Find the coordinates of the circumcenter of the triangle with the given vertices. (-7,-1) (-1,-1) (-7,-9)

The initial investment was approximately $2,603.88, which is option (b).

Probability is a measure of the likelihood of an event occurring.

We can use the formula for compound interest:

A = [tex]P(1+r/n)^{nt}[/tex]

where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, we know that the final amount A is $3,820, the annual interest rate r is 5.5% (or 0.055 as a decimal), the interest is compounded 6 times a year (n = 6), and the time period is 7 years.

So we can rearrange the formula to solve for P:

P = A/[tex]P(1+r/n)^{nt}[/tex]

Plugging in the values, we get:

P = 3820 / [tex](1+0.055/6)^{6*7}[/tex]

P ≈ $2,603.88

Therefore, the initial investment was approximately $2,603.88, which is option (b).

To learn more about compound interest from the given link:

https://brainly.com/question/14295570

#SPJ1

Step-by-step explanation:

a) Since the temperature of the oven is decreasing by a percentage of its current temperature each minute, the function that best represents this situation is an exponential function.

b) Let T be the temperature of the oven in degrees Fahrenheit at time x minutes after it was turned off. The initial temperature of the oven was 450° F, and the temperature decreases by 10% each minute. This can be expressed as:

T = 450(0.9)^x

Therefore, the function that models the situation is:

f(x) = 450(0.9)^x

where f(x) is the temperature of the oven in degrees Fahrenheit x minutes after it was turned off.

Answer:

Step-by-step explanation:

To find:-

Answer:-

We are here given that the right angle is made up of two angles viz 8z° and (3z+2)° .

As we know that the measure of a right angle is 90° , so the sum of the two angles would also be 90° . Hence here ,

→ 8z + 3z + 2 = 90

→ 11z + 2 = 90

→ 11z = 90-2

→ 11z = 88

→ z = 88/11

→ z = 8

Hence the value of z is 8 .

Using the arithmetic sequence formula we know that the 14 term of the given sequence is 41.

An arithmetic series is one that has the following formula: a, a + d, a + 2d, a + 3d, a + 4d,...

The common difference of the sequence is d, and the number an is the first term.

An arithmetic sequence's nth term is determined by the formula a = a + (n - 1)d.

So, we have the sequence:

2, 5, 8, 11, 14

Common difference = 5 - 2 = 3

Then, the formual is:

aₙ = a + (n - 1)d

Then, insert values:

aₙ = a + (n - 1)d

a₁₄ = 2 + (14 - 1)3
a₁₄ = 2 + (13)3

a₁₄ = 2 + 39

a₁₄ = 41

Therefore, using the arithmetic sequence formula we know that the 14 term of the given sequence is 41.

Know more about an arithmetic sequence here:

https://brainly.com/question/6561461

#SPJ1

Answer:

It will take Jaime 36 days to run 96 miles.

Step-by-step explanation:

The formula for rate is:

[tex]\boxed{\sf Rate=\dfrac{Distance}{Time}}[/tex]

Therefore, Jaime's run rate is:

[tex]\implies \sf Rate=\dfrac{8\;miles}{3\;days}=\dfrac{8}{3} \;miles\;per\;day[/tex]

Rearrange the rate formula to isolate time:

[tex]\implies \sf Time=\dfrac{Distance}{Rate}[/tex]

To find how long it will take for Jaime to run 96 miles, substitute the distance and rate into the formula and solve for time:

[tex]\implies \sf Time=\dfrac{96\;miles}{\frac{8 \;miles}{3\;days}}[/tex]

[tex]\implies \sf Time=96\;miles \times \dfrac{3\;days}{8\;miles}[/tex]

[tex]\implies \sf Time= \dfrac{288}{8}\;days[/tex]

[tex]\implies \sf Time= 36\;days[/tex]

Therefore, it will take Jaime 36 days to run 96 miles.

To win the game, your team needs to score more than   [tex]35[/tex] points, which means: 3f + 7t > 35 three possible game-winning combinations are:

[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]

[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]

[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]

Each of these combinations would result in your team scoring more than 35 points and winning the game.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=).

For example, the argument [tex]"2x + 3 = 9"[/tex]  asserts that the phrase [tex]"2x + 3"[/tex]  equals the number "9." The purpose of equation solving is to determine the value or values of the variable(s) that allows the equation to be true.

Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation. [tex]"x2 + 2x - 3 = 0."[/tex]    Lines are utilised in many different areas of mathematics, such as  algebra, calculus, and geometry.

Let's let f be the number of field goals scored by your team and t be the number of touchdowns scored by your team.

a) To win the game, your team needs to score more than 35 points, which means:

3f + 7t > 35

We can simplify this inequality by dividing both sides by 1:

3f + 7t/1 > 35/1

3f + 7t > 35

b) Now, we need to find possible values for f and t that make this inequality true. Since we are looking for positive integer values for f and t, we can start by testing different values for t and solving for f:

If t = 5, then 3f + 7(5) > 35, so 3f > 0 and f > 0. Possible solutions are f = 1, f = 2, f = 3, and so on.

If t = 6, then 3f + 7(6) > 35, so 3f > 7 and f > 2. Possible solutions are f = 3, f = 4, f = 5, and so on.

If t = 7, then 3f + 7(7) > 35, so 3f > 14 and f > 4. Possible solutions are f = 5, f = 6, f = 7, and so on.

c) So, three possible game-winning combinations are:

[tex]t = 5, f = 11: 3(11) + 7(5) = 63[/tex]

[tex]t = 6, f = 8: 3(8) + 7(6) = 62[/tex]

[tex]t = 7, f = 5: 3(5) + 7(7) = 56[/tex]

Each of these combinations would result in your team scoring more than 35 points and winning the game.

Learn more about equation here:

brainly.com/question/649785

#SPJ1

Oscar Corporation can effectively allocate its 2000 labor hours to build Inventory for its three products, ensuring efficient production and maximizing profits

Based on the information provided, let's assume that the three products produced by Oscar Corporation are Product A, Product B, and Product C.

1. Determine the labor hours required for each product.
First, we need to know the labor hours required to produce one unit of each product. This information is essential in order to allocate the available labor hours effectively.

Calculate the labor efficiency for each product.
Divide the total number of units produced by the labor hours required for each product. This will help us determine the most efficient product in terms of labor utilization.

Allocate the available labor hours.
Using the labor efficiency data, allocate the 2000 available labor hours among the three products. Prioritize the most efficient product to maximize production.

Calculate the number of units produced for each product.
Multiply the allocated labor hours for each product by its respective labor efficiency to determine the number of units that can be produced.

Evaluate and adjust if necessary.
Review the results and adjust the allocation of labor hours if needed to meet the company's goals or demand for each product.

By following these steps, Oscar Corporation can effectively allocate its 2000 labor hours to build inventory for its three products, ensuring efficient production and maximizing profits.

To Learn More About Inventory

https://brainly.com/question/27846648

#SPJ11

The population will exceed 2627 after approximately 6.08 units of time.

A lοgarithm is a mathematical functiοn that tells us what expοnent is needed tο prοduce a given number, when that number is expressed as a pοwer οf a fixed base. In οther wοrds, lοgarithms tell us hοw many times we need tο multiply the base by itself tο get the desired number.

To solve for t when the population exceeds 2627, we can set the equation equal to 2627 and solve for t:

p(t) = 1000[tex]e^{(0.21t)}[/tex] = 2627

Dividing both sides by 1000, we get:

[tex]e^{(0.21t)}[/tex] = 2.627

Taking the natural logarithm of both sides, we get:

0.21t = ln(2.627)

Solving for t, we get: t = ln(2.627)/0.21 ≈ 6.08

Therefore, the population will exceed 2627 after approximately 6.08 units of time.

Learn more about exponential growth on:

brainly.com/question/12490064

#SPJ1

2 1/6 years in months is 26/1 as a fraction.

Answer:26 months or 26/1 months

 the income tax payable on a salary of Birr 5200 is Birr 320.

In Ethiopia, income tax is calculated based on a progressive tax system where the tax rate increases as the taxable income increases. The formula for calculating income tax on monthly salary is as follows:

Taxable income = Gross monthly salary - Deductions

Tax payable = Tax rate * (Taxable income - Tax threshold) - Allowances

Where:

1. Gross monthly salary: Total salary before any deductions.

2. Deductions: Includes mandatory deductions such as employee social security contributions, pension contributions, and other authorized deductions.

3. Taxable income: Gross monthly salary minus deductions.

4. Tax rate: The percentage of tax applicable to the taxable income based on the tax bracket.

5. Tax threshold: The minimum amount of taxable income before tax is applicable.

6. Allowances: Includes authorized tax deductions such as dependant's allowance and other authorized allowances.

To calculate the income tax on a salary of Birr 5200, we need to determine the taxable income first. Let's assume that the gross monthly salary is Birr 5200, and there are no deductions.

Taxable income = Birr 5200 - 0 = Birr 5200

Next, we need to determine the tax rate applicable to this taxable income based on the tax bracket. For the taxable income range of Birr 5251 to 7800, the tax rate is 10%. Therefore, the tax rate applicable to Birr 5200 is 10%.

Tax rate = 10%

Now, we need to determine the tax threshold and the allowances applicable to this taxable income. Let's assume that the tax threshold is Birr 2000, and there are no allowances.

Tax threshold = Birr 2000

Allowances = 0

Using the formula mentioned earlier, we can calculate the income tax payable as follows:

Tax payable = 10% * (Birr 5200 - Birr 2000) - 0

Tax payable = Birr 320

Therefore, the income tax payable on a salary of Birr 5200 is Birr 320.

To derive the formula to calculate income tax on Birr x, we can use the same formula mentioned earlier. We can express the formula in terms of x as follows:

Taxable income = x - Deductions

Tax payable = Tax rate * (Taxable income - Tax threshold) - Allowances

Where:

1. x: Gross monthly salary.

2. Deductions: Includes mandatory deductions such as employee social security contributions, pension contributions, and other authorized deductions.

3. Taxable income: Gross monthly salary minus deductions.

4. Tax rate: The percentage of tax applicable to the taxable income based on the tax bracket.

5. Tax threshold: The minimum amount of taxable income before tax is applicable.

6. Allowances: Includes authorized tax deductions such as dependant's allowance and other authorized allowances.

We can use this formula to calculate the income tax payable on any salary falling within the Birr 5251 to 7800 taxable income range.

In conclusion, income tax in Ethiopia is calculated based on a progressive tax system, where the tax rate increases as the taxable income increases. To calculate income tax on a salary of Birr 5200, we need to determine the taxable income, tax rate, tax threshold, and allowances applicable to that salary. We can use the same formula to calculate income tax on any salary within the Birr 5251 to 7800 taxable income range.

To know more about income tax payable  click here:

brainly.com/question/17111566

#SPJ1

1. The Similarity between AD and AB is that AD is half the length of AB.

2. The areas of triangles ACD and BDC are equal.

3. We can say that if AC is the longest side, then CB is the shortest side

4. False, The relationship between AD and AB is that AD is half the length of AB.

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

1) Since D is the midpoint of AB, we know that AD and DB have the same length. Therefore, we can say that:

AD = DB

Substituting AB for AD + DB, we can simplify to:

AB = AD + AD

or

AB = 2AD

So, the relationship between AD and AB is that AD is half the length of AB.

2) The areas of triangles ACD and BDC are equal, and we can write:

Area of ACD = (1/2) * AC * AD

Area of BDC = (1/2) * BC * DB

Since AD = DB, we can substitute and get:

Area of BDC = (1/2) * BC * AD

So, we can see that the areas of ACD and BDC are equal, and their bases AD and DB have the same length. Therefore, triangles ACD and BDC are equal in area and shape (they are congruent).

3) we can say that if AC is the longest side, then CB is the shortest side

4) False,

The relationship between AD and AB is that AD is half the length of AB.

Learn more about Polygons here

brainly.com/question/1051944

#SPJ1

The answer of the given question based on the Angular speed is (a) the angular speed of a point on Mars' equator is π/2 radians per day. (b) the linear speed of a point on the equator of Mars is approximately 889.33 miles per day.

Linear speed, also known as tangential speed, is the distance traveled by an object in a straight line per unit of time. It is the speed at which an object is moving along its path, tangent to the path at any given point. Linear speed is calculated by dividing the distance traveled by the time taken to travel that distance. The units of linear speed are typically expressed in meters per second (m/s), miles per hour (mph), or kilometers per hour (km/h), depending on the system of measurement used.

(a) The angular speed of a point on Mars' equator is the angle (in radians) that a point on the equator sweeps out as Mars rotates on its axis. Since Mars completes one rotation every 24 hours, the angular speed is:

angular speed =(2πradians)/ (24 hours)= π/12radians per hour

To find the angular speed in radians per day, we need to multiply by the number of hours in a day:

angular speed = (π/12 radians per hour) * (24 hours per day) = π/2 radians per day

Therefore, the angular speed of a point on Mars' equator is π/2 radians per day.

(b) The linear speed of a point on the equator is the distance traveled by a point on the equator in a certain amount of time. The distance traveled by a point on the equator in one rotation is equal to the circumference of the circle with a diameter of miles, which is:

C = πd = π(6794) ≈ 21343.98 miles

Since Mars rotates once every 24 hours, a point on the equator travels the circumference of the circle in 24 hours. Therefore, the linear speed of a point on the equator in miles per day is:

v = C/24 ≈ 889.33 miles/day

So the linear speed of a point on the equator of Mars is approximately 889.33 miles per day.

To know more about Angular speed visit:

https://brainly.com/question/31064524

#SPJ1

The volume of wax is required to make 1 candle is 22.92 cu. in.

A cone is a tri solid geometric object with an apex that is pointed at the top and a circular base. A cone has a vertex and one face.

Given data:

Let the radius of the cone be 'r'.

circumference c = 2*π*r

c = 2*π*r

12 =  2*3.14*r

r = 6/3.14

r = 1.91

Volume of cone V = 1/3 * π * r² *h

Put the values:

V = 1/3 * 3.14 * 1.91² *6

V = 22.92 cu. in.

Know more about the shape of cone

https://brainly.com/question/808471

#SPJ1

Correct question:

A company makes candles in the shape of the cones. Their best selling candles has a height of 6 inches and the circumference of 12 inches What is the volume  of wax is needed to make 1 candle.

The  required answers to fill in the blank is Numeracy or mathematical.

Numeracy or mathematical skill is the ability to understand and use numbers to solve real-world problems. In personal and professional life, math skills are essential for managing finances, creating budgets, analyzing data, and making informed decisions.

By using math to plan and organize their finances, individuals can effectively manage their income, expenses, and savings. This skill also helps in making decisions related to investments, loans, and other financial products.

Developing math skills can lead to better financial stability, as well as improved problem-solving and decision-making abilities in various aspects of life.

Thus, required answers to fill in the blank is Numeracy or mathematical.

To know more about Numbers visit:

brainly.com/question/28210925

#SPJ1

The best height he can jump is 2.5 meters. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

It is believed that the four fundamental operations, often known as "arithmetic operations," adequately explain all real numbers. Division, multiplication, addition, and subtraction are the mathematical operations that come before quotient, product, sum, and difference.

We are given that Ivan Ukhov  jumps 2.4 metres which is 4% lower than the best height he can jump.

Let the best height be 'x'.

So, from the above information, we get

⇒ x - 0.04x = 2.4

⇒ 0.96x = 2.4                     (Using subtraction)

⇒ x = 2.5                             (Using division)  

Hence, the best height he can jump is 2.5 meters.

Learn more about arithmetic operations from the given link

brainly.com/question/30283549

#SPJ9

Using the point-slope form of the equation of a line. the x-intercept of the line is [tex]-2.5[/tex].

To find the x-intercept of the line, we need to find the point where the line intersects the x-axis. We know that the y-coordinate of this point is zero, because it is on the x-axis. Let's call the x-coordinate of this point "x".

We also know that the line passes through the point (-2.5,0), because it is 2.5 units to the left of the origin. Using the point-slope form of the equation of a line, we can write the equation of the line as:

[tex]y - 0 = m(x - (-2.5))[/tex]

where m is the slope of the line. To find the slope, we can use the fact that the line passes through the point  [tex](0,1)[/tex] and [tex](-2.5,0)[/tex]:

[tex]m = (1 - 0) / (0 - (-2.5)) = 1 / 2.5 = 0.4[/tex]

Substituting this into the equation of the line, we get:

[tex]y = 0.4(x + 2.5)[/tex]

To find the x-intercept, we set y to zero and solve for x:

[tex]0 = 0.4(x + 2.5)[/tex]

[tex]-2.5 = x[/tex]

Therefore, the x-intercept of the line is  [tex]-2.5.[/tex]

Learn more about intercept here:

https://brainly.com/question/14180189

#SPJ1

The vertical distance between two points is just the distance between the two y coordinates. Distance is positive.

|-12|+17 = 29 units

Answer: the answer is 29 trust me

Step-by-step explanation: don't have time for explanation sorry

Answer:

VX=33

Step-by-step explanation:

VW=2z-1

WX=z+3

XV=3z

VW=a

WX=b

XV=c

a+b+c=2z-1+z+3+3z

Perimeter=6z+2

P=68

68=6z+2

66=6z

z=11

VX=3x11

VX=33

Answer:

The file is attached below.

I disagree with Meghan.

Step-by-step explanation:

Hello!

The line plot is attached below.

I disagree with Meghan as the least amount of time someone recited the alphabet is 4 seconds and the greatest is 7.5 seconds.

The difference between these two numbers would be 3.5 seconds, which is not the same as 4 seconds.

Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.

Significant digits, also known as significant figures or sig figs, are the digits in a number that are considered to be accurate or meaningful. They represent the precision or reliability of a measurement or calculation.

In a number, all digits except for leading zeros are considered to be significant. For example, in the number 0.00456, there are three significant digits (4, 5, and 6), while the zeros before the 4 are not significant.

The rules for determining the number of significant digits in a number are:

All non-zero digits are significant.

Zeros between non-zero digits are significant.

Leading zeros are not significant.

To find the expected CO₂ level in the atmosphere by the end of 2030, we need to calculate the total increase in CO₂ levels from 2012 to 2030 and then add it to the 2012 CO₂ level of 396 ppm.

To calculate the total increase in CO₂ levels, we can use the following formula:

Total increase in CO₂ levels = rate of increase × time

where the rate of increase is 2.10 ppm per year and the time is the number of years from 2012 to 2030, which is 18 years.

Total increase in CO₂ levels = 2.10 ppm/year × 18 years = 37.8 ppm

Therefore, the expected CO₂ level in the atmosphere by the end of 2030 would be:

Expected CO₂ level = 2012 CO₂ level + total increase in CO₂ levels

Expected CO₂ level = 396 ppm + 37.8 ppm

Expected CO₂ level = 433.8 ppm

Rounding to the same number of significant digits as the measurement with the least number of significant digits (which is "350 ppm"), the expected CO₂ level by the end of 2030 would be 430 ppm.

To know more about rate visit:

https://brainly.com/question/31103012

#SPJ1

As 80 percentage of 25 classmates is equal to 20. Krysti should have ordered 20 small t-shirts for her 25 classmates

Error is when a mistake is made while solving a mathematical problem.

Krysti's error in finding the number of small t-shirts is that she forgot to multiply the percentage by the total number of classmates.

If Krysti wanted to find the number of small t-shirts she should have ordered, she should have multiplied

80% * 25.

=0.8 * 25

= 20.

To explain it in another way, Krysti could have also 100/25 and then 80 divided by the answer that is 4. This would also give the same result of 20.

Krysti's error was that she did not correctly use percentages to find the number of small t-shirts she should have ordered.

For more questions related to Error

https://brainly.com/question/11472659

#SPJ9

Answer:

Step-by-step explanation:

If the equation is changed from y = x^2 to y = (1/4)x^2, the parabola will become wider.

The rate per hour for the ferris wheel is 144 people per hour.

Your pay for each hour of labour is expressed as an hourly rate. You might need to estimate your income for other applications or modify your personal budget after comparing the hourly and salaried pay rates.

The ferris wheel can accommodate 60 people in 25 minutes.

To find out how many people could ride the ferris wheel in 4 hours, we need to convert 4 hours to minutes, since the given rate is in minutes.

1 hour = 60 minutes

4 hours = 4 x 60 minutes = 240 minutes

So, in 4 hours, the ferris wheel could accommodate 240/25 = 9.6 (rounded to the nearest whole number) cycles of 60 people.

The total number of people that could ride the ferris wheel in 4 hours would be 9.6 x 60 = 576 people.

Now, to find the rate per hour, we divide the total number of people (576) by the number of hours (4):

Rate per hour = Total number of people / Number of hours

Rate per hour = 576 / 4 = 144 people/hour

Therefore, the rate per hour for the ferris wheel is 144 people per hour.

Learn more about rate per hour on:

https://brainly.com/question/30400778

#SPJ9

Answer:

a = 8

Step-by-step explanation:

4 x 2 = 8

8 x 2 = 16

Helping in the name of Jesus.

The required perimeter of the given triangle is 23 units respectively.

Triangles are closed, two-dimensional shapes with three sides, three angles, and three vertices.

A triangle is part of a polygon. A triangle is a polygonal form with three sides.

These points meet at the vertex, which forms an internal angle at the junction of two triangle sides.

Every triangle has three sides, three vertices, and three internal angles.

So, to get the perimeter of the triangle, count the unit as follows:

7 units + 7 units + 9 units

To find the triangle, we need to add the length of the 3 sides as follows:

7 + 7 + 9 = 23 units

Therefore, the required perimeter of the given triangle is 23 units respectively.

Know more about triangles here:

https://brainly.com/question/1058720

#SPJ1

The function is decreasing for x < -6, or over the interval (–∞, –6).

What is a graph?

In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines). Graphs are often used to represent relationships between objects or to model complex systems.

The derivative of the function y = |x + 6| is equal to -1 for x < -6 and 1 for x > -6. At x = -6, the derivative is undefined, but the function is not decreasing there, so we don't need to consider that point.

Thus, the function is decreasing for x < -6, or over the interval (–∞, –6). Therefore, the answer is A. (–∞, –6).

To learn more about graph from the given link:

brainly.com/question/17267403

#SPJ1

Answer:

I think its 75 degrees and brainliest would be greatly appreciated

The limit of the determinant as [tex]t[/tex] approaches 0 is [tex]-\infty[/tex].

To evaluate this limit, we can use the fact that the determinant is a linear function of each row, and that the limit of a sum is the sum of the limits. Therefore, we can compute the limit of each row separately.

Starting with the first row, we have:

[tex]\lim_{t\to 0} \int_0^t \frac{u}{\sinh(u)} du

= \lim_{t\to 0} \frac{\int_0^t \frac{u}{\sinh(u)} du}{t} \cdot t

= \lim_{t\to 0} \frac{\frac{t}{\sinh(t)} - 1}{t} \cdot t

= \lim_{t\to 0} \frac{1-\sinh(t)}{t\sinh(t)} = 1[/tex]

[tex]\lim_{t\to 0} \cos(t)

= 1[/tex]

[tex]\lim_{t\to 0} \sum_{n=1}^{\infty} \frac{1}{n+t+i}

= \sum_{n=1}^{\infty} \lim_{t\to 0} \frac{1}{n+t+i}

= \sum_{n=1}^{\infty} \frac{1}{n+i}

= \psi(i+1) \approx 0.643 + 0.41i[/tex]

where [tex]\psi(z)[/tex] is the digamma function.

Therefore, the limit of the first row is [tex]1 \cdot 1 \cdot \psi(i+1) = \psi(i+1)[/tex].

Moving on to the second row, we have:

[tex]\lim_{t\to 0} \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right)

= \lim_{t\to 0} \frac{e^t}{t} - \lim_{t\to 0} \frac{e^t}{t^2}

= 1 - \infty = -\infty[/tex]

[tex]\lim_{t\to 0} \binom{5}{2} t^2

= 0[/tex]

[tex]\lim_{t\to 0} \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right)

= \prod_{n=1}^4 \lim_{t\to 0} \left(\sqrt{1+nt} - 1\right)

= \prod_{n=1}^4 \sqrt{1+n} - 1

= 4\sqrt{2} - 5[/tex]

Therefore, the limit of the second row is [tex]-\infty \cdot 0 \cdot (4\sqrt{2} - 5) = 0[/tex].

Finally, for the third row, we have:

[tex]\lim_{t\to 0} i\binom{5}{3} t^3 \sin(2t) = 0[/tex]

[tex]\lim_{t\to 0} \sum_{n=1}^{5} n^2 e^{int}

= \sum_{n=1}^{5} n^2 \lim_{t\to 0} e^{int}

= \sum_{n=1}^{5} n^2

= 55[/tex]

[tex]\lim_{t\to 0} \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) = 28[/tex]

Therefore, the limit of the third row is [tex]0 \cdot 55 \cdot 28 = 0[/tex].

Putting everything together, we get:

[tex]\lim_{t\to 0} \det\left(\begin{bmatrix} \displaystyle \int_0^t \frac{u}{\sinh(u)} du & \cos(t) & \displaystyle \sum_{n=1}^{\infty} \frac{1}{n+t+i} \\ \displaystyle \frac{d}{dt} \left(e^t \ln \left(\frac{1}{t}\right) \right)

& \binom{5}{2} t^2 & \displaystyle \prod_{n=1}^4 \left(\sqrt{1+nt} - 1\right) \\ i\binom{5}{3} t^3 \sin(2t) & \displaystyle \sum_{n=1}^{5} n^2 e^{int} & \binom{8}{2} t^2 + i\binom{5}{2} t^3 \cos(3t) \end{bmatrix}\right) = \det\left(\begin{bmatrix} \psi(i+1) & 1 & 0 \\ -\infty & 0 & 4\sqrt{2}-5 \\ 0 & 55 & 28 \end{bmatrix}\right) = -\infty[/tex]

To learn more about : determinant

https://brainly.com/question/24254106

#SPJ11