The cost of putting on a play is $500 for the theater rental, $500 for the actors, and $750 for set decorations and costumes. If tickets are sold for $25 each, how many tickets need to be sold to reach the break-even point?

Answers

Answer 1

Answer:

The total cost of putting on the play is $500 for theater rental + $500 for actors + $750 for set decorations and costumes = $1750.

To reach the break-even point, the revenue from ticket sales needs to equal the total cost, so $1750 = $25 x (number of tickets sold).

Solving for the number of tickets sold, we can divide both sides by $25: $1750 / $25 = (number of tickets sold).

This gives us: 70 = number of tickets sold.

Therefore, Mr. Curry needs to sell 70 tickets to reach the break-even point.

Step-by-step explanation:


Related Questions

Range and domain ??
{(-3,0), (3,-7), (-1,-6), (-1,-5), (-5, -1)}

Answers

Answer:

Domain = -3, 3, -1, 15
Range = 0, -7, -6, -5, -1

Which of the following inequalities does the graph represent?


Number line -5 to +5 in single-integer increments - assessment graphic

Responses

–3 < t < 4

–3 < t < 4

t < –3 or t > 4

t < –3 or t > 4

–3 ≤ t ≤ 4

–3 ≤ t ≤ 4

t ≤ –3 or t ≥ 4

Answers

The statement t < –3 or t > 4 is the inequality that the graph represents.

What is inequality?

Inequality in mathematics is when two values are not equal. It can be expressed using symbols such as >, <, ≥ and ≤. This can be used to compare two values, express a range of values, or indicate that one value is greater or less than another. Inequality is a powerful tool for solving mathematical problems, as it can be used to deduce relationships between different variables.

The graph represents the inequality t < –3 or t > 4. This can be seen by the number line, which has the integers -5 to 5 incrementally marked, with the bars extending beyond the -3 and 4 markers. This indicates that the value of t is less than -3 or greater than 4, but not equal to either of these values. Therefore, the statement t < –3 or t > 4 is the inequality that the graph represents.

To know more about inequality click-
https://brainly.com/question/24372553
#SPJ1

Solve the following system of equations:
-2x + 3y = 7
y = 3x + 7
(-5, -1)
(-2, 1)
(-1,4)
(1,3)

Answers

The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.

What is the solution to the equation?

The possible value of the variables that satisfy the equation which is known as the solution of the equation.

The equations are given below.

-2x + 3y = 7            ...1

y = 3x + 7               ...2

From equations 1 and 2, then we have

- 2x + 3(3x + 7) = 7

- 2x + 9x + 21 = 7

7x = - 14

x = - 2

Then the value of 'y' is given as,

y = 3(-2) + 7

y = - 6 + 7

y = 1

The solution of the equations 3y - 2x = 7 and y = 3x + 7 will be (-2, 1). Then the correct option is B.

More about the solution of the equation link is given below.

https://brainly.com/question/22613204

#SPJ9

ting is making a circular garden with a radius of 6 feet.How far across is the garden at its widest point?What is the length of edging material to the nearest hundredth needed to enclose the garden?Use 3.14

Answers

The length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

Describe Circumference of circle?

The circumference of a circle is the distance around its outer boundary, also known as its perimeter. It is one of the fundamental properties of a circle, along with its radius and diameter.

Since the garden is circular, its widest point is its diameter, which is twice the radius. Therefore, the widest point of the garden is 12 feet across.

To find the length of the edging material needed to enclose the garden, we need to find the circumference of the circle. The formula for the circumference of a circle is C = 2πr, where r is the radius and π (pi) is approximately 3.14. Substituting,  r = 6 into the formula, we get:

C = 2π(6)

C = 12π

To approximate this value using 3.14, we can substitute π = 3.14 and get:

C ≈ 12(3.14)

C ≈ 37.68

Therefore, the length of edging material needed to enclose the garden is approximately 37.68 feet to the nearest hundredth.

To know more about radius visit:

https://brainly.com/question/1296843

#SPJ1

What's the value x?
The value of x is often used in algebra, meaning a value that isn't known yet. It is called a variable, or unknown

Answers

The value x is used often in algebra to specify an unknown variable.

What is Variable?

Variables are often alphabets or letters used to represent an unknown number or value.

It is called a variable because it may change it's value according to the value of the others.

x is a variable which is commonly used to solve problems in algebra.

It represents the unknown variable.

We have to do certain operations to find the value of y.

Consider the equation, x + 5 = 13.

Here x is a unknown variable.

We can find the value of x as x = 13 - 5 = 8

Hence x is commonly used to represent an unknown variable.

Learn more about Variables here :

https://brainly.com/question/17344045

#SPJ9

pleas answer!!!!!!!!!!
why do i have to put 29 characters in the box

Answers

The rate of decrease is 89%.

The function shows exponential decay.

What is exponential decay?

An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.

The exponential decay function:

Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.

Given:

An exponential function,

y = 8600(0.11)ˣ.

When we put x = 0,

we get,

y = 8600

And when we put x = 1

we get,

y = 946

So, 1 - r = 0.11

Rate of decrease, r = 0.89

Therefore, the function shows exponential decay.

To learn more about exponential decay;

https://brainly.com/question/14344314

#SPJ1

A grocery store sells a bag of 3 oranges for $0.90. How much does one orange cost?

Answers

Answer:

$0.30

Step-by-step explanation:

They tell you that a bag of 3 is $0.90. 3 can go into 90 a total of 30 times. 0.90/3 is 0.30

Answer:

first take a total price and then divided by the total bags to get price of each

Step-by-step explanation:

0.90÷3=0.30

1. b^3/b^0
2. a•x^5/ a•x^4
3. a • b²•a²•b³
4. b-2•b²•a⁰
Use the properties of exponents to rewrite each
expression in the text box.

Answers

The following expressions solved with the properties of exponents;

ax

a³ × b⁵

b

How to solve using properties of exponents?

b³ / b⁰

= b^(3-0)

= b³

a•x⁵ / a•x⁴

= ax⁵ / ax⁴

= ax^(5-4)

= ax¹

= ax

a • b²• a²•b³

= a^(1+2) × b^(2+3)

= a³ × b⁵

b^-2•b²•a⁰

= b^(-2+2) × a⁰

= b¹ × 1

= b

Therefore, the properties of exponents states that when numbers of the same base are divided, the exponent will be subtracted and

when numbers of the same base are multiplied, the exponent will be added.

Read more on the properties of exponents:

https://brainly.com/question/3187898

#SPJ1

0.003/19.43 what is the answer

Answers

Answer:

0.000154

Step-by-step explanation:


Answer:

0.000154

Step:

ROUND PLEASE AND THANK YOU!!!!!!

Answers

The secant-secant product theorem states that if 2 secant segments are drawn to a circle from an external point, then the product of the length of one of the secants and its external portion is equal to the product of the length of the other secant and its external portion.

The length of the first secant in the image is x + 18, and the second is 24 + 16.

x + 18 times 18 = 40 times 16

18x + 324 = 640

18x = 316

x= approximately 17.6

what is the axis of symmetry of this quadratic? -5x² + 70x + 3

Answers

Answer:

x=7

Step-by-step explanation:

You graph it and find the middle point that would create a line through it and see where it his the x-axis.

I need help with this one and can u explain it

Answers

Answer:

x = 8

Step-by-step explanation:

Vertically opposite angles are congruent.

          5x + 9 = 57 - x

 Add x to both sides,

      5x +x + 9 = 57

           6x + 9 = 57

Subtract 9 from both sides,

                  6x = 57 - 9

                  6x = 48

Divide both sides by 6,

                 x = 48 ÷ 6

                x = 8

Investigate the Trigonometric Ratios for 30 Degrees (3 points)
Hyp= 2.63
30 degrees
Adj = 2.278
Opp = 1.315
I have set this to make a 30 degree triangle.
Record the lengths of the three sides in the table below.
Adjust the red dot to change the size of your triangle.
Record the next set of measurements for that triangle.
Repeat until you have done 3 triangles, each for a 30
degree reference angle.
Triangle
1
2
3
Hypotenuse Opposite
Adjacent

Answers

The next set of measurements for the triangle are as follows:

                        Triangle 1            Triangle 2           Triangle 3

Hypotenuse:    5.26                    7.89                     10.52

Opposite:          2.63                   3.945                   5.26

Adjacent:          4.556                  6.834                   6.834

How to find the triangle measures while maintaining angle 30 degrees

This is done using the concept of similar triangles,

Similar triangles are two triangles that have the same shape but may be scaled to different sizes. In other words, similar triangles have the same angles, but their sides may be proportional.

In the problem, the proportion of the sides are equal and this will maintain the size of the angle

let the size of the angle be x

Sin x = opposite / hypotenuse

Sin x = 2.63 / 5.26 = 3.945 / 7.89 = 5.26 / 10.52 = 0.5

x = arc sin (0.5)

x = 30

To maintain same proportion the triangles where all a scaled version of the given triangle

Learn more about similar triangles at:

https://brainly.com/question/2644832

#SPJ1

help me on this and tell me if i got them right

Answers

The volume of a rectangular prism is 320 m³.

What is a rectangular prism?

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases. A cuboid is also a rectangular prism. The cross-section of a cuboid and a rectangular prism is the same. Volume of a rectangular prism = Area of a base × Height.

1) Given that, base area is 40 m² and height is 8 m.

So, the volume = 40×8

= 320 m³

2) 2) In the basketball game, Scott attempted 14 free throws.

He made half of them = 14/2

= 7

So, he made 7 throws

3) Today's high is 47 degrees Fahrenheit.

The weatherman says it will hit freezing tonight.

So, the temperature is represented as -47 degrees.

4) The given numbers are 5489 and 6752

Now, the sum is 5489 +6752

= 12241

Estimated to the nearest thousand as 12000.

5) Jace had 38 paper airplanes at home.

Christopher gave him 14 more paper airplanes to play with at home. Then Ameera gave him 29 paper airplanes.

So, total airplanes= 38+14+29

= 81

So, Jace had total 81 paper airplanes.

Therefore, the volume of a rectangular prism is 320 m³.

To learn more about the rectangular prism visit:

https://brainly.com/question/27812749.

#SPJ1

How can you solve real-world and mathematical problems with numerical and algebraic equations and inequalities?

Answers

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

What is Linear Inequality?

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

Solution:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

To learn more about Linear Inequality from

https://brainly.com/question/24372553

#SPJ1

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

What is Linear Inequality?

In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.

According to question:

Equations and inequalities based on numbers and algebra are effective tools for tackling both mathematical and real-world issues. The general steps you can take to use equations and inequalities to tackle such issues are listed below:

1. Consider the issue carefully and note what you are looking for. You can use this to decide which variables to include in your equations.

2. The equations that describe the issue should be written down. This could entail writing expressions that relate the variables or utilizing formulas.

3. Use algebraic strategies to solve the equations, such as grouping like terms, multiplying or dividing both sides of the equation by a constant, or focusing only on one side of the problem's variables.

4. Verify your answers to make sure they make sense in light of the issue at hand.

To know more about Linear Inequality visit:

brainly.com/question/24372553

#SPJ1

Help! Brainliest! Need help with 10, 12, and 13. I really appreciate it!!

Answers

The required  ST² = TW × RT has been proven for the triangle RST where SW is perpendicular from vertex S to RT.

What are Similar triangles?

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,
For the triangle RST where SW is perpendicular from vertex S to RT

Rewrite the equation,
ST² = TW × RT
ST/TW = RT/ST

It implies triangle SWT is similar to triangle RST,

Where,

∠S = ∠W and ∠T = ∠T

So triangle SWT is similar to triangle RST, by AA postulate of similarity.

If triangles are similar,
ST/TW = RT/ST   [became valid statement]

ST² = TW × RT

Thus, ST² = TW × RT hence proved.

Learn more about similar triangles here:

brainly.com/question/25882965

#SPJ9

Use the distributive property to write an expression that is equivalent to 12+4=___.
Please I need help

Answers

Using the distributive property to write the expression, we have:

12+4 = 4(3 + 1)

How to use the distributive property to write an expression?

The distributive property states that a(b + c) = ab + ac, where a, b, and c are any real numbers.

We can use this property to write an expression that is equivalent to 12 + 4 as follows:

12 + 4 = 4(3) + 4 (here, we have factored out 4 from 12 using the distributive property)

         = 4(3 + 1) (we have combined the terms inside the parentheses)

Therefore, 12 + 4 is equivalent to 4(3 + 1).

Learn more about distributive property on:

https://brainly.com/question/2807928

#SPJ1

Jimmy is an accountant who also works part-time as a museum tour guide. Information from his tax worksheet is wages from accounting job, $75,937.84; wages from museum job, $14,937.92; interest, $839.40; and dividends, $123.45. What is Jimmy’s total income?

Answers

Jimmy’s total income is the sum of all the incomes which is $91838.61 .

How to determine Jimmy's income?

You should understand that total income' refers to the sum of certain incomes (in cash and, in some circumstances, in kind) of the statistical unit during a specified reference period .

Now in the given question ,

The given parameters that will help us to determine the income are

wages from accounting job,             $75,937.84;

interest,                                                   $839.40

wages from museum job,                  $14,937.92;

dividends,                                                $123.45.

Therefore Jimmy's total income is the sum of all the incomes

$(75,937.84 + 839.40 + 14,937.92 + 123.45)

Total income = $91838.61

learn more about total income , visit:

brainly.com/question/21121917

#SPJ1

Can someone please help?? Thank you soo much

Answers

Khadija would have to pay $27.8 (7.5 x 4 - 1.7) to buy 4 pounds of apples.

What is cost?

Cost the monitorial associated with the purchase of production of food or service if can include the prices of materials of which is over it and other expenses that are related to the production of the good of service cost is a major fraction when deciding whether to purchase a product something as it is and indicator of the value of the product of sound service.

The expression for the cost to buy  x  pounds of apples is: 7.5x - 1.7, where x represents the number of pounds of apples purchased. For example, if Khadija wanted to buy 3 pounds of apples, the cost would be calculated by 7.5x - 1.7, which is equal to 22.6 dollars.

To know more about cost click-
https://brainly.com/question/25109150
#SPJ1

The diameter of a circle is 16 ft. Find its area to the nearest whole number.

Answers

Answer:

the area of the circle is approximately

201.06 ft^2

Help please…………………………………..

Answers

The value of the wanted limit is:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4 = 64[/tex]

So the correct option is the third one.

How to find the limit?

Here we know that:

[tex]\lim_{x \to 0} f(x) = 4[/tex]

And we want to find the value of the limit:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4[/tex]

Notice that because neither the fraction nor the power depend on the value of x, we can put the limit inside the parenthesis to get:

[tex]\lim_{x \to 0} \frac{1}{4} (f(x))^4 = \frac{1}{4} (\lim_{x \to 0} f(x))^4[/tex]

And we know that the thing inside the parenthesis is 4, then:

[tex]\frac{1}{4} (\lim_{x \to 0} f(x))^4 = \frac{1}{4} (4)^4 = 4^3 = 64[/tex]

Learn more about limits at:

https://brainly.com/question/5313449

#SPJ1

Kirill purchased 20 cows, pigs and chickens for $3,447. If cows cost $750 each, pigs cost $60 each, and chickens cost $3 each, and he bought two more chickens than
pigs, how many of each animal did he buy?

Answers

Let's use variables to represent the number of cows, pigs, and chickens that Kirill bought.

Let's use c for the number of cows, p for the number of pigs, and h for the number of chickens.

From the problem, we know that:

c + p + h = 20 (he bought 20 animals in total)
750c + 60p + 3h = 3447 (the total cost of the animals)

We also know that he bought two more chickens than pigs, so:

h = p + 2

Now we can use these three equations to solve for c, p, and h. One way to do this is to use substitution. Solving one of the equations for one of the variables and then substituting that expression into the other equations, we get:

p = h - 2 (from the relationship between h and p)

c + (h - 2) + h = 20 (substituting into the first equation)

c + 2h = 22

c = 22 - 2h (solving for c)

Substituting the expressions for c and p into the second equation, we get:

750(22 - 2h) + 60(h - 2) + 3h = 3447

16500 - 1500h + 60h - 120 + 3h = 3447

-1437h = -13083

h = 9

Now we can use the expressions for h and p to find c:

c + (9 - 2) + 9 = 20

c = 4

Therefore, Kirill bought 4 cows, 7 pigs, and 9 chickens.
The answer is 32














Ssmsmskmssmkkmam

Find the value of the X, Triangle Similarity

Answers

The value of 'x' in similar triangles is 6.9 units.

What is a triangle?

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, A line segment parallel to one side of the triangle divides the other two sides in the ratio of their respective lengths.

Therefore, The ratio can be formed as,

13/5 = 18/x.

13x = 90.

x = 6.9 units.

learn more about triangles here :

https://brainly.com/question/29083884


#SPJ1

How do you find multiples of 3 and 5?

Answers

To find multiple of 3 and 5 we need to add 15 to the previous multiple of 15.

To find multiples of 3 and 5, you can use the following steps:

1. Start with the number 3 and 5, respectively.
2. Add 3 or 5 to the previous number to get the next multiple. For example, 3 + 3 = 6, 6 + 3 = 9, and so on. Similarly, 5 +    5 = 10, 10 + 5 = 15, and so on.
3. Repeat step 2 until you have found the desired number of multiples.

Here are the first 10 multiples of 3 and 5:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Note that some numbers, such as 15 and 30, are multiples of both 3 and 5. These are called common multiples.

To know more about common multiples click on below link:

https://brainly.com/question/13696879#

#SPJ11

2.
(08.02 LC)

Solve nine times two thirds.

Leave your answer as an improper fraction.

A) eleven twenty sevenths
B) eighteen twenty sevenths
C) eleven thirds
D) eighteen thirds

Pls help

Answers

The fraction of nine times two thirds is 18/3 (option D)

What is fraction ?

A fraction is a way of representing a part of a whole or a ratio between two numbers. It consists of two numbers written one above the other and separated by a horizontal line called a fraction bar.

The number above the fraction bar is called the numerator, and it represents the part of the whole or the quantity being considered. The number below the fraction bar is called the denominator, and it represents the total number of equal parts into which the whole has been divided.

Given by the question:

Nine times two thirds can be written as:

9 × 2/3 = 18/3=6

Simplifying this fraction, we can divide both the numerator and denominator by their greatest common factor of 3, which gives:

18/3
so the correct option is D.

To know more about fraction visit:

https://brainly.com/question/29766013

#SPJ1

Pls help me thanks :)))

Answers

Answer:

y = - 1 , y = 17

Step-by-step explanation:

y² - 16y + 64 = 81 ← y² - 16y + 64 is a perfect square

)y - 8)² = 81 ( take the square root of both sides )

y - 8 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 8 to both sides )

y = 8 ± 9

then

y = 8 - 9 = - 1

x = 8 + 9 = 17

Which statement is true about the end behavior of the
graphed function?
O As the x-values go to positive infinity, the function's
values go to negative infinity.
O As the x-values go to zero, the function's values go to
positive infinity.
O As the x-values go to negative infinity, the function's
values are equal to zero.
O As the x-values go to positive infinity, the function's
values go to positive infinity.

Answers

As the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.

What is a function?

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The graph of the function is given below.

From the graph, we can conclude that the value of the graph is always positive. So, the function will be an exponential function.

From the graph, as the x-values go to positive infinity, the function's values go to positive infinity. Then the correct option is D.

More about the function link is given below.

https://brainly.com/question/5245372

#SPJ9

How do you visualizationa Kruskal algorithm?

Answers

Visualizing Kruskal's algorithm involves representing the graph, its edges, and the minimum spanning tree in a visual format.

To visualize a Kruskal algorithm, you need to follow the steps below:

1. Sort all the edges in ascending order of weight.
2. Create a new graph G' with the same vertices as the original graph G, but no edges.
3. Start with the smallest edge and add it to G' if it doesn't create a cycle. Repeat this step until you have added all the edges or you have a minimum spanning tree.
4. If you have a minimum spanning tree, you can visualize it by drawing the graph with the edges included in G'.

Here is an example:

Original graph G:

A---2---B---3---C
|       |
4       1
|       |
D---5---E

Step 1: Sort the edges in ascending order of weight: 1, 2, 3, 4, 5

Step 2: Create a new graph G' with the same vertices as G, but no edges.

Step 3: Start with the smallest edge (1) and add it to G'. This doesn't create a cycle, so we can add it.

G':
A       B---1---C
|       |
4       1
|       |
D       E

Next, add the second smallest edge (2) to G'. This also doesn't create a cycle, so we can add it.

G':
A---2---B---1---C
|       |
4       1
|       |
D       E

Continue this process until you have added all the edges or you have a minimum spanning tree.

Step 4: Visualize the minimum spanning tree by drawing the graph with the edges included in G'.

Minimum spanning tree:

A---2---B---1---C
|       |
4       1
|       |
D       E

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

To know more about minimum spanning tree click below:

https://brainly.com/question/13148966#

#SPJ11

can someone PLEASE help me ASAP! Due today!! I will give brainliest.

Show work please

Answers

The surface area of the given figure is 200 yd².

What is Surface Area?

The area of a three dimensional object on it's outer surface is called the surface area of the object.

Representing the figure as three dimensional, this consists of two triangular bases and three rectangular faces.

Area of triangle = [tex]\frac{1}{2}[/tex] × base × height

                          = [tex]\frac{1}{2}[/tex] × 6 × 4

                          = 12 yards²

Area of two triangular faces = 12 × 2 = 24 yd²

Of the three rectangular faces, two of them have a length of 11 yd and width of 5 yd.

Area of a rectangle = Length × Width

Area of two rectangular faces = 2 × Length × Width

                                                  = 2 × 11 × 5

                                                  = 110 yd²

Area of the third rectangular face = 11 × 6 = 66 yd²

Total surface area = 24 yd² + 110 yd² + 66 yd²

                              = 200 yd²

Hence the total surface area is 200 yd².

Learn more about Surface Area here :

https://brainly.com/question/29101132

#SPJ1

suppose that a motorboat is moving at ​40ft/s when its motor suddenly​ quits, and that 10 s later the boat has slowed to ​20 ft/s. assume that the resistance it encounters while coasting is proportional to its​ velocity, so that ​dv/dtkv. how far will the boat coast in​ all?

Answers

The boat will coast a total distance of approximately 40/ln(0.5)/(-10) ft.

To solve this problem, we can use the concept of exponential decay. If we let v(t) be the velocity of the boat as a function of time t, then we can write the differential equation that describes its motion as:

dv/dt = -kv(t)

where k is the proportionality constant between resistance and velocity. We can separate variables and integrate both sides to get the velocity as a function of time:

∫(dv/dt) = -k∫(v(t))dt

v(t) = Ce^(-kt)

where C is an arbitrary constant of integration. We can use the initial condition v(0) = 40 ft/s to find C:

C = 40

So the velocity of the boat as a function of time is:

v(t) = 40e^(-kt)

We can use the condition v(10) = 20 ft/s to solve for k:

20 = 40e^(-10k)

Taking the natural logarithm of both sides:

ln(0.5) = -10k

k = ln(0.5)/(-10)

Next, we can use the velocity as a function of time to find the distance traveled by the boat:

∫(v(t))dt = ∫(40e^(-kt))dt = 40/k * (1 - e^(-kt))

Let's call the total distance traveled by the boat "D". Then we can write:

D = 40/k * (1 - e^(-kt))

We can plug in the value of k we found earlier and evaluate the expression at t = ∞:

D = 40/ln(0.5)/(-10) * (1 - e^(-∞)) = 40/ln(0.5)/(-10)

To learn more about distance here:

https://brainly.com/question/15172156

#SPJ4

Other Questions
Why are natural killer cells considered to be part of the innate immune response?Describe the process whereby natural killer cells kill other cells and the role of macrophages in the process.What treatments or other options does Shanice have to counteract the natural killer cell deficiency? what is the icd 10 code for osteoarthritis of left knee? All vertebrate embryos follow a commondevelopmental path due to their common ancestry. All have a set of very similar genes that define their basic body plan. As they grow, the differences that will distinguish the embryos as adults become more and more apparent. The study of this development can yield insights into the process of evolution.Why is this evidence of evolution? a notebook is 8 inches tall and 10 inches wide what is its area? What was the summary in Marbury vs Madison? Where did Miguel Hidalgo fight for independence? Shown are graphs of the position functions of two runners, A and B, who run a 100-m race and finish in a tie. (a) Describe and compare how the runners run the race. (b) At what time is the distance between the runners the greatest? (c) At what time do they have the same velocity? What would be the 50th term than? Besides generating new combos of alleles, recombination also provides what functions? What is ferrous sulfate? What is carotid artery stenosis? 9. A pharmacist received a prescription call-ing for 30 capsules, each to contain /200gr of nitroglycerin. How many 0.4-mg ni-troglycerin tablets would supply theamount required?15 the distance from one trough to another trough is called a What is the signal observed at ppm carbon nmr residual? Simplifying algebra radicalsPlease help!! What is symbol of microliter ? Dandelions have wind-dispersed seeds that germinate and grow wherever they fall. They are neither clumped, nor evenly dispersed. This is an example of ___ dispersion. what is medical term that means abnormal condition of a pancreatic stone ? Blueprint3 inDeck3 in1 in1 in1 InThe area of the scale drawing issquare inches.If the scale is 1 inch = 4 feet, the area of the actual deck would beNumerically, the value of the area of the actual deck would beBased on these results, if the scale is 1 inch = k feet, the area of the actual deck would be "square feet.times the value of the area of the scale drawing.square feet What does a 1 standard deviation increase mean?