An autonomous first order ordinary differential equation is any equation of the form: dy/dt = f(y).
1. Stable: The equilibrium solution y(t) = c is stable if all solutions with initial conditions y0 ‘near’
y = c approach c as t → ∞.
2. Unstable: The equilibrium solution y(t) = c is unstable if all solutions with initial conditions y0 ‘near’ y = c do NOT approach c as t → ∞.
3. Semi-stable: The equilibrium solution y(t) = c is semistable if initial conditions y0 on one side of c lead to solutions y(t) that approach c as t → ∞, while initial conditions y0 on the other side of c do NOT approach c.
Find the equilibrium points for the differential equation (1) and determine whether each is asymptotically stable, semistable, or unstable.
The graph of y0 as a function of y, and the phase line. (It’s important that α is positive – if it were negative, we’d have very different behavior).
We can see that there are two equilibrium solutions: y = 0, which is unstable, and y = 1, which is stable.
To learn more about differential equation visit : brainly.com/question/14620493
#SPJ4
A tank can be filled by an inlet pipe in 12 hours and emptied by a drain pipe in 16 hours. How long will it take to fill the tank if both pipes are left open?
It will take 48 hours, to fill the tank if both pipes are left open simultaneously.
We are given the following data -
The time taken to fill the tank by inlet pipe = 12 hrs
so, the rate of filling = 1/12
The time taken to empty the tank by drain pipe = 16 hrs
so, the rate of emptying = - 1/16
Therefore, the total work done by both pipes can be given by the following formula -
(1/rate of filling) + (1/rate of emptying) = (1/rate of net change)
1/12 + (-1/16) = (1/Rn)
Therefore, (1/Rn) = 1/12 - 1/16 = 1/48
To find how long it will take to fill the tank, we need to find the reciprocal of the rate of net change:
1/Rn = 1/(1/48)
Rn = 48
So it will take 48 hours, to fill the tank if both pipes are left open.
Read more about pipes and cisterns:
brainly.com/question/27864377
#SPJ4
henry the donkey has a very long piece of pasta. he takes a number of bites of pasta, each time eating 3 inches of pasta from the middle of one piece. in the end, he has 10 pieces of pasta whose total length is 17 inches. how long, in inches, was the piece of pasta he started with?
The piece of pasta he started with was 34 inches long.
Defining a problem, identifying its underlying cause, locating, ranking, and selecting potential solutions, as well as putting those ideas into practice, are all steps in the issue-solving process. Diagnose the circumstance to keep your attention on the issue and not merely its symptoms.
Let x be the length of the original piece of pasta.
After taking bites, he has (x - 3) pieces of pasta, each 17/10 inches long.
So, the total length of all pieces of pasta is (x - 3) * 17/10 = 17 inches.
Therefore, x = 10 * 17/7 + 3 = 34 inches.
To learn more about inches here:
https://brainly.com/question/16311877
#SPJ4
Find x, y, and z. Enter your answer in simplest radical form.
Enter the correct values in the boxes.
x=?
y=?
z=?
2. Use a number line to show the temperature rising by 20 degrees and dropping by 20 degrees.
3. Use a number line to find the temperature if it was -7 degrees today, and rises by 20 degrees tomorrow.
Answer:
see graph attached
Step-by-step explanation:
Dustin’s math classroom has 2 bulletin boards side by side. The teacher said the length of one
board is 1. 25 yards, and the other is 1. 75 yards. What is the total length in feet of the two
bulletin boards side by side?
The total length in feet of the two bulletin boards side by side is 9 feet.
The total length of the bulletin boards when calculated side by side will be done using addition operation. The expression that will form for calculation is -
The total length = length of one bulletin board + length of second bulletin board
Keep the values in formula -
The total length = 1.25 + 1.75
Performing addition on Right Hand Side of the equation
The total length of the two bulletin boards = 3 yards
The total length in feet = 3 × (3 feet)
Performing multiplication
Total length = 9 feet
The total length in feet is 9 feet.
Learn more about length calculations -
https://brainly.com/question/28108430
#SPJ4
A publishing industry report predicts that magazine subscriptions will drop by 8% each year,
If this prediction is correct, then how many subscribers will a magazine with 85,630
subscribers have in 8 years?
Suppose the prediction of an annual drop in magazine subscriptions of 8% is correct. In that case, the number of subscribers that a magazine with 85,630 subscribers will have in 8 years, using an exponential function, is 43,947.
What is an exponential function?The exponential function is an expression in the form of f(x) = bˣ, where the b constant is called the base and the x variable is called the exponent.
Exponential functions may describe exponential growth or exponential decay.
Exponential decay refers to a decrease or drop, where the decay rate is known.
The annual drop in magazine subscriptions = 8%
The number of current magazine subscribers = 85,630
The number of years for the prediction = 8 years
Decay factor = (1 - 8%) = 0.92
The number of magazine subscribers in 8 years = 85,630 x 0.92^8
= 85,630 x 0.5132189
= 43,947
Learn more about exponential functions at https://brainly.com/question/2456547
#SPJ1
The Lockheed Martin F-22
Military Raptor can travel
3,000 miles in 2 hours.
What is it's top speed?
Answer:
1,500
Step-by-step explanation:
It's preetty fast but it cannot be the record holder of " Lockheed SR-71 Blackbird " Which it's top speed i 2,100 miles per hour !!
Francesca bought a dress to wear to a wedding. The sales tax for the dress is 6%. She also paid $35, which was not taxed, to have the dress altered. If Francesca paid the store a total of $126.16. Which equation can you solve to determine the price of the dress?
The equation that can be used to determine the price of the dress
is x + 0.06x + 35 = 126.16.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Assuming the cost of the dress Francesca bought to be 'x'.
We know, 6% = 0.06 in decimal and She also paid $35 which was not taxed to have the dress altered.
Therefore, The equation to determine the cost of the dress would be,
x + 0.06x + 35 = 126.16.
1.06x = 126.16 - 35.
1.06x = 91.16.
learn more about numerical expressions here :
https://brainly.com/question/29199574
#SPJ1
Nasim went to the store to buy some coffee. The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount. With the coupon, how much would Nasim have to pay to buy 3 pounds of coffee? Also, write an expression for the cost to buy p pounds of coffee, assuming at least one pound is purchased.
Nasim have to pay for 3 pounds of coffee is $10.75.
The expression for p pounds of coffee is 4.75p - 3.5.
What is Expression ?
A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
The price per pound of the coffee is $4.75 per pound and he has a coupon for $3.50 off the final amount.
and, Nasim have to pay to buy 3 pounds of coffee.
So, Nasim have to pay for 3 pounds of coffee.
= 3 x 4.75 - 3.50
= 14.25 - 3.5
= $10.75
and, the expression for p pounds of coffee is
= 4.75p - 3.5
Learn more about Expression here:
https://brainly.com/question/14083225
#SPJ1
Mrs. Hitchcock gave a test to each of her two classes and calculated the averages. Her Theater class has a standard deviation of 18. 7, and her British Literature class has a standard deviation of 1. 2.
Which class most likely larger? Why?
A the British Literature class, because the standard deviation is lower
B the Theater class, because the standard deviation is higher
C the British Literature class, because the standard deviation is higher
D the Theater class, because the standard deviation is lower
(A) The British literature class is most likely larger, because the standard deviation is lower.
A high standard deviation suggests that the observed data is very variable around the mean. This suggests that the observed data is widely dispersed. Instead, a modest or low standard deviation would suggest that the majority of the observed data is closely packed around the mean.
The standard deviation measures the degree of dispersion of a set of data. Each data point is compared to the average of all the data points, and standard deviation gives a determined value that indicates whether the data points are clustered together or dispersed.
Hence, when standard deviation is lower the class is most likely to be larger in number.
To learn more about standard deviation here:
https://brainly.com/question/23907081
#SPJ4
Find perimeter and area of the rectangle simplify completely.
The perimeter of the rectangle = (6 x + 8) meters. and the Area is
2x² +10x.
How to find perimeter of rectangle?step 1: The first side's length is (x+ 5) metres, while the second side's breadth is (2x+ 1) metres.
Now, the RECTANGLE'S PERIMETER = 2 (LENGTH + WIDTH).
Here, perimeter is equal to 2 ((x+ 5) m + (2x + 1) m) or 2 (x + 5 + 2x +1) = 2(3x + 4) = 6x + 8
Therefore, the rectangle's perimeter is equal to (6 x + 8) metres.
step 2:
Area of a rectangle equals length times breadth
Given:
Size = x+5
Thickness = 2x+1
Area of rectangle = length breadth = (x+5) (2x+1) = 2x (x+5) (2x+1) =2x2+5+4x+1 =2x2+10x, according to the query.
The area is therefore 2x2 + 10x.
To learn more about Perimeter and Area refers to;
https://brainly.com/question/13811125
#SPJ1
the feather on an arrow form two congruent parallelograms. the parallelograms are reflection of each other over the line that contains their shared side show that m
Question Down Below: (Please i really need to complete this right now) Please anyone :(
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
How to calculate the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Let x = number of vegetarian meals
Let y = number of meats.
The inequality to represent the constraints will be:
x + y ≥ 325
x + 2y = 600
In this case, the daily budget is 600.
Subtract the equations
y = 275
Number of meats = 275
Number of vegetarian meals = 325 - 275 = 50
Learn more about inequalities on;
brainly.com/question/24372553
#SPJ1
given f(x) = -x2 - x, find f(-9)
Answer:
-72
Step-by-step explanation:
Assuming it is -x^2 - x and not (-x)^2, then you simply plus in -9 for x:
-(-9)^2-(-9) = -72
At 6 a. M. , the temperature is 19. 4°C. Between 6 a. M. And noon, the temperature rises 3. 8°C. Between noon and 6 p. M. , the temperature falls 2. 5°C.
How much greater is the temperature at 6 p. M. Than it was at 6 a. M. ?
1. 3°C
6. 3°C
13. 1°C
20. 7°C
The temperature at 6 PM at greater than morning temperature at 6 AM by 1.3° C.
We know initially the temperature is 19.4° C.
The new temperature at noon will be = Temperature at 6 AM + temperature after noon
Keep the values
The new temperature at noon will be = 19.4 + 3.8
Performing addition
The new temperature at noon will be = 23.2° C
Temperature at 6 PM = Temperature at noon - temperature fall between noon and 6 PM
Keep the values
Temperature at 6 PM = 23.2 - 2.5
Performing subtraction
Temperate at 6 PM = 20.7° C
The difference between the temperature = 20.7 - 19.4
Performing subtraction
The difference between the temperature is 1.3° C.
Learn more about temperature change -
https://brainly.com/question/28551912
#SPJ4
What are the x and y for only
3x+2y=34
Constants are fixed values that never change, whereas variables are values that can change but are often initialized to “0” or another default value because the program's user will supply the actual values.
What is variables?In programming, a variable is a value that may vary depending on outside variables or data that has been provided to the program. A program normally consists of instructions that tell the computer what to do and data that it utilizes while running.
The correct values for the variables x and y are 8 and 5, respectively.
[tex]3 \times 8 + 2 \times 5=34[/tex]
[tex]24 + 10 =34[/tex]
[tex]\frac{1}{2}\times 8+2 \times 5=14[/tex]
[tex]4 + 10 =14[/tex]
Constants and variables are typically categorized as certain data kinds. Each data type specifies and restricts the data's shape.
An integer expressed as a decimal number or a string of text characters with a set maximum length are examples of data types. Each object in object-oriented programming includes the data variables of the class of which it is an instance.
Therefore, The methods of the object are made to deal with the actual values that are presented to it when it is utilized.
Learn more about variables here:
https://brainly.com/question/17344045
#SPJ1
Write 1476 to the nearest 10
Answer:
1480
Step-by-step explanation:
To the nearest 10, is the 10s place. 76 is closes to 80, so round 1476 to 1480. Hope this helps!
Shaggy shaggy Raghu scooby boy doo ok
The original price of a salt lamp is $92 after a 20% discount
Answer: $115
Step-by-step explanation:
92 is the price after a 20% discount, so it is 80% of the original value.
So, solve, 92÷0.80=115
So the original price was $115
pls help fast it due today
Answer:
ch.1 = 12x1.2=14.4
ch.2=10.5x1.2=12.6
ch.3=39.3x1.2=47.16
Step-by-step explanation:
You just have to multiply all the chapters by 1.2
i think if im wrong im sorry
Answer: 14.4, 12.6, 49.16
Step-by-step explanation:
Multiply each number by 1.2
12x1.2=14.4
10.5x1.2=12.6
39.3x1.2=49.16
chapter 1 : 14.4
chapter 2: 12.6
chapter 3: 49.16
Andy is using wooden boards that are 0. 45 feet wide to build a deck. How many rows of boards are needed to completely cover a space that is 21 feet wide?
Andy is using wooden boards that are 0. 45 feet wide to build a deck. The number of rows of boards are needed to completely cover a space is 47 rows of boards.
Divide the total width (21 feet) by the width of each board (0. 45 feet):
21 / 0. 45 = 46. 666666
Round the result up to the next whole number:
47 rows of boards
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each.
To know more about division here
https://brainly.com/question/21416852
#SPJ4
an auto dealer has 8 different cars and 4 different trucks. how many ways are there to select two vehicles?
There are 66 ways to choose two vehicles from the dealer's inventory.
A combination is a grouping of items from a larger set in which the order of the items is irrelevant. In other words, it is a method of selecting a subset of items from a larger set without regard for their order of selection.
The formula C(n, k) = n! / (k! (n - k)!) can be used to calculate the number of combinations.
where n represents the total number of items in the set and k represents the number of items in the combination.
The exclamation mark (!) represents the factorial function, which is the sum of all positive integers up to a certain number.
The number of ways to select two vehicles from 8 cars and 4 trucks is 8 + 4 = 12 vehicles.
To find the number of combinations, we use the formula for combinations, which is:
C(n, k) = n! / (k! (n - k)!)
where n is the total number of vehicles and k is the number of vehicles we want to choose.
So, for n = 12 and k = 2,
we have:
So, putting the value in above formula:
We will get it as:
C(12, 2) = 12! / (2! (12 - 2)!) = (12 * 11) / (2 * 1) = 66
For more questions on Permutation and Combination
https://brainly.com/question/28065038
#SPJ4
Evaluate the following. 4 x 5 - 18 divided 3 - 8
Answer: The answer would be
Step-by-step explanation:
28/3
in decimal form- 9.3 (3 keeps going)
Mixed Number- 9 1/3
Please help!!!
What are some of the important steps to consider when solving an exponential or logarithmic equation? How can identities and logs help you to solve these equations? How are identities and logarithms confusing? Cite examples that help illustrate your ideas, and show steps to solve such equations in your post. Ask clarifying questions about anything you find confusing
Solving exponential and logarithmic equations requires a strong understanding of the properties of exponents and logarithms, as well as the use of logarithmic identities and inverse operations. It is important to simplify expressions and isolate the variable using basic algebraic operations, logarithmic identities, and inverse functions.
When solving exponential or logarithmic equations, there are several important steps to consider:
Simplify the equation using basic algebraic operations, such as multiplication, division, addition, and subtraction.
Isolate the exponential or logarithmic expression on one side of the equation.
Use the properties of exponents or logarithms to simplify the expression, if possible.
Use logarithmic identities such as logarithmic rules and change-of-base formula to simplify the expression.
Solve for the variable by using inverse operations.
Check your answer by substituting it back into the original equation and verifying that both sides are equal.
Identities and logs can be helpful in solving exponential and logarithmic equations because they provide a set of rules that can be used to simplify expressions. For example, logarithmic identities such as log(a * b) = log(a) + log(b) and log(a/b) = log(a) - log(b) can be used to simplify expressions containing products and quotients.
However, identities and logarithms can also be confusing because they involve complex concepts and require a solid understanding of logarithmic properties. This can make solving exponential and logarithmic equations challenging for some students.
To know more on exponential and logarithmic equations
https://brainly.com/question/3181916
#SPJ4
Dylan drove from Liverpool to Sunderland at an average speed of 50 mph for 3 hours and 30 minutes. He then drove from Sunderland to Edinburgh at an average speed of 65 mph for 2 hours. Work out how many miles Dylan travelled in total.
Answer:
305 miles
Step-by-step explanation:
You want to know how far Dylan travelled if he drove 50 mph for 3.5 hours and 65 mph for 2 hours.
DistanceDistance is the product of speed and time. The total distance Dylan travelled will be the sum of lengths of the legs of his trip.
distance = speed · time
total distance = speed1 · time1 + speed2 · time2
= (50 mi/h)(3.5 h) +(65 mi/h)(2 h) = 305 mi
Dylan travelled a total of 305 miles.
The value of x is 40% of y. What are possible values for x and y? *
Answer:
x = 40 and y = 100
Step-by-step explanation:
random number 100
40% of 100 = 0.40 * 100 = 40
Can someone help me please? I'm struggling :(
Answer:
Ariel's plant is 1.6 inches taller than Dyani's.
It doesn't seem that you can multiply the measurement of Dyani's plant anymore than Ariel's. So I believe that would be 0 inches.
Step-by-step explanation: You can multiply Dyani's measurement with number like 1.0, 1.2, etc. You still wouldn't be able to multiply it anymore.
I hope this helps!
solve for x.
2x°
24°
Answer: x = 33°
Step-by-step explanation: 2x° + 24°-24 = 90°-24 2x/2 = 66/2 x = 33°
divide using synthetic division
(x^4-12x^2-6)/(x+3)
The quotient is x³-3x²-3x+9 and the remainder is -33.
What is synthetic division?Synthetic division is a method used to perform the division operation on polynomials when the divisor is a linear factor.
When we divide a polynomial p(x) by a linear factor (x - a) (which is a polynomial of degree 1), Q(x) is the quotient polynomial and R is the remainder.
p(x)/q(x) = p(x)/(x- a) = Quotient + (Remainder/(x - a))
p(x)/(x - a) = Q(x) + (R/(x - a))
Given that, (x⁴-12x²-6)/(x+3)
Here, (x⁴+0x³-12x²+0x-6)/(x+3)
Now,
-3| 1 0 -12 0 -6|
| -3 9 9 -27|
________________
1 -3 -3 9 |-33
So, remainder = -33 and quotient = x³-3x²-3x+9
Therefore, the quotient is x³-3x²-3x+9 and the remainder is -33.
Learn more about the synthetic division here:
brainly.com/question/29809954.
#SPJ1
Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts? Show your work.
A sentence constructed up of variables, numbers, or both is known as an expression in mathematics.
What does expression mean?A mathematical expression is a sentence with at least two numbers or variables, at least one mathematical operation, and at least single mathematical operation. Math allows for addition, subtraction, multiplication, and division.
Using variables, numbers, or both, a mathematical expression is a phrase. A symbol in an expression can never be equal. Examples include these expressions. Equations are mathematical statements that demonstrate the equality of two expressions.
According to the given information:Let the equation be 2x + 10
Where, x = 15
substitute the values in the above equation, we get
= 2(15) + 10
= 40
To learn more about expression refer to:
brainly.com/question/1859113
#SPJ1
Using the expression you found in part a, how many minutes will it take to make and pack an order for 15 parts? Show your work.
Given expression is:
2x + 10