The boat will coast approximately 16752.9 feet (or about 3.17 miles) in the first 2 minutes after its motor quits.
From the problem statement, we know that the velocity of the boat, v, changes from 83 ft/s to 23 ft/s over a period of 1 second. Therefore, we can write:
[tex]dv/dt = -k v^2[/tex]
Separating variables and integrating from v = 83 at t = 0 to v = 23 at t = 1, we get:
[tex]∫83^23 dv / v^2 = ∫0^1 -k dt[/tex]
=> [1/83 - 1/23] = k
So the equation for the velocity of the boat as it coasts is:
[tex]dv/dt = -[(1/83 - 1/23)] v^2[/tex]
The differential equation is separable:
[tex]dv/v^2 = -[(1/83 - 1/23)] dt[/tex]
Integrating both sides, we get:
-1/v = [(1/83 - 1/23)] t + C
where C is an integration constant. Using the initial condition v(0) = 83, we get:
C = -1/83
Substituting this back, we have:
-1/v = [(1/83 - 1/23)] t - 1/83
Solving for v, we have:
v(t) = 83 / [1 + (83/23 - 1) t]
To find the distance traveled, we integrate v(t) from t = 0 to t = 120:
s =[tex]∫0^120 v(t) dt[/tex]
Substituting v(t) and simplifying, we have:
s = 23 ln(1 + 3.6087t) + 60.391t + C
where C is another integration constant. Using the initial condition s(0) = 0, we get:
C = 0
Therefore, the distance traveled by the boat in the first 2 minutes after its motor quits is:
s = 23 ln(1 + 3.6087t) + 60.391t
Evaluating this expression at t = 120 seconds, we get:
s = 23 ln(433.044) + 7246.92 ≈ 16752.9 ft
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2
The area of a rectangular window is 3726 cm².
If the length of the window is 69 cm, what is its width?
Width of the window: cm
Actividades de Apertura
a) Dos ángulos rectos.
b) Dos ángulos agudos.
c) Dos ángulos suplementarios.
d) Dos ángulos complementarios
e) Dos rectas paralelas.
f) Dos rectas perpendiculares
g) Una recta transversal.
Las actividades de apertura son descripciones de diferentes relaciones geométricas. Aquí está la explicación de cada una:
a) Dos ángulos rectos tienen una medida de 90 grados.
b) Dos ángulos agudos tienen una medida menor a 90 grados.
c) Dos ángulos suplementarios suman a 90 grados.
d) Dos ángulos complementarios suman a 90 grados.
e) Dos rectas paralelas no se cruzan.
f) Dos rectas perpendiculares se cruzan en un ángulo recto de 90 grados.
g) Una recta transversal corta a dos o más rectas, creando ángulos en los puntos de intersección.
Qué es Dos ángulos rectos?Dos ángulos rectos son dos ángulos que tienen una medida de 90 grados. En geometría, un ángulo recto es un ángulo que tiene una medida de 90 grados y se representa con una línea diagonal que forma cuatro cuartos iguales.
Los ángulos rectos son importantes en la construcción y el diseño, ya que permiten la creación de formas simples y precisas. Por ejemplo, dos ángulos rectos pueden ser utilizados para formar un cuadrado o un rectángulo, mientras que un ángulo recto y un ángulo agudo pueden ser utilizados para formar un triángulo rectángulo.
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Factorise 3y²+12y ‼️‼️‼️
Answer:
3y(y + 4)
Explanation:
[tex]3y^{2} + 12y\\3(y^{2} + 4y)\\3y(y + 4)\\[/tex]
answer and explain for 10 points.
Answer:
The answer is 6 with a remainder of 2.
Step-by-step explanation:
3 times 6 is 18.
Then if you subtract 18 from 20 you get 2.
So 3 goes into twenty, 6 times, and you get a remainder of 2.
Solve pls! Lots of points! Question down below!
Answer:1024 grid squares
Step-by-step explanation:
Let's call the side length of the original piece of graph paper "x".
Since, side length of the cut out square is then (x-2) because the cut out square has to have an integer number of grid squares, and each side of the square would take up 2 grid squares on the graph paper.
The number of grid squares in the cut out square is then (x-2)^2.
The number of grid squares left on the graph paper is 124, so we have:
x^2 - (x-2)^2 = 124
Expanding the right side:
x^2 - x^2 + 4x - 4 = 124
Simplifying:
4x = 128
therefore:
x = 32
therefore original graph paper contains 32 grids i.e 32^2 = 1024
Answer:
any of {128, 133, 140, 160, 224, 320, 380, 700, 1024}
1024 if the original grid was square
Step-by-step explanation:
You want to know how many grid squares are on a piece of graph paper if a square number of grid squares can be cut from it to leave 124 grid squares.
Square graphIf the graph is square to begin with, a square of x² can be removed from its size (x+a)² to leave 124 squares. That is ...
(x +a)² -x² = 124
(a)(2x+a) = 124
The factor pairs of 124 are ...
124 = 1·124 = 2·62 = 4·31
Of these, only 2 and 62 differ by an even number, so we have a=2 and x=30.
The graph paper could be 32 units square originally, having 1024 grid squares.
Rectangular graphThere is nothing in the problem statement that requires the original graph paper be square. If it is not necessarily square, there are 13 possible shapes it could be. Those have 9 different possibilities for numbers of grid squares.
The graph paper could have originally had this number of grid squares:
128 = 4×32 = 8×16. The square removed is 2².133 = 7×19. The square removed is 3².140 = 5×28 = 7×20 = 10×14. The square removed is 4².160 = 8×20 = 10×16. The square removed is 6².224 = 14×16. The square removed is 10².320 = 16×20. The square removed is 14².380 = 19×20. The square removed is 16².700 = 25×28. The square removed is 24².1024 = 32×32. The square removed is 30². . . . . discussed above__
Additional comment
You may notice that removing a 24×24 square from a graph that is 25×28 leaves no border on one side.
These values were found using a search script.
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Susan bought 2/5 as many boxes of butter cookies as chocolate cookies. She spent $156 altogether. Each box of butter cookies cost $2 less than each box of chocolate cookies. The total cost of the chocolate cookies was $84 more than the total cost of the butter cookies. How many boxes of cookies did Susan buy?
Susan bought 6 boxes of chocolate cookies, and 2/5(6) = 2.4 or 2 boxes of butter cookies.
How to find number of boxes of cookies did Susan buy?Let's call the number of boxes of chocolate cookies that Susan bought "C". Then, she bought 2/5 as many boxes of butter cookies, which is 2/5C.
Let's call the cost of each box of chocolate cookies "x". Then, the cost of each box of butter cookies is x-2, since each box of butter cookies costs $2 less.
We know that the total cost of the chocolate cookies was $84 more than the total cost of the butter cookies. This can be expressed as:
Cx = 2C/5(x-2) + 84
Simplifying this equation, we get:
3/5Cx = 84 + 2/5C(2)
Multiplying both sides by 5/3, we get:
Cx = 140 + 4C/3
We also know that the total cost of all the cookies was $156, which can be expressed as:
Cx(x) + (2/5C)(x-2) = 156
Substituting Cx from the previous equation, we get:
(140 + 4/3C)(C) + (2/5C)(C-2) = 156
Simplifying and solving for C, we get:
C = 6
So Susan bought 6 boxes of chocolate cookies, and 2/5(6) = 2.4 or 2 boxes of butter cookies.
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A plumbing company charges $50 for a house visit plus $35 per hour for the labor. Write an equation in slope-intercept form that models the situation
Convert 2000 feet per minute to miles per hour. Round to the nearest tenth.
A. 17600 miles per hour
B. 22.7 miles per hour
C. 154.8 miles per hour
D. 1363.6 miles per hour
Answer:
Step-by-step explanation:
You are currently converting speed units from foot per minute to miles per hour 1 ft/min = 0.011363636 mph foot per minute ft
so 0.011363636 times 2000 equals 27.727272
so your answer is [B]
The quadrilateral is a trapezoid. What is the value of x?A)48B)4C)25D)5
The quadrilateral is a trapezoid, the value of x is 5 in given trapezoid.
An isosceles trapezoid can be defined as a trapezoid whose non-parallel sides and base angles have the same measure. That is, if the two opposite sides (bases) of a trapezoid are parallel and the two non-parallel sides are of equal length, it is an isosceles trapezoid. See the diagram below. It indicates that sides c and d are of equal length and opposite sides a and b (the base of the trapezoid) are parallel to each other.
The given trapezoid is An isosceles trapezoid .
From the given diagram, the expression below is true:
2(5x - 1) = 21 + 27
(21+27)/2 = 5x -1
24 = 5x-1
x=5
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The given question is incomplete, the complete question is:
The quadrilateral is a trapezoid. What is the value of x?
A)48
B)4
C)25
D)5
and the Question image is attached in image section.
Regis leans a 10-foot ladder against a wall. The base of the ladder makes a 65 angle with the ground.
A: What is the distance, In feet, from the base of the ladder to the base of the wall? Round to the nearest tenth of a foot.
B: Regis needs to move the ladder so that it reaches a window 9.6 feet above the ground.
How many feet closer to the building does he need to move the base of the ladder?
The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.
What is trigonometry?Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The length of the ladder is 10 feet. And the inclination angle is 65°. Then the distance from the bottom of ladder to the wall is given as,
cos 65° = x / 10
x = 4.23 feet
If the ladder reaches a window 9.6 feet above the ground, then the angle is given as,
sin θ = 9.6 / 10
sin θ = sin 73.74°
θ = 73.74°
The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.
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2[73-(4x5)]
I think the answer is 106 but can someone double check? Thanks
Answer:
yes its 106
Step-by-step explanation:
brainly removed my answer
Mrs. Thapa wishes to grow flowers on the hanging bowls at her home. She brings 16 hemispherical bowls from the market having internal diameter 21 cm and uniform thickness 0.5 cm each and fills the bowls with compost completely. (i) If 1 cm³ of compost weighs 2.31 gm, find the total weight of required compost. (ii) If she covers outer curved surface of each bowl with polythene sheet, find the total amount of polythene
Answer:
(i) The volume of each hemispherical bowl can be calculated as follows:
Volume of a hemispherical bowl = (2/3) x pi x (d/2)^3, where d is the internal diameter of the bowl.
Substituting d = 21 cm, we get:
Volume of a hemispherical bowl = (2/3) x pi x (21/2)^3 = 4851.97 cubic centimeters
The total volume of compost required to fill all 16 bowls is therefore:
Total volume of compost = 16 x 4851.97 = 77631.52 cubic centimeters
If 1 cm³ of compost weighs 2.31 gm, then the total weight of required compost is:
Total weight of compost = 77631.52 x 2.31 = 179231.83 grams or 179.23 kilograms
Therefore, Mrs. Thapa would need 179.23 kilograms of compost to fill all 16 hemispherical bowls.
(ii) The outer curved surface area of each hemispherical bowl can be calculated as follows:
Outer curved surface area of a hemispherical bowl = 2 x pi x (d/2)^2, where d is the internal diameter of the bowl.
Substituting d = 21 cm, we get:
Outer curved surface area of a hemispherical bowl = 2 x pi x (21/2)^2 = 693.84 square centimeters
The total outer curved surface area of all 16 bowls is therefore:
Total outer curved surface area = 16 x 693.84 = 11101.44 square centimeters
If Mrs. Thapa covers the outer curved surface of each bowl with polythene sheet, then the total amount of polythene required would be equal to the total outer curved surface area of all 16 bowls.
Therefore, the total amount of polythene required would be 11101.44 square centimeters.
Step-by-step explanation:
help i dont understand this fully
Find the volume of a rectangular prism with the following dimensions: V = lwh Length:
4m Width
: 0.3 m Height
: 1.5 m
Answer:
1.8 m³
Step-by-step explanation:
You want the volume of the rectangular prism with dimensions L=4 m, W = 0.3m, H = 1.5 m.
VolumeThe volume formula is given in the problem statement:
V = LWH
Substituting the given values of L, W, H, we find the volume to be ...
V = (4 m)(0.3 m)(1.5 m)
V = 1.8 m³
The volume of the rectangular prism is 1.8 cubic meters.
In physics lab, you measure three quantities: x, y, and z. Suppose that x=2.5 kg, y=0.8 m, and z=4.9 kg/m. Which of the mathematical combinations might be meaningful?(x/y) - z(x/z) - yx+y+z(xz) + yxyzx - (y/z)xy/z(x-y)/z
In physics lab, when you measure three quantities of x, y, and z, you can use these mathematical combinations to find meaningful relationships between these quantities:
(x/y) - z(x/z) - yx - (yz)In this case, x=2.5 kg, y=0.8 m, and z=4.9 kg/m.
Based on the given quantities' scale, we know that x, y, and z have a relationship where:
z = x/y
Then, the mathematical combinations that might be meaningful are:
- (x/y) - z: This combination gives you the difference between the ratio of x and y, and z. This could be meaningful if you are trying to find the difference between two quantities that have different units.
- (x/z) - y: This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.
- x - (yz): This combination gives you the difference between the ratio of x and z, and y. This could be meaningful if you are trying to find the difference between two quantities that have different units.
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The data in the table was produced by a researcher studying the
number of vegetables people ate for one week. Group A and Group B,
each with 20 people, recorded the vegetables that they ate. If a person
is chosen at random from those who ate at least 7 vegetables, what is
the probability that the person belonged to Group A?
The probability that the person belonged to Group A is given as follows:
Probability = number of people in Group A that ate at least 7 vegetables / total number of people that ate at least 7 vegetables.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
The outcomes for this problem are given as follows:
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Consider Juan Soto's wins above replacement statistics for the four seasons in the table. In which season did he have the greatest value to his team?
Answer: 2021
Step-by-step explanation:
HELP ME PLEASEEEE
Round each fraction to help you estimate the solution for the following equation
nine-tenths minus four-tenths equals.
Options
1. 0
2. 1/2
3. 1
4. 1 1/2
PLEASE HELP DUE TOMORROW:
Instructions: Fill in each matching colored box with same solution that makes each equation true. For example, if one red box was 3 then all the other red boxes must be 3. (JUST AN EXAMPLE)
Answer:
red=7
pink=4
purple=15
dark pink=22
gray=18
Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $45 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $250, how many hours did the plumber work?
The equation to the context is 50x + 45 = 250 and the plumber worked for 4.1 hours.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Let, 'x' represents the number of hours worked by the plumber.
Therefore, The equation can be represented as,
50x + 45 = 250.
50x = 205.
5x = 20.5.
x = 20.5/5.
x = 4.1 hours.
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-112-11 > -6+13a
Answer: x>
Answer:
a < -9
Step-by-step explanation:
-112-11 > -6+13a
-123 > -6 + 13a
-117 > 13a
-117 / 13 > a
-9 > a
a < -9
Write a letter to the editor of a newspaper, making the public aware of rising air and noise pollution in your area. (rdmcoyvtvs meat for fuñ)mention the bad air quality index that appears in the newspaper daily and write about the bad effects of air and noise pollution and suggest some measures to curb it.
Follow=Follow
like
don't forget to make brainalist and keep smiling
Answer: Dear Editor,
I am writing to bring to your attention the serious issue of rising air and noise pollution in our area. The daily air quality index that appears in the newspaper highlights the extent of the problem, and I believe it is important for the public to be aware of its effects.
Air pollution has been linked to a number of health problems, including respiratory issues, heart disease, and even cancer. The presence of harmful pollutants in the air we breathe is cause for concern and demands immediate attention. Similarly, noise pollution can lead to hearing loss, sleep disturbance, and increased stress levels.
It is imperative that we take action to curb the effects of air and noise pollution. There are several measures that can be taken, both by individuals and by the government. On an individual level, we can reduce our carbon footprint by using public transportation, carpooling, or biking instead of driving alone. We can also plant trees and install air purifiers in our homes.
The government, on the other hand, can take steps to regulate industrial emissions, enforce stricter penalties for violators, and promote the use of clean energy sources. Additionally, they can create green spaces and establish noise-free zones in residential areas.
In conclusion, the rise in air and noise pollution is a pressing issue that affects the health and well-being of everyone in our community. I urge the public to take this matter seriously and support efforts to reduce its impact. Together, we can work towards a cleaner and healthier future.
Sincerely,
[Your Name]
Step-by-step explanation:
there are 14 people in an office with 5 different phone lines. if all the lines begin to ring at once, how many groups of 5 people can answer these lines?
There are 2002 groups of 5 people that can answer the 5 phone lines.
This is a combination problem, because we want to choose groups of 5 people from a group of 14, and the order in which we choose the people does not matter.
The formula for the number of combinations of n objects taken r at a time is:
C(n,r) = n! / (r! * (n-r)!)
In this case, we want to choose 5 people out of a group of 14, so we can plug those values into the formula:
C(14,5) = 14! / (5! * (14-5)!)
Simplifying the factorial terms:
C(14,5) = (1413121110) / (54321)
C(14,5) = 2002
Therefore, there are 2002 groups of 5 people that can answer the 5 phone lines.
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On a coordinate plane, how are the locations of the points (2 , -1) and (2 , 1) related?
On a coordinate plane, locations of the points (2 , -1) and (2 , 1) related by reflection across the x-axis.
It is given that the locations of the two points are (2 , -1) and (2 , 1).
We have to find the relation between two points.
From the given points (2 , -1) and (2 , 1), it is clear that the y-coordinates are same but the sign of x-coordinates are opposite.
If a figure is reflected across the y-axis, then we change the sign of y-coordinate and the x-coordinates remain same,
So, it is reflection across the x-axis.
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The graph of f(x) = ce^x crosses the y -axis at (0, c) where c is some constant: Where does the graph of g (x) = f(x)- d cross the y -axis? The graph of g (x) = f(x) -d crosses the Y ~axis
The graph of g(x)=f(x)-d crosses the y-axis at (0,c-d).
What does y-intercept mean?
The point on a line where it crosses the y-axis is known as the y-intercept. To put it another way, it is the value of y when x is equal to 0.
It is given that graph [tex]f(x)=ce^{x}[/tex] crosses the y-axis at (0,c).
Because at x=0,
[tex]f(0)=ce^{0}\\f(0)=c[/tex].
So, if g(x)=f(x)-d
[tex]g(x)=ce^{x}-d[/tex]
when x=0:
[tex]g(0)=ce^{0}-d\\g(0)=c-d[/tex]
So the graph of g(x)=f(x)-c touches the y-axis at (0,c-d).
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9
?
Encuentra la longitud de arco del semicirculo.
PROBLEM SOLVING
Question 8
Three sets of traffic lights (A, B and C) all turn red at 9 a.m. exactly. Light set A turns red every 2 minutes, light
set B turns red every 3 minutes and light set C turns red every 5 minutes. How long does it take for all three
lights to turn red again at the same time?
A map of a highway has a scale of 2 inches = 33 miles. The length of the highway on the map is 6 inches. There are 11 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch = 30 miles. How far apart are the rest stops on the new map?
Thus, the required rest stops are approximately 4.09 miles apart on the new map.
What is the scale factor?The scale factor is defined as the ratio of the modified change in length to the original length.
Here,
The total length of the highway in miles can be found by using the scale of the original map. Since 2 inches on the map represent 33 miles in reality, 6 inches on the map represent:
= 6 inches × (33 miles/2 inches) = 99 miles
Since there are 11 equally spaced rest stops along the highway,
= (99 miles)/(11 intervals) = 9 miles per interval
To create the new map with a scale of 1 inch = 30 miles, we need to use a scale factor of (1/2) × (30/33) = 15/33.
Therefore, the distance between each rest stop on the new map can be found by multiplying the distance between rest stops on the old map by the scale factor,
= (9 miles per interval) × (15/33) = 4.09 miles per interval
So, the required rest stops are approximately 4.09 miles apart on the new map.
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If 30% of a number is 42 and 70% of the same number is 98, find 40% of that number.
Answer:
56 is 40% of the original number
Step-by-step explanation:
Let [tex]n[/tex] represent the original number
We are given that
30% of number is 42
70% of the same number is 98
Lets convert the precents to decimals
30% as a decimal is [tex]0.3[/tex]
70% as a decimal is [tex]0.7[/tex]
We can create an equation for each scenario
[tex]0.3n=42\\0.7n=98[/tex]
We can choose either one to evaluate [tex]n[/tex].
[tex]0.3n=42[/tex]
Lets solve for [tex]n[/tex].
Divide both sides by [tex]0.3[/tex].
[tex]n=\frac{42}{0.3}[/tex]
Evaluate [tex]\frac{42}{0.3}[/tex].
[tex]n=140[/tex]
Now that we know what the original number is we can calculate what 40% of the number is.
40% as a decimal is [tex]0.4[/tex].
[tex]140*0.4=56[/tex]
Why would you want to transform a set of raw scores into a set of z-scores? Check all that apply. a. To make a distribution with a mean of 1 and a standard deviation of 0 b. To be able to describe the location of a raw score in the distribution of raw scores c. To make all the transformed scores greater than 0 d. To make it possible to compare scores from two different distributions
For a z-score, We transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions i.e. D.
What exactly is the z-score?
The z-score is a statistical measurement that describes a value's relationship to the mean of a collection of values. The z-score formula is
z = (x - μ)/σ
x = data point
μ = mean
σ = standard deviation
Mean:- The sum of a collection of numbers divided by the total number of numbers in the set is known as the arithmetic mean, sometimes known as the arithmetic average or simply the mean or average. A survey, experiment, or observational research is usually used to create the collection.
Now,
As Z-scores are standardized scores that identify and define each score's exact placement within a distribution. We may conduct meaningful comparisons of z-scores across various samples or groups by converting our data (raw score).
hence,
We transform a set of raw scores into a set of z-scores because we can compare scores from two different distributions.
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