for the base and height of the pennant, we get 15 square inches of surface area. This means that Austin needs to cover 15 square inches of surface area with paint in order to finish the task.

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Answer : a ) Variance = (21 - 6.5)^2/12 = 13.7708, b) 1, 21 <= x, c) Probability = 0.5862, D) Probability = 0.8552

The uniform distribution on the interval (6.5, 21) can be represented as U(6.5, 21).
(a) The mean and variance of a uniform distribution can be calculated using the following formulas:
Mean = (a + b)/2
Variance = (b - a)^2/12
where a and b are the lower and upper bounds of the distribution, respectively.
For the given distribution, a = 6.5 and b = 21.
Therefore, the mean and variance of depth are:
Mean = (6.5 + 21)/2 = 13.75
Variance = (21 - 6.5)^2/12 = 13.7708

(b) The cdf of a uniform distribution can be calculated using the following formula:
F(x) = (x - a)/(b - a)
For the given distribution, F(x) = (x - 6.5)/(21 - 6.5) for 6.5 <= x < 21.
Therefore, the cdf of depth is:
F(x) = {
0, x < 6.5
(x - 6.5)/14.5, 6.5 <= x < 21
1, 21 <= x

(c) The probability that observed depth is at most 10 can be calculated using the cdf:
P(X <= 10) = F(10) = (10 - 6.5)/14.5 = 0.2414
The probability that observed depth is between 10 and 15 can be calculated using the cdf:
P(10 <= X <= 15) = F(15) - F(10) = (15 - 6.5)/14.5 - (10 - 6.5)/14.5 = 0.5862

(d) The standard deviation of a uniform distribution can be calculated using the following formula:
Standard deviation = sqrt(Variance)

For the given distribution, the standard deviation is:
Standard deviation = sqrt(13.7708) = 3.7118
The probability that the observed depth is within 1 standard deviation of the mean value can be calculated using the cdf:
P(13.75 - 3.7118 <= X <= 13.75 + 3.7118) = F(13.75 + 3.7118) - F(13.75 - 3.7118) = (13.75 + 3.7118 - 6.5)/14.5 - (13.75 - 3.7118 - 6.5)/14.5 = 0.5118
The probability that the observed depth is within 2 standard deviations of the mean value can be calculated using the cdf:
P(13.75 - 2*3.7118 <= X <= 13.75 + 2*3.7118) = F(13.75 + 2*3.7118) - F(13.75 - 2*3.7118) = (13.75 + 2*3.7118 - 6.5)/14.5 - (13.75 - 2*3.7118 - 6.5)/14.5 = 0.8552

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The z-values of the sampling distributions are;

A sampling distribution is a probability distribution obtained through the repeated sampling of a specified population.

The z-value for a sampling distribution can be obtained using the formula;

[tex]z = \frac{\bar{x} -\mu}{\frac{\sigma}{\sqrt{N} } }[/tex]

Where;

[tex]\bar{x}[/tex] = The sample mean

μ = The population mean = 156

σ = The population standard deviation = 23

N = The sample size

The z-values for the sampling distributions are therefore;

1) The number of observations selected from the population, is 76, and the sample mean is; [tex]\bar{x}[/tex] = 162, we get the following z-value.

When, N = 76 and [tex]\bar{x}[/tex] = 162

2) The selected observations is 92, and the sample mean is; [tex]\bar{x}[/tex] = 151, we get the following z-value.

When, N = 92 and [tex]\bar{x}[/tex] = 151

3) The number in the random sample, N = 102 and the sample mean is; [tex]\bar{x}[/tex] = 151, we get;

When, N = 102 and [tex]\bar{x}[/tex] = 151

4) The number of observations in the random sample, N = 120 and the sample mean is; [tex]\bar{x}[/tex] = 149, we get;

When, N = 120 and [tex]\bar{x}[/tex] = 149

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In the given functions  [tex]5^x[/tex] function is increasing because 5>1.

Let's first define functions so that we may better comprehend the monotonicity and rising and decreasing functions. In its simplest form, a function is a relationship between input and output in which each input is associated with exactly one outcome.

To better understand monotonicity and rising and decreasing functions, let's first define what a function is. A function, in its most basic form, is a relationship between input and output in which each input is connected to precisely one result.

During the duration of their whole domain, functions might alter, growing, shrink, or stay the same. Functions are both continuous and differentiable in the defined intervals.

Functions can change over the course of their entire domain, either increasing, decreasing, or remaining constant. In the specified intervals, functions are both continuous and differentiable.

We have all the functions that are exponential

So when we shall check all the given function

We observe that we have functions of the form:

f (x) = A[tex]b^x[/tex]

When

b > 1 The function grows

b <1 Function decreases

Hence [tex]5^x[/tex] function is increasing.

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An equation that represents this situation include the following: D. y = -2x + 9.50.

In order to write a linear equation to describe this situation, we would assign variables to the cost of the drinks and the cost of the popcorn respectively, and then translate the word problem into a linear equation as follows:

Since Ben purchased 2 drinks and a bag of popcorn at the movie theater, for a total cost of $9.50, a linear equation that models the situation is given by this mathematical expression:

2x + y = 9.50

By making y the subject of formula, we have:

y = -2x + 9.50

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Answer:

2.50 p + 1.50p

Step-by-step explanation:

if you buy an item x amount of times you would times the two to figure out the total cost of that type of item then add with the other

According to proportionality, the virus will spread at a rate of 12475 students per day.

If five college students with the flu return to an isolated campus of 2500 students, and the rate at which the virus spreads is proportional to both the number of students infected and the number of students not infected, then we can use the following formula to find the rate of spread:

Rate of spread = (number of students infected) x (number of students not infected)

In this case, the number of students infected is 5 and the number of students not infected is 2500 - 5 = 2495. So, the rate of spread is:

Rate of spread = 5 x 2495 = 12475

This means that the virus will spread at a rate of 12475 students per day, assuming that the rate of spread is proportional to both the number of students infected and the number of students not infected.

It is important to note that this is a simplified model and does not take into account other factors that may affect the rate of spread, such as the effectiveness of quarantine measures or the individual immune systems of the students. However, it does give us an idea of how quickly the flu can spread in a population of 2500 students.

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It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

Calculating the time required to fill the bucket:

To solve this problem, use the concept of proportionality to calculate the time required. Use the concept of percentage increase to find the volume of the larger bucket, which was 67% larger than the 3-gallon bucket.

Here we have

A hose fills a 3-gallon bucket in 9 seconds.

The volume of the bucket which is 167% more than 3 gallons

= 167% of 3 gallons = [167/100] × 3 = 5.01 gallons

It took 9 seconds to fill 3 gallons

The time required to fill 5.01 gallons = 9/3 × [5.01]

= 15.03 seconds

Therefore,

It took 15.03 seconds to fill the 67% larger than the 3-gallon bucket

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The marginal revenue when 100 units are sold is approximately $17.12. Selling one additional unit at this point would yield approximately $17.12 in additional revenue.

To find the marginal revenue, we first need to find the derivative of the total revenue function with respect to x, which is the definition of marginal revenue:

R(x) = 2200x/(ln(9x+9))

Using the quotient rule, we get:

R'(x) = (2200(ln(9x+9)) - 2200x(1/(9x+9))(1/(9x+9)))/(ln(9x+9))^2

Simplifying this expression, we get:

R'(x) = 2200(9x)/(9x+9)^2ln(9x+9)^2

Substituting x=100, we get:

R'(100) = 2200(9(100))/((9(100)+9)^2ln(9(100)+9)^2 = $9.77 (rounded to the nearest cent).

Interpretation: The marginal revenue when 100 units are sold is $9.77. This means that selling one additional unit of the product will increase the total revenue by approximately $9.77.

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Complete question:

The total revenue, in dollars, from the sale of x units of a product is given by R(x)=2200x/(ln(9x+9)). Find the marginal revenue when 100 units are sold. (Round your answer to the nearest cent.) Interpret your result.

Therefore , the solution of the given problem of probability comes out to be -y^(β-1)/[(β-1)Β(1, β)] .

The primary goal of the structures in the style known as parameters is the determination of the likelihood that a claim is accurate or that a specific event will occur. Any number between 0 and 1, at which 1 typically denotes certainty but also 0 typically denotes potential, can be used to symbolise chance. A probability diagram shows the chance that a specific event will occur.

Here,

We are aware that X's PDF is provided by:

If x is between 0 and 1 and 0 otherwise, f(x) Equals 1/B

where represents the size factor.

The formula for Yn's cumulative distribution function (CDF) is

=> F(y) = P(Yn ≤ y) = [P(Xi > y)]ⁿ = [1 - P(Xi ≤ y)]ⁿ

Using the CDF of the beta distribution, we have:

=> F(y) = [1 - Β(1, β; y)]ⁿ

We can approximate Yn by a normal distribution with mean and variance given by the following formulas using the continuity adjustment and central limit theorem:

=> E(Yn) = Β(2, β; 1)/Β(1, β) and Var(Yn) = E(Yn) - [Β(1, β; 1)/Β(1, β)]²

Therefore, we have:

=> (Yn - E(Yn))/sqrt(Var(Yn)) → N(0,1)

With the formulas for E(Yn) and Var(Yn) substituted, we obtain:

=> (Yn - Β(2, β; 1)/Β(1, β))/sqrt[Β(2, β; 1)/Β(1, β) - [Β(1, β; 1)/Β(1, β)]²] → N(0,1)

We need to work out the solution to determine b:

where is the CDF's usual standard value.

After applying the limit and taking the logarithm of both sides, we obtain:

=> F(y) = lim n log[n] = lim n n log

=> [1 - B(1, β; y)] = lim n -n (y, n)/(1, n)

L'Hopital's law gives us:

=> lim n -d/dy [n -(1, y)/n -(1, y)] = lim nn y(-1), ((1, )) ^2Β(2, β; y)

=> -y^(β-1)/[(β-1)Β(1, β)]

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Based on the information provided in the question, The expected value of the sample mean is approximately 497.92 million dollars.

To calculate the expected value of the sample mean, first calculate the mean of the population ($10.82 million) and then multiply it by the sample size (46).
Mean of Population * Sample Size = Expected Value of Sample Mean
$10.82 million * 46 = $497.92 million
Expected Value of Sample Mean = $497.92 million

A sample mean is a statistical measurement that shows the mean value of the data in a sample. It is determined by summing all of the values in the sample and dividing the total by the number of observations.

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Answer:

y = 2/3x + 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

We know

m = 2/3

Y-intercept is located at (0, 6)

So, our equation is y = 2/3x + 6

Option #1: point-slope form: y - y1 = m ( x - x1 )

y - 4 = 2/3 ( x - (-3) )     or     y - 4 = 2/3 ( x + 3 )

Option #2: slope-intercept form: y = mx + b

Take the point-slope and solve for y:

     y - 4 = 2/3 ( x + 3 )

     y - 4 = 2/3 x + 2

          y = 2/3 x + 6  

Answer:

plot it on -4

Step-by-step explanation:

Answer: -3

Step-by-step explanation:

The fixed charge for a taxi ride is Rs. 5 and the charge per km is Rs. 7.

Given that the charge for a 12 km ride is Rs. 89 and for a 20 km ride is Rs. 145, we can form two equations in terms of the fixed charge (c) and the charge per km (x).

Solving these equations, we get c = 5 and x = 7. Therefore, the fixed charge for a taxi ride is Rs. 5 and the charge per km is Rs. 7. To find the charge for a 30 km ride, we can substitute these values in the formula

c + 7x, which gives us 5 + 7x30 = Rs. 215.

89 = c + 12x ---------------(1)

145 = c + 20x -------------(2)

Solving equations 1 and 2, we get,

8x = 56

x = 7.

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Complete Question:

The car hire charges in a city comprised of a fixed charge together with the charge for the distance covered. For a journey of 12 km, the charge paid is Rs 89 and for a journey of 20 km, the charge paid is Rs 145. What will a person have to pay for traveling a distance of 30 km?

By speed fοrmula, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

Speed is defined as the distance travelled by an οbject in a given amοunt οf time. Speed is a scalar quantity, meaning that it has magnitude but nο directiοn.

Mathematically, speed is calculated as fοllοws:

speed = distance/time

Where "distance" is the distance travelled by the οbject, and "time" is the time it takes fοr the οbject tο travel that distance.

We can use the fοrmula:

time = distance/speed

where distance is the distance frοm the star tο Earth, and speed is the speed οf light.

Putting the values, we get:

time = (3.9 x 10¹⁴ km) / (3.0 x 10⁵km/s)

Simplifying, we can divide the distances and divide the pοwers οf ten:

time = 1.3 x 10⁹ s

Therefοre, light frοm the star takes abοut 1.3 x 10⁹secοnds tο reach Earth.

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The force exerted by the brick on the window is equal in magnitude but

opposite in direction to the force exerted by the window on the brick.

When a brick hits a window and smashes it, there are two forces

involved: the force exerted by the brick on the window and the force

exerted by the window on the brick.

According to Newton's third law of motion, for every action, there is an

equal and opposite reaction.

The magnitude of the forces involved depends on several factors,

including the mass of the brick, its velocity, the angle of incidence, and

the strength of the window. The force exerted by the brick on the

window will be the impact force, which is the force applied over a short

period of time during the collision.

The impact force will depend on the momentum of the brick, which is

the product of its mass and velocity.

It's not possible to say which force is larger because the two forces are

equal in magnitude but opposite in direction, according to Newton's third

law of motion.

The strength of the window will also play a role, as a stronger window

will be able to resist a higher impact force before breaking.

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The area of the circle which contains the 45° sector as required to be determined is; 345.4 cm².

As evident from the task content; A 45° sector in a circle has an area of 13.75π cm².

Hence, since the sector is 45° and the sum of angles in the circle would be 360°; it follows that the area of the circle is; 360/45 = 8 times the area of the sector.

Area of circle = 8 × 13.75π

= 8 × 13.75 × 3.14

= 345.4 cm².

Ultimately, the area of the circle is; 345.4 cm².

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