the boat will coast for a distance of 400 ln(2) ft, which is approximately 277.3 ft.
To find how far the boat will coast, we need to use the concept of differential equations. The equation that describes the velocity of the boat at any time "t" after its motor quits is given by:
dv/dt = -k*v
where "v" is the velocity of the boat at time "t", "k" is the proportionality constant, and the negative sign indicates that the velocity is decreasing with time.
We can solve this differential equation to obtain the velocity of the boat as a function of time:
v(t) = v(0) * e^(-k*t)
where "v(0)" is the initial velocity of the boat (40 ft/sec).
Using the given information, we can set up two equations:
v(10) = 20 (velocity after 10 sec)
v(0) = 40 (initial velocity)
Plugging these values into the equation, we get:
20 = 40 * e^(-10k)
Solving for "k", we get:
k = ln(2)/10
Now, we can integrate the velocity equation to find the distance the boat travels during the coasting period:
d = [tex]\int\limits^{\infty}_{10} {v(t)} \, dt[/tex]
Plugging in the values, we get:
d = (40/k) * [e^(-k*10) - 0] = 400 ln(2) ft
To explain the solution, we used the concept of differential equations to model the motion of the boat as it coasts after its motor quits. We used the given information to solve for the proportionality constant "k", which allowed us to find the velocity of the boat at any time.
Finally, we integrated the velocity equation to find the distance the boat travels during the coasting period. The key to this problem was using the concept of differential equations to model the motion of the boat and setting up the appropriate equations to solve for the unknowns.
To learn more about distance click on,
https://brainly.com/question/30631058
#SPJ4
Complete question is:
Suppose that a motorboat is moving at 40 ft/sec when its motor suddenly quits, and then 10 sec later the boat has slowed to 20 ft/sec. Assume, that the resistance it encounters while coasting is proportional to its velocity. How far will the boat coast in all?
help pls
Find the value of the following expression and round to the nearest integer:
Answer:
53
Σ900(1.04)n+1
n=1
Submit Answer
Solve using substitution
3x-2y=3
y=6+4x
The system using substitution has its solution to be (-1.8, -1.2)
How to solve the system using substitutionFrom the question, we have the following parameters that can be used in our computation:
3x-2y=3
y=6+4x
By susbstitution, we have the following equation
3x - 12 - 8x = 3
Evaluate the like terms
so, we have the following representation
-5x = 9
Divide by 5
x = -1.8
So, we have
y= 6 + 4 * -1.8
Evaluate
y = -1.2
Hence, the value of y is -1.2
Read more about equations at
https://brainly.com/question/2972832
#SPJ1
Which value of x makes the equation
5(x - 2) - 4 = 6 true?
A. 2
B. 3
C. 4
D. 5
Answer:
Step-by-step explanation:
5x - 10 - 4 = 6
5x - 14 = 6
5x = 20
x = 4
Option C is the solution
Need answers stat trigonometry
The value of x to the nearest tenth are as follows;
x = 47.0 units.
x = 25.1 units.
x = 23.8 units.
x = 29.7 units.
x = 21.1°.
x = 39.6°.
x = 58.0°.
x = 72.9°.
How to determine the value of x?From the image attached above, we can logically deduce that the triangle is a right-angled triangle with the following side lengths:
Opposite side = x.
Adjacent side = 25.
Therefore, we would determine the value of x by using Tan trigonometric function:
Tanθ = Opposite side/Adjacent side
Tan45 = 25/x
x = 25Tan62
x = 47.0 units.
For right-angled triangle 3, we have:
Sin26 = 11/x
x = 11/0.4384
x = 25.1 units.
For right-angled triangle 4, we have:
Sin48 = x/32
x = 32sin48
x = 23.8 units.
For right-angled triangle 5, we have:
Cos12 = 29/x
x = 29/0.9782
x = 29.7 units.
For right-angled triangle 6, we have:
Cosθ = 14/15
θ = cos⁻¹(0.9333)
θ = 21.1°.
For right-angled triangle 7, we have:
Tanθ = 19/23
θ = tan⁻¹(0.8261)
θ = 39.6°.
For right-angled triangle 8, we have:
Cosθ = 9/17
θ = cos⁻¹(0.5294)
θ = 58.0°.
For right-angled triangle 9, we have:
Sinθ = 43/45
θ = sin⁻¹(0.9556)
θ = 72.9°.
Read more on right-angled triangle here: https://brainly.com/question/2223099
#SPJ1
g questions: if a set of grades for a class has a large range and a small standard deviation, what can you say about the class? include an interpretation that is specific to grades in a class.
If a set of grades have a large range and a small standard deviation, it means that there are few students with high marks and few with low marks. Most students falls in the average region.
Range is the difference between the maximum value and the minimum value. So for the range to be higher, there must be at least one very high grade and at least a very low grade. If the maximum mark scored by the highest scorer is 95 and 10 for the lowest, the range will be 95- 10 = 85.
If one scored 99 and the lowest scorer got 5, then the range is 99-5 = 94. So higher the range means there is great difference between the highest and lowest grade.
Standard deviation means how much the value deviates from average. If it is low, that means most of the students scored near to the average.
So high range and low standard deviation means, there are few high scorers and few low scores. But most students falls in the average category.
For more information regarding standard deviation and range, kindly refer
https://brainly.com/question/27951674
#SPJ4
the riverton high rockets won their regional basketball tournament and were awarded this trophy. what is the approximate volume of the trophy?
V Prism is V = B × h=9.5*4=38
the volume of a sphere is V = 4/3 π r³=4/3*22/7*9.5=10.47
V=10.47+38=48.476
A measurement of three-dimensional space is volume. It is frequently expressed in numerical form using SI-derived units, as well as different imperial or US-customary units. In contrast to how much space the container actually occupies, the volume of a container is typically thought of as its capacity, or the amount of fluid it could hold. Volume was initially measured using naturally occurring vessels of a comparable shape and then with standardized containers. Arithmetic formulas can be used to quickly calculate the volume of several straightforward three-dimensional shapes. If a formula for the shape's boundary is known, it is possible to use integral calculus to determine the volumes of more complex shapes. objects in the zero, one, and two dimensions have no volume.
Learn more about volume from
brainly.com/question/463363
#SPJ4
The reading group checked out 36 library books. 17 books are fiction, 10 are biographies, and some are science. How many books are science?
Answer:
9 science books
Step-by-step explanation:
Step 1) 36 - 17 = 19
Step 2) 19 - 10 = 9
a committee of 3 is to be selected to plan the annual company picnic. how many different committees are possible that contain at least 2 secretaries?
There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.
Assume that there are n total secretaries employed by the business.
Either we can select 2 secretaries and 1 non-secretary member, or we can select all 3 members to be secretaries in order to form a committee with at least 2 secretaries.
Out of n, there are binom n2 ways to select two secretaries, and binom n-21 ways to select a non-secretary member from the remaining n-2 non-secretaries.
This means that there are binom n ways to form a committee with 2 secretaries and 1 non-secretary member.
There are binom ways to select each of the three members to serve as a secretary.
There are a total of binom n2 binom n-21 + binom n3 possible committees with at least 2 secretaries.
for such more questions on probability
brainly.com/question/29439341
#SPJ4
These tables represent the relationships between x and y for two different sets of data. Which statements correctly describe the relationships between x and y for each table? Table A represents a multiplicative relationship because y is 2.5 times x, O and Table B represents an additive relationship because y is 2 more than O X. Table A represents an additive relationship because y is 1.5 more Othan x, and Table B represents a multiplicative relationship because y is 3 times x. Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X. Both tables represent additive relationships. In Table A, y is 1.5 more than x, and in Table B, y is 2 more than x.
Answer:
Both data sets represent multiplicative relationships. In Table A, y is 2.5 times x, and in Table B, y is 3 times X
Step-by-step explanation:
Self-explanatory
Every value of y in Table A is 2.5 times x value
and
every value of y in table B is 3 times x value
f (x) = (x - 6)2(x + 2)2
DONE
The roots of the equation, f (x) = ( x - 6 )²( x + 2 )² are 6 and - 2.
What is the root of function?The root of the function is calculated by setting the function equal to zero.
The given function is f (x) = ( x - 6 )²( x + 2 )²
we will separate the two equation and set them equal to zero.
( x - 6 )² = 0 ---- equation ( 1 )
or
( x + 2 )² = 0 -------- equation ( 2 )
from the first equation, x = 6
from the second equation, x = - 2
Learn more about roots of equations here: https://brainly.com/question/27114236
#SPJ1
The complete question is below:
Find the roots of f(x) = (x - 6)² (x + 2)²
This circle has a diameter of 40 centimeters. What is the radius?
Answer: 20 centimeters
Step-by-step explanation:
The radius is half the diameter so then the radius is 20 centimeters.
The distance between the center of the circle to its circumference is the radius. The diameter is always double the radius. Hence, the formula is derived by dividing the diameter by 2.
40/2 = 20cm.What percentage of winners driving a chevrolet won with an average speed of at least miles per hour?
The percentage of winners driving a Chevrolet who won with an average speed of at least miles per hour is fifty percent (50%).
We can infer that for a Chevrolet car,
the percentage of average speed (in miles/hour) for the range of 150-159.9 is 25%,
the percentage of average speed (in miles/hour) for the range of 160-169.9 is 18.75%,
and the percentage of average speed (in miles/hour) for the range of 170-179.9 is 6.25%.
Thereby, the percentage of winners of the race who were driving a Chevrolet and had an average speed of at least 150 miles/hour is,
50%.
Learn more about percentages on
https://brainly.com/question/29306119?referrer=searchResults
#SPJ4
Marcia's cost, in dollars, to wash her car can be calculated using the expression below,
where m represents the number of minutes the car wash will run.
0.25m +1.50
Evaluate the expression for m = 20, and interpret the meaning of the result.
When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.
What is Expression?An expression is combination of variables, numbers and operators.
Given that Marcia's cost, in dollars, to wash her car can be calculated using the expression
0.25m +1.50
Zero point two five plus one point five.
In the expression m represents the number of minutes the car wash will run.
We need to find the value of expression when m is 20
0.25(20)+1.50
5+1.50
6.5
When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.
Hence, Marcias cost $6.5 to wash her car for 20 minutes.
To learn more on Expressions click:
https://brainly.com/question/14083225
#SPJ9
Tina would like to withdraw an annual salary of $35,756 from an account paying 2.2% compounded annually for 35 years once she retires. Given this information, determine the amount needed in her account in order for her to reach her goal. Round to the nearest cent.
2. If 3x² - 2x - 16 = 0, then x = ?
F. -8/3 or -2
G. 3/8 or 2
H. -2 or 8/3
J. -2 or 3/8
K. 2 or 8/3
Answer: H. -2 or 8/3
Step-by-step explanation:
3x^2-2x-16=0
Multiply 3 times 16
x^2-2x-48=0
find two numbers that will add up to equal -2 and will be multiplied to get -48. (-8 and 6)
(x-8)(x+6)
divide both numbers by 3 but since you cannot divide 8 and 3 you will move the 3 in front of the x.
(3x-8)(x+2)
Set both equal to 0.
3x-8=0 x+2=0
x= 8/3 x=-2
What is the range of function f?
A.{y|4 < y < ∞}
B. {y|-∞}< y < ∞}
C. {yl-∞ < y < 0}
D.{y|-∞< y < 4}
PLEASE HELP!!! Will give brainliest.
Answer:
The system of equation is y=12x+5
Step-by-step explanation:
What is the equation of the line that passes through the point (-3,1)(−3,1) and has a slope of \frac{2}{3}
3
2
?
Answer:
y = (2/3)x + 3
Step-by-step explanation:
first we need to find the y-intercept
we can do this by using what is given, the point (-3,1) and the slope (2/3)
using the slope-intercept formula: y = mx + b.
m = slope
b = y intercept
we can plug in the x and y values we were given
so,
1 = (2/3)(-3) + b
we can now easily solve for b
1 = (2/3)(-3) = b
first multiply
1 = -2 + b
then add 2 to both sides, this way we isolate b
3 = b
now that we have the y intercept we can write the equation of the line
y = (2/3)x + 3
if you really wanted to, you can check if this is correct by plugging in the point again and seeing if the equation is true.
1 = (2/3)(-3) + 3
multiply first
1 = -2 + 3
add the like terms
1 = 1
Triangle ABC has angle measures as noted below. Please note this triangle is not drawn to scale, and the longest leg of the figure may not be the longest leg of the actual triangle.
You will need to use the expressions for the angles given below.
m∠A) 3(x + 5)
m∠B) 5x+15
m∠C) 7x
Identify the angle relationship and setup your equation with the given expressions.
What is the value of x? Show your work.
What is the measure of angle A, B, & C? Show your work and make sure to identify which is which.
GIVING 70 POINTS FOR RIGHT ANSWER NEED ASAP (please and ty)
Answer:
m∠A = 45°;m∠B = 65°;m∠C = 70°.-----------------------------------
Recall triangle angle sum property, the sum of three interior angles is 180°.
Add up the three angle measures, then solve the equation for x:
m∠A + m∠B + m∠C = 1803(x + 5) + 5x + 15 + 7x = 1803x + 15 + 12x + 15 = 18015x + 30 = 18015x = 150x = 10Substitute the value of x and find the value of each angle:
m∠A = 3(10 + 5) = 3(15) = 45m∠B = 5*10 + 15 = 50 + 15 = 65m∠C = 7*10 = 70Need this for a math lesson
Answer:
maximum score = 92
Step-by-step explanation:
the maximum score is the largest value in the data set.
maximum score = 92
An experiment consists of tossing a coin and casting a die then observing the outcomes. Describe an appropriate sample space for this experiment.
A fair coin and a fair six-sided die, the sample space can be represented as:
{ (H,1), (H,2), (H,3), (H,4), (H,5), (H,6), (T,1), (T,2), (T,3), (T,4), (T,5), (T,6) }
where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.
The sample space for this experiment can be described as the set of all possible outcomes of the coin toss and die cast. One way to represent the sample space is to use the Cartesian product of the sample space for the coin toss and the sample space for the die cast.
where H represents heads and T represents tails for the coin toss, and the numbers 1 through 6 represent the numbers on the die.
Each element in this sample space represents a possible outcome of the experiment, where the first element represents the outcome of the coin toss and the second element represents the outcome of the die cast. This sample space contains 12 possible outcomes, each with an equal probability of 1/12.
For such more questions on sample space
https://brainly.com/question/10558496
#SPJ4
what are 3 ways to solve 26x14
Answer:
i think this the answer
Step-by-step explanation:
26×14=ans
20×14+6×14=the same answer
10×26+4×26=same answer
how many slices of pizza did he eat
Answer: The answer is 3 slices
Step-by-step explanation:
if you cut a pizza into 12 peices and devide it by 4 people each person gets 3
In the World of Numbers, there are many number-machines, which work in the following way: the machine adds the two beginning digits of the number and replaces them by their sum. For example, beginning with the number 87312 and using six machines we obtain:
87312-15312-6312-912-102-12-3
How many such machines should be used in order to get to the number 450 from the number 900?
The number of machines used in order to get to the number 450 from the number 900 is 9.
What is an expression?An expression contains more than one term with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
900 to 450
We need a number of machines such that 450 is the last output starting from 900.
Now,
If we subtract 50 from each consecutive number we get,
900, 850, 800, 750, 700, 650, 600, 550, 500, 450
So,
We use 9 machines to get 450 from 900.
Thus,
9 machines should be used in order to get to the number 450 from the number 900.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ9
What is 5’7 in cm
Please can I have help
Step-by-step explanation:
Sure, I'd be happy to help!
5 feet 7 inches is equivalent to 170.18 cm.
The prices and weights of three boxes of cereal are shown below.
Brand A: $1.99 for 12 ounces Brand B: $2.29 for 16 ounces Brand C: $2.99 for 18 ounces
If you choose among these three boxes, what is the lowest unit price, in dollars, you can pay? If necessary, round your answer to the nearest cent.
Answer:
Brand b
Step-by-step explanation:
brand a is 0.165 per ounce
brand b is 0.143 per ounce
brand c is 0.166 per ounce
A charity needs to report its typical donations received. The following is a list of the donations from one week.
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 45.2 is the most accurate to use to show that they need more money.
The median of 49 is the most accurate to use, since the data is skewed.
The mean of 49 is the most accurate to use to show that they have plenty of money.
The mean of 45.2 is the most accurate to use, since the data is skewed.
The measure of center should the charity use to accurately represent the data is The mean of 49 is the most accurate to use to show that they have plenty of money, the correct option is C,
What are mean and median?The mean is the average value which can be calculated by dividing the sum of observations by the number of observations
Mean = Sum of observations/the number of observations
Median represents the middle value of the given data when arranged in a particular order.
We are given that;
The list of donation is as follows
11, 18, 35, 39, 45, 45, 46, 47, 49, 49, 50, 50, 50, 50, 56, 57, 58, 59
Now,
Mean is the middle term of the data
Here,
Middle term of data=49
Therefore, the mean of the given list will be 49.
Learn more about mean and median;
https://brainly.com/question/17060266
#SPJ1
An approximate solution to an equation is found using this iterative process
a) The values are given as follows:
i) x1: -0.5.
ii) x2: -0.280125.
b) The solution of the equation is of: -0.25410169644.
How to calculate the valueThe equation in this problem is given as follows:
y = (x³ - 1)/4.
The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.
Then the values are given as follows:
x1 = -1 -> attributed.
x2 = ((-1)³ - 1)/4 = -0.5.
x3 = ((-0.5)³ - 1)/4 = -0.28125.
x4 = ((-0.281255)³ - 1)/4 = -0.25556212524.
x5 = ((-0.25556212524)³ - 1)/4 = -0.25417281837
x6 = ((-0.25417281837)³ - 1)/4 = -0.25410513385
x7 = ((-0.25410513385)³ - 1)/4 = -0.25410185521.
x8 = ((-0.25410185521)³ - 1)/4 = -0.25410169644. -> difference less than six decimal places.
Learn more about iterations on
https://brainly.com/question/29722121
#SPJ1
An approximate solution to an equation is found using this iterative process.
Xₙ₊₁= (Xₙ)³ - 1 / 4 and x₁= -1
a)
(i) Work out the value of x₂
(ii) Work out the value of x₃
b) Work out the solution to 6 decimal places
PLS HELP! Write 5x = -2y + 6 in slope intercept form and explain your answer
Answer: 5/2x-3
Step-by-step explanation: you would subtract 6 from both sides.
5x = 2y + 6
-6 -6
6-6=0 so they would cross out. and you can't subtract 5x from 6 because they aren't like terms. Your new equation would look like 5x-6 = 2y.
Now you need to get the y alone. To do that you need to divide everything by 2 so that the 2y crosses out. 5x-6 = 2y
-----------------
2 2 2
I'm trying to visually show it sorry if it looks weird. one you divide everything. (5/2) (-6/2) (2/2) you'll need to clean everything up.
Since you can't simply 5/2 leave it as a fraction. Which makes your answer: 5/2x - 3 = y or y = 5/2x - 3
In order to keep the numbers in the proper place-value column
The order of the place value in increasing order is equal to units , tens , hundreds , thousands , ten-thousand and so on.
The value of every digit present in any number depends on the position of the digit in a number.The place of the digit in the number represents its place value of the digit in a number.Starting position of a digit is ones or units.After unit the place value is tens.In ascending order the place value of all the digit in any given number is represented as units , tens , hundreds , thousands , ten- thousands, so on.Therefore, the order of the place value in ascending order of the place of the digit is given by units , tens , hundreds , thousands , ten-thousand and so on.
The given question is incomplete, I answer the question in general according to my knowledge:
What is the order of the place value ?
Learn more about place value here
brainly.com/question/27734142
#SPJ4
