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
The median wait time for Speed Slide is
2 minutes longer than the median
wait time for Wave Machine. The IQR for
both rides is 6 minutes.
Express the difference in the medians as a
multiple of the IQRs.
The difference in the medians is
the IQR.
times
The difference in the medians is 1/3 times the IQR.
How to calculate the interquartile range (IQR)?Mathematically, interquartile range (IQR) of a data set and it is typically calculated as the difference between the first quartile (Q₁) and third quartile (Q₃):
Interquartile range (IQR) for Speed Slide = Q₃ - Q₁
Interquartile range (IQR) for Speed Slide = 12 - 6
Interquartile range (IQR) for Speed Slide = 6.
For the interquartile range (IQR) for Wave Machine, we have:
Interquartile range (IQR) for Wave Machine = 14 - 8
Interquartile range (IQR) for Wave Machine = 6.
For the required expression, we have the following:
2 = 6x
x = 2/6
x = 1/3.
Read more on interquartile range (IQR) here: brainly.com/question/17658705
#SPJ1
Answer:
The difference in the medians is 1/3 times the IQR.
Step-by-step explanation:
hope this helps!
HELP ASAP WILL GIVE BRAINILEST
Answer:
A, D
Step-by-step explanation:
8/5 + 2/5y
Factor out the 2/5, which gives you:
2/5(4 + 1y) = 2/5(5 + y)
or,
Factor out 1/5, which gives you:
1/5(8 + 2y)
So both A and D are equivalent
Is Paul's Online Math Notes a good enough source for self-teaching calculus 3 and ODE?
Yes, Paul's Online Math Notes is a good enough source for self-teaching calculus 3 and ODE.
The site is well-organized, with clear explanations and plenty of examples and practice problems. It also includes a section on differential equations, which is helpful for those studying ODE.
However, it is always a good idea to supplement your learning with additional resources, such as textbooks, online videos, and practice problems from other sources.
This will help you gain a deeper understanding of the material and ensure that you are well-prepared for exams.
To know more about differential equations click below:
https://brainly.com/question/14620493#
#SPJ11
Solve the
y - 4x = 7
simultaneous equations
y = x² + x - 3
Solve for x
Please help urgent
The measure of the angle using the sine rule will be 50.28 degrees.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The value of the angle 'x' is given by the sine of angle 'x'. Then the equation is given as,
sin x = 30 / 39
x = sin⁻¹(30 / 39)
x = 50.28°
The measure of the angle using the sine rule will be 50.28 degrees.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ1
Given the sequence 2 and one half comma 2 and one third comma 2 and one fourth comma and continues comma what is f (n)?
f of n equals 2 plus 1 over the quantity 1 plus n
f of n equals 2 plus 1 over n
f of n equals n plus 1 over the quantity 1 plus n
f of n equals 3 minus 1 over n
The function f(n) that generates this sequence is 2 + 1/(n+1). This function takes an input of n and outputs the corresponding term in the sequence.
What is an arithmetic sequence?
A progression or sequence of numbers known as an arithmetic sequence maintains a consistent difference between each succeeding term and its predecessor. The common difference in that mathematical progression is the constant difference.
Here, we have
Given: the sequence 2 and one-half comma 2 and one-third comma 2 and one-fourth comma and continues.
Each term in the sequence is 2 plus a fraction where the denominator is one more than the term number. For example:
In the first term, n=1, and the fraction is 1/2
In the second term, n=2, and the fraction is 1/3
In general, the n-th term in the sequence will have the fraction 1/(n+1).
Hence, the function f(n) that generates this sequence is 2 + 1/(n+1). This function takes an input of n and outputs the corresponding term in the sequence.
To learn more about the arithmetic sequence from the given link
https://brainly.com/question/6561461
#SPJ1
What is the area of the parallelogram?
Area of the parallelogram is 65 square meter.
What is Parallelogram?Parallelogram is a type of polygon with four sides, four angles and four vertices. It is a type of Quadrilateral.
Opposite sides are parallel, and the opposite sides and opposite angles are equal.
Area of the parallelogram = Base × Height
From the figure,
Length of base = AB = 3 m + 10 m = 13 m
Height is also given as 5 m.
Area of the parallelogram ABCD = 13 m × 5 m
= 65 m²
Hence the required area of the parallelogram is 65 m².
Learn more about Parallelogram here :
https://brainly.com/question/19187448
#SPJ1
Can 0 degree and 90 degree form a pair of complementary non adjacent
A 0 degree and 90 degree can form a pair of complementary angles, but 90 degree and an angle that is not adjacent cannot form a pair of complementary angles.
In mathematics, complementary angles are two angles whose sum is 90 degrees. So, if one angle is 0 degrees, the other angle would have to be 90 degrees in order for them to be complementary. However, if one angle is 90 degrees, it cannot form a pair of complementary angles with an angle that is not adjacent (i.e. next to it).
To understand why, consider a straight line, which is equivalent to 180 degrees. If one angle is 90 degrees, it takes up half of the line, leaving the other half for the other angle.
If the other angle is not adjacent, it would have to be placed somewhere on the other half of the line, which is already taken up by the 90 degree angle. Therefore, the two angles cannot add up to 90 degrees and cannot be complementary.
To learn more about complementary click on,
https://brainly.com/question/1425570
#SPJ4
the number of widgets that a manufacturing plant can produce varies jointly as the number of workers and the time that they have worked. find the constant of proportionality k yo 2 decimal places if 575 workers work 14 hours and can produce 32280.5 widgets.
The constant of proportionality is 4.01.
The number of widgets that can be produced is 42,225.30.
What is the constant of proportionality?
Joint variation is when a variable depends on more than one variable.
The equation that represents joint variation is:
z = kwt
Where:
z = dependent variable k = constant of proportionality w = first independent variable t = second independent variable32280.5 = k x 14 x 575
k = 32280.5 / (14 x 575)
k = 4.01
Number of widgets that can be produced by 585 workers in 18 hours
w = 4.01 x 18 x 585
w = 42,225.30
To learn more about joint variation, please check: https://brainly.com/question/30466316
#SPJ1
Jeremy needs to buy soccer supplies for his team. He bought 3 packs of shin guards and 2 soccer balls. He then bought 5 packs of shin guards and 3 soccer balls $76.45. What is the cost for a soccer ball?
Based on a system of equations, the cost of a soccer ball is $15.50.
What is a system of equations?A system of equations is two or more equations solved concurrently or at the same time.
A system of equations can also be described as simultaneous equations.
Shin Guards Soccer Balls Total Cost
First purchase 3 2 $48.97
Second purchase 5 3 $76.45
Let the cost of shin guards per unit = x
Let the cost of soccer balls per unit = y
Equations:Equation 1: 3x + 2y = 48.97
Equation 2: 5x + 3 y = 76.45
Multiply Equation 1 by 1.5:
Equation 3: 4.5x + 3y = 73.455
Subtract Equation 3 from Equation 2:
5x + 3 y = 76.45
-
4.5x + 3y = 73.455
0.5x = 2.995
x = 5.99
Substitute x = 5.99 in Equation 1:
3(5.99) + 2y = 48.97
17.97 + 2y = 48.97
2y = 31
y = 15.5
= $15.50
Learn more about simultaneous equations at brainly.com/question/148035.
#SPJ1
Question Completion:Jeremy needs to buy soccer supplies for his team. He bought 3 packs of shin guards and 2 soccer balls for $48.97.
What is the Surface Area of this prism?
Answer:
164
Step-by-step explanation:
4 x 10 = 40
40 x 2 = 80 (there are two sides with the same measurements)
---
3 x 4 = 12
12 x 2 = 24 (there are two sides with the same measurements)
----
10 x 3 = 30
30 x 2 = 60 (there are two sides with the same measurements)
60 + 80 + 24 = 164
Write an equation that represents the relationship between the distance the car
has traveled in miles, d, and the amount of gas left in the tank in gallons, x.
Answer: The relationship between the distance a car has traveled in miles, d, and the amount of gas left in the tank in gallons, x, can be represented by the equation:
d = r * m
where r is the fuel efficiency of the car in miles per gallon and m is the amount of gas consumed in gallons.
Since x is the amount of gas left in the tank, we can write:
x = m_0 - m
where m_0 is the initial amount of gas in the tank.
Combining the two equations, we get:
d = r * (m_0 - x)
This equation represents the relationship between the distance the car has traveled in miles, d, and the amount of gas left in the tank in gallons, x.
Step-by-step explanation:
what is the perimeter of the parallelogram?
The perimeter of the parallelogram is 24 units
How to determine the perimeter of the parallelogramThe formula for calculating the perimeter of a parallelogram is given as;
P = 2( a+ b)
Given that the parameters are;
P is the perimeter of the parallelograma is the length of a sideb is the length of the height of the parallleogramFrom the diagram shown, we have the values as the distance between points, we have ;
a = 4 - 1
a = 3
b = 4
Substitute the values
Perimeter , P = 2(3×4)
expand the bracket
Perimeter, P = 24 units
Learn about parallelogram on:
https://brainly.com/question/10744696
#SPJ1
Use Unit Cubes to Build
Solid Figures
Open Ended Describe two different right rectangular
prisms that can be made using 24 unit cubes.
The number of rectangular prisms that can be made by 24 unit cubes, two having dimensions mentioned below.
1. 3 units by 4 units by 2 units.
2. 2 units by 3 units by 4 units
What are Units ?To measure and compare various things we use one term which is known as a unit. When all of the measuring units are the same, comparison is simple. Depending on their intended usage, different units can be categorized.
For example, for length measurement we use units like:- meter, centimeter, inch, miles.
One possible right rectangular prism that can be made using 24 unit cubes has dimensions of 3 units by 4 units by 2 units.
This means it has 3 layers of 4 unit cubes each, with each layer having 2 rows of 3 unit cubes.
Another possible right rectangular prism that can be made using 24 unit cubes has dimensions of 2 units by 3 units by 4 units.
This means it has 2 layers of 3 unit cubes each, with each layer having 4 rows of 2 unit cubes.
To know more about Units check:
https://brainly.com/question/30168372
#SPJ9
A furniture store donated a percent of every sale to hospitals. The total sales were $7,200 so they store donated $288. What percent of $7,200 was donated to hospitals?
Answer:
Step-by-step explanation:
x% OF 7200 = 288
x/100*7200 = 288
x=288/72=4
4% was donated
How many 65 kg in pounds ?
65 kg is equivalent to approximately 143.3 pounds and both are unit of measurement of weight.
To convert kilograms to pounds, we multiply the weight in kilograms by the conversion factor of 2.20462. Therefore, to convert 65 kg to pounds, we can multiply 65 by 2.20462, which gives us approximately 143.3 pounds.
It's important to note that kilograms and pounds are both units of weight, but they are used in different parts of the world. Kilograms are the standard unit of weight in most countries, while pounds are commonly used in the United States and some other countries.
Converting between units of measurement is a valuable skill, especially when communicating or traveling internationally. Knowing how to convert from kilograms to pounds, or vice versa, can help you understand weight measurements in different contexts.
Online conversion tools or calculators can be useful resources to quickly and accurately convert between units of measurement as needed.
To know more about conversion factor click on below link:
brainly.com/question/28366871#
#SPJ11
Steven multiplies all the integers from -99 to -90, including -99 and -90 Should his answer be positive or negative? Explain your thinking.
The product of all integers from -99 to -90, including -99 and -90, will be positive.
How to find the sign of the productThe product of an even number of negative integers will be positive, while the product of an odd number of negative integers will be negative.
In this case, we have 10 negative integers, which is an even number. Therefore, the product of all these integers will be positive.
However, the product of a positive and a negative integer is negative, so we need to keep track of the sign changes that occur when we multiply the integers.
We can start by multiplying the two extremes, -99 and -90. The product of these two integers is positive, so at this point, the answer is positive. However, as we multiply more and more of the integers between -99 and -90, we'll eventually reach an even number of positive integers
Learn more about positive and negative integers at:
https://brainly.com/question/19258349
#SPJ1
I need help with the image below
The value of x is -29
How to determine the valueIt is important to note that;
a diameter of a circle will always pass through the centertwo diameters of a circle will necessarily intersect at the centerWe have the diameters as;
-9x + 104 and 3x + 82
Also note that angles at the center is 360 degrees
This is then represented as;
-9x + 104 + 3x + 82 = 360
collect the like terms
-6x = 360 - 186
subtract the values
-6x = 174
Make 'x' the subject of formula, we get;
x = 174/-6
x = -29
Learn about diameters at: https://brainly.com/question/390660
#SPJ1
How do you find the percentage of yield in caculator?
To find the percentage of yield in a calculator, you can follow these steps:
1. Determine the actual yield and the theoretical yield of the reaction. The actual yield is the amount of product that was actually produced in the reaction, while the theoretical yield is the amount of product that should have been produced based on the balanced chemical equation.
2. Divide the actual yield by the theoretical yield to find the decimal form of the percentage yield.
3. Multiply the decimal form of the percentage yield by 100 to find the percentage yield.
For example, if the actual yield of a reaction is 15 grams and the theoretical yield is 20 grams, the percentage yield would be:
(15/20) x 100 = 75%
Therefore, the percentage yield of the reaction is 75%.
To know more about chemical equation click below:
https://brainly.com/question/30087623#
#SPJ11
how much 8 oz in ml?
The 8 fluid ounces(oz) of water is equivalent to 236.588 milliliters.
To convert 8 ounces (oz) to milliliters (ml), we need to know the density of the substance. The conversion factor will vary depending on what we are measuring. Here are some common conversion factors:
1 fluid ounce of water weighs 29.5735 grams, which is equivalent to 29.5735 ml.
1 fluid ounce of milk weighs 30 grams, which is equivalent to 28.4131 ml.
1 fluid ounce of honey weighs 21 grams, which is equivalent to 20.0784 ml.
For example, let's say we want to convert 8 fluid ounces of water to milliliters. We know that 1 fluid ounce of water weighs 29.5735 grams, and that 1 milliliter of water also weighs 1 gram (since water has a density of 1 g/mL). Therefore, we can use the following formula to convert 8 fluid ounces of water to milliliters:
8 oz x 29.5735 g/oz x 1 mL/1 g = 236.588 ml
So 8 fluid ounces of water is equivalent to 236.588 milliliters.
To learn more about ounces please click on below link
https://brainly.com/question/29374025
#SPJ4
Last month,Jodie spent $178 on groceries,$238 on utilities,and $1,750. How much did Jodie spend in all?
Jodie spent a total of $2,166 last month on groceries, utilities, and other expenses.
To find out how much Jodie spent in all, we need to add up all of her expenses. We can do this by using the following formula:
Total expenses = Groceries + Utilities + Other expenses
Plugging in the given values, we get:
Total expenses = $178 on groceries + $238 on utilities + $1,750
Adding these values together, we get:
Total expenses = $2,166
Therefore, Jodie spent a total of $2,166 last month.
Here to learn more about Expenses at the link https://brainly.com/question/25169847
#SPJ11
What numbers do i put in the blanks
The solutions of the system are y = -8 and x = 9.
What is the system of equations?One or many equations having the same number of unknowns that can be solved simultaneously are called simultaneous equations. And the simultaneous equation is the system of equations.
Given:
A system of equations,
5x + 6y = -3 {Equation 1}
8x + 8y = 8 {Equation 2}.
Multiply 8 into equation 1 and multiply by 5 into equation 2,
and subtract the equation,
we get,
40x + 48y - 40x - 40y = -24 - 40
8y = -64
y = -8 and x = 9
Therefore, the solutions are y = -8 and x = 9.
To learn more about the system of equations;
brainly.com/question/13729904
#SPJ1
Which statement is true of triangles FGH and F'G'H?
Step-by-step explanation:
I suspect this to be a trick question.
because 2 statements are correct :
B and C.
according to the definition, two triangles are similar if their corresponding angles are congruent (identical) and corresponding sides are proportional (the ratio between the length of corresponding sides is equal for all pairs of corresponding sides, or, in other words, there is one scale factor for all 3 pairs of corresponding sides).
in fact, each criteria alone is sufficient.
if all 3 corresponding angles are identical between both triangles, the corresponding pairs of sides will be proportional.
if all 3 pairs of corresponding sides are proportional, then the corresponding angles are identical.
and the triangles are similar.
The princess Trail is 2.5 miles long. How many feet long is the princess Trail? Asp
princess trail is 13200 foot long
thank you
Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.
Answer:
Step-by-step explanation:
y=9700(0.909)^x
# If the base of an exponential function is an element of the set (0,1) the function is decreasing as the value of 'x' is increasing from negative infinity to positive infinity.
the function y=9700(0.909)^x is an exponential function with a coefficient 9700 and base 0.909, as we increase the value of x from negative infinity to positive infinity, the value of y decreases. So the change between two consecutive 'y' values as 'x' increases indicate decay rather than growth.
And it can be written as y=9700(1-0.091)^x, therefore the percentage decrease is 9.1%
Why is verifying trig identities so hard?
Verifying trig identities can be difficult because they involve manipulating complex equations with multiple trigonometric functions that have various associated angles and coefficients.
For example, the Pythagorean Identity states that sin2θ + cos2θ = 1, which must be verified by using the identity sin2θ = 2sinθcosθ and substituting it into the equation. This results in a complex equation: 2sinθcosθ + cos2θ = 1, which must then be simplified and rearranged in order to show that it is true for all values of θ. Furthermore, trig identities can involve multiple steps that involve multiple functions and angles, which can make verifying them even more difficult.
Learn more about identity here:
https://brainly.com/question/30339186
#SPJ4
What is the unit cost of trail mix?
The unit cost per pound of trail mix, in dollars is $3.75.
How to calculate Unit price of an item?
To calculate the unit price of an item, you have to understand that unit price means price per unit. To find the unit price we divide the total cost by the amount of items we are given in the question.
Given :
15x - 4y = 0
Where ,y is total cost in dollars of the trail mix and x is the number of pounds bought.
To calculate , unit cost of trial mix , we need to calculate y
Therefore , from equation 15x - 4y = 0
We can say that,
y =(15/4)x
For unit cost we need to substitute x = 1
Thus, y = (15/4)*1
or
y = (15/4)
or
y = 3.75
Hence, the unit cost per pound of trail mix, in dollars is $3.75.
Learn more about Unit Cost at:
https://brainly.com/question/26959824
#SPJ1
2. Tell whether each function is linear. If so, graph
the function.
2y = -4x
The function 2y = -4x is linear and the graph is given below.
What is Linear Function?A linear function can be defined as the function whose graph is a straight line. It can also be defined as the function with one or more variables and the exponent of the variable is 1.
Here the given function is 2y = -4x.
The function is linear since the exponent of the two variables x and y are 1.
This can be written as,
y = -4x / 2
y = -2x
This is a proportional function with slope -2.
Graph will be a decreasing function.
The points on the graph includes (-2, 4), (-1, 2), (0, 0), (1, -2) and (2, -4).
Hence the graph of the function is given below.
Learn more about Linear Functions here :
https://brainly.com/question/21107621
#SPJ9
Look at the first two systems of equations from the table
above.
y=2x-1
y=x+1
and
y = 4x +3
y=2x+3
Notice that in both systems the slopes are different.
However, in one of the systems, the y-intercepts of the
two equations are different, but in the other system, the y-
intercepts are the same. The table above states that both
of these systems has only one solution.
How is that possible?
Answer:
Let -5x+y=-3 be the first equation, and 3x-8y=24 be the second. Let's manipulate the first equation by adding 5x to both side; resulting in y=-3+5x, or 5x-3. Now let's plug in 5x-3 for wherever y has been in the second formula. 3x-8(5x-3)=24. This is now pretty straightforward to solve for x. We distribute the 8 into (5x-3) and get 3x-40x-24=24. -48=27x. x=-48/27, x=-16/9.
Now let's plug in the x for either one of the equations to get y. 3(-16/9)+8y=24. -16/3+8y=24. 8y=24+16/3. 24y=72+16. 24y=88. y=88/24, y=11/3.
Step-by-step explanation:
There is a sales tax of $25 on an item that costs $310 before tax. The sales tax on a second item is $10. How much does the second item cost before tax?
The percentage of sales tariff is 8.06%. Then the second item cost before the tariff will be $124.
What is the percentage?Any product's quantity is given as if it were a percentage of one hundred. The ratio can be written as 100. The word "%" means "100%" in English. The sign for it is the letter "%".
The percentage is given as,
[tex]\text{Percentage (P) }= \dfrac{ \text{Final value - Original value}}{\text{ Original value }} \times 100[/tex]
An item that costs $310 before the tariff carries a $25 sales tariff. The sales tax % is then provided as,
[tex]\rm P = \left ( \dfrac{25}{ 310} \right ) \times 100[/tex]
P = 0.0806 x 100
P = 8.06%
The sales tax on a second object is $10. Then the second object cost before the tariff is given as,
⇒ $10 / 0.0806
⇒ $124
The percentage of sales tariff is 8.06%. Then the second item cost before the tariff will be $124.
More about the percentage link is given below.
https://brainly.com/question/8011401
#SPJ9