The solution of the initial value problem remains finite as t approaches infinity if the eigenvalues of the system are negative or have negative real parts.
The eigenvalues of a system determine the stability of the solution. Negative eigenvalues indicate that the solution will approach a steady state as time goes on. Positive eigenvalues indicate that the solution will diverge, or grow without bound, as time goes on. If the real parts of the eigenvalues are negative, the solution will approach a steady state, but if the real parts of the eigenvalues are positive, the solution will diverge as t approaches infinity.
In order to check for finite solution for a given initial value problem, one needs to evaluate the eigenvalues of the system, and check their real parts. If they are negative, the solution will remain finite, otherwise the solution will diverge as t approaches infinity.
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[tex]ax ^{2} + bx + c[/tex]
quadratic expression:
factorise 6a^2+15a+a
Answer:
2a(3a + 8)
Step-by-step explanation:
Combine like terms
6a2 + 15 + a
6a2 + 16a
which expression is equivalent to i55
The equivalent expression for given complex number i^55 is -i.
What are complex numbers?
Complex numbers are the numbers that are expressed in the form of a+ib where, a,b are real numbers and ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
An imaginary number is usually represented by ‘i’ or ‘j’, which is equal to √-1. Therefore, the square of the imaginary number gives a negative value.
Since, i = √-1, so, i^2 = -1
Now,
complex number i^55=(i^4)^13(i^2*i)
=1^13(i^2*i) (i^4=1)
=1(-1*i) (i^2=-1)
Hence,
i^55=-i
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6(x+1)=24, what is x supposed to be?
Answer:
x = 3
Step-by-step explanation:
6(x+1)=24
6x + 6 = 24
6x = 18
x = 3
Let's check
6(3 + 1) = 24
6(4) = 24
24 = 24
So, x = 3 is the correct answer.
Answer: 3
Step-by-step explanation:
Expand:
6x + 6 = 24
6x = 18
x = 3
Put the value into the equation:
6(3+1) = 24
6 * 4 = 24
24 = 24
Correct! :>
While observing the fare meter in a taxi, a student records the following data: Reading on Taxi Fare Meter Time (minutes) Meter Reading 0 $6.75 10 $13.25 20 $19.75 30 $26.25 Does the increase in price represent linear growth or exponential growth, and what is the constant growth rate or growth factor per minute?
The increase in price represents linear growth and the constant growth rate or growth factor per minute = 0.65 per min.
What is linear growth?A linear growth is defined as the type of growth that is always at the same rate while exponential growth is the type of growth that increases with time.
From the data recorded by the student, the amount collected every 10 minutes by the driver = $6.5
If 10 minutes = 6.5
1 minute = X
Make X the subject of formula;
X = 6.5/10
X = 0.65
Therefore, the growth rate per minute = 0.65/min
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If 1+x+x*2=3 then 1-x-x*2= ?
Yesterday diego successfully made 16 field goals today he made 125% as many how many successful field goals did diego make today
Answer:
20 goals
Step-by-step explanation:
The percentage 125 is over 100. So it's going to be 125/100 ×16. so the answer is 20
i dont get this pls help!
Based on data from the environmental protection agency, 18 gallons of water is used on average to take a shower, which translates to one trillion gallons of water used for showers across the united states. Which activities can help conserve water when taking showers? check all that apply.
The human body and 70% of the earth are both made of water. In the modern world, there are millions of marine species that live in water. Similarly, water is essential to humankind.
Water is necessary for all major enterprises in one way or another. But this priceless resource is running out faster and faster. Most of the causes are exclusively human-made. Water conservation is therefore more important than ever. You will understand the significance of water conservation and how limited it is. We can instill the following activities in our daily life to conserve water.
Installing low-flow showerheadsFixing leaks in the showerTaking shorter showersCollecting and reusing greywater from the shower for irrigation or other non-potable usesUsing a water-saving shower valveInstalling a shower timerUsing a bucket in the shower to collect and reuse greywaterTo know more about water conservation visit :
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Answer: C, D, E
C: Turn the shower off when shampooing
D: Turn the shower off completely after use
E: Use showerheads that use less water
Step-by-step explanation:
Just did it on edge and got them right :)
$abcdef$ is a concave hexagon with exactly one interior angle greater than $180^\circ.$ (the diagram of $abcdef$ below is not drawn to scale.) noah measured the marked angles, getting $80^\circ$, $85^\circ$, $95^\circ$, $105^\circ$, $120^\circ$, and $125^\circ.$ what interior angle measure of the hexagon, in degrees, is missing from noah's list?
The sum of angles in a hexagon is 720⁰. The missing interior angles in Noah's list is 110⁰
The sum of interior angles of a triangle is equal to 180⁰. The sum of interior angles of a polygon is equal to:
sum of interior angles of a polygon = number of triangles x 180⁰
A hexagon consists of 4 triangles, hence, the sum of interior angles in a hexagon = 4 x 180⁰ = 720⁰
In general, we can find the sum of interior angles in a polygon using the formula:
(n - 2) x 180⁰
Where n = number of sides
In the given problem, let's denote the missing interior angle as q. The sum of interior angles are:
80⁰ + 85⁰ + 95⁰ + 105⁰ + 120⁰ + 125⁰ + q = 720⁰
610⁰ + q = 720⁰
q = 720⁰ - 610⁰ = 110⁰
The picture in your question is missing. Most likely it was like on the attached picture.
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Two trains leave the railroad station at noon. The first train travels along a straight track at 95 mph. The second train travels at 75 mph along another straight track that makes an angle of 130° with the first track. At what time are the trains 400 miles apart? Round your answer to the nearest minute.
Answer:
2:36pm
Step-by-step explanation:
Let's say it takes x hours after leaving the station when the trains are 400 miles apart
Let's refer to the two trains using the letters A and B for easier reference
A is the train that travels on a straight track due East
B is the train that travels on a track 130° relative to the path of train A
A travels at a speed of 95 mph
B travels at a speed of 75 mph
Let the distance between the two trains be 400 miles after they have traveled an unknown [tex]x[/tex] hours. We have to determine [tex]x[/tex]
After [tex]x[/tex] hours, train A would be [tex]95x[/tex] miles from the railroad station and train B would be [tex]75x[/tex] miles from the station
We can visualize this situation as given in the attached image.
You can see that A = 95x, B = 75x and the longest side is 400 miles
We will use the law of cosines to determine x
The Law of Cosines (also called the Cosine Rule) says:
[tex]c^2 = a^2 + b^2 - 2ab\cos (\theta)[/tex]
where [tex]\theta[/tex] is the angle opposite c i.e. the angle bounded by a and b which are the other two sides
Using the diagram as a reference we see
c = 400, a = 95x, b= 75x, [tex]\theta =[/tex] 130°
Using this information and plugging values into the cosine rule formula we get
[tex]c^2 = a^2 + b^2 -2ab \cos(\theta)\\\\c^2 = (95x)^2 + (75x)^2 - 2(95x)(75x)\cos(130^\circ)\\\\c^2 = 9025x^2 + 5625x ^2 - 14250x^2\cdot \cos(130^\circ)\\\\[/tex]
[tex]c^2 = x^2(9025 + 5625 -14250 \cdot \cos130^\circ)\\\\\\c^2 = x^2(14650 - (14250 \times -0.64278))\\[/tex]
[tex]c^2 = (14650 - (-9159.72343))x^2\\\\c^2 = (14650 + 9159.72343)x^2 \\\\c^2 \approx 23809.7234x^2\\\\[/tex]
But we know that c = 400 since that's what the question says
So we get
[tex]23809.7234x^2 = 400^2\\\\23809.7234x^2 = 160000\\\\x^2 = \dfrac{160000}{23809.7234} \approx 6.71994\\\\\\x = \sqrt{6.71994} = 2.59228\\\\\textrm{Rounding to nearest tenth}\\x = 2.6 \textrm{ hours}\\\\[/tex]
So the two trains will be 400 miles apart 2.6 hours after they have left the station.
2.6 hours = 2 hours and 36 minutes
So the trains will be 400 miles 2 hours and 36 minutes after they have left the station
Since they have left at noon, they are 400 miles apart at 2:36pm
Mr. Angelou moved closer to his family. He used to live 89 miles away and now purchased a home 51 miles away from his family. What is the percent decrease in distance from his home to his family now? Be sure to round to the nearest hundredth.
Answer:
43.70%
Step-by-step explanation:
g what is the difference between the asymmetrical model and symmetrical model of public relations, and provide an example of each.
The major difference between asymmetrical model and symmetrical model is that one deal with the public with help of organization and other with interacting with people directly.
The asymmetrical model offers a more "scientifically convincing" method of reaching out to important audiences. Here, content makers carry out research to better comprehend the attitudes and actions of the target audience. It is still asymmetrical or unbalanced because this paradigm uses persuasive communication to the organization's advantage rather than the audiences.
According to the symmetrical model, a public relations professional should function more as a bridge between an organization and its target audiences than as a persuasive force. Practitioners operate as negotiators in this situation and use communication to make sure that everyone involved, not just the company they work for, benefits.
Asymmetric Digital Subscriber Line (ADSL) is an example of asymmetric communications and when a company uses surveying as an IMC tool, it is initiating two-way symmetrical communication with its audiences.
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find the product (n+7)(n-2)
Triangle E F G is shown. Which statements regarding Triangle E F G are true? Select three options. E F + F G greater-than E G E G + F G greater-than E F E G minus F G less-than E F E F minus F G greater-than E G E G + E F less-than F G
Answer:
It will be located in the explanation
Step-by-step explanation:
A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item? a system of equations. 8 x plus 8 y equals 200. 12 x plus 15 y equals 348. A system of equations. 8 x plus 8 y equals 200. 15 x plus 12 y equals 348. A system of equations. 8 x plus 8 y equals 348. 12 x plus 15 y equals 200. A system of equations. 8 x plus 8 y equals 348. 15 x plus 12 y equals 200.
If volleyball team purchased 15 jackets, 12 pairs of sweatpants for $348 and basketball team purchases 8 jackets , 8 pairs of sweatpants for $200, the the system of equations that represent the situation is (b) [tex]15x+12y = 348[/tex] and [tex]8x+8y = 200[/tex] .
let the number of jackets purchased be = x ;
let the number of pairs of sweatshirts purchased be = y ;
the volley ball team purchased 15 jackets and 12 pairs of sweatpants for $348 ,
that means the equation that represents the situation is :
[tex]15x+12y = 348[/tex] .
Also given that , the basketball team purchased 8 jackets and 8 pairs of sweatpants for $200 ,
that means the equation that represents the situation is :
[tex]8x+8y = 200[/tex] .
Therefore , the system of equations are [tex]15x+12y = 348[/tex] and [tex]8x+8y = 200[/tex] .
The given question is incomplete , the complete question is
A sports apparel supplier offers teams the option of purchasing extra apparel for players. A volleyball team purchases 15 jackets and 12 pairs of sweatpants for $348. A basketball team purchases 8 jackets and 8 pairs of sweatpants for $200. Let x represent the price of a jacket and let y represent the price of a pair of sweatpants. Which system of equations can be used to find the price of each item ?
(a) 8x + 8y = 200 ; 12x + 15y = 348 ;
(b) 8x + 8y = 200 ; 15x + 12y = 348 ;
(c) 8x + 8y = 348 ; 12x + 15y = 200 ;
(d) 8x + 8y = 348 ; 15x + 12y = 200 .
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A TV was priced at 250 euros before VAT of 20% was added on. What was the selling price of the TV?
The selling price of the TV before the VAT of 20% is 250 euros
What is Value Added Tax (VAT)?Value Added Tax is a tax that is assessed on products and services at every point in the supply chain. From the point of production until the point of sale, a certain value is applied at each stage (a small portion of the overall tax).
The problem is a percentage problem, requiring a tax of 20% before the tax the selling price of the TV is 250 euros
However when the tax of 20% is added the new price will be calculated as follows
For an increment of 20% the factor for multiplication is 1.2 hence
price after tax = 250 euros * 1.2
price after tax = 300 euros
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20 POINTS FOR WHOEVER CAN ANSWER THIS, HELP MEEEEE!!!!
To find the distance between two points in a coordinate plane, we can use the Pythagorean theorem.
The distance between (2, 4) and (5, -2) can be found using the following steps:
Find the difference in the x-coordinates: 5 - 2 = 3
Find the difference in the y-coordinates: -2 - 4 = -6
Use the Pythagorean theorem to find the distance: d = √(3^2 + (-6)^2) = √(9 + 36) = √45
So the distance between (2, 4) and (5, -2) is √45.
write an expression to represent the total area as the sum of the areas of each room
The sum of the areas of the room will be → S = ∑ 2{[tex]$L_{i} B_{i} + B_{i} H_{i} + H_{i} L_{i}[/tex]}.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given are the area of each separate room.
Assume the sum of the areas of the room will be {S}. Let the dimensions of the room be -
[tex]$L_{i},\; B_{i},\; H_{i}[/tex]
where {i} is the room number.
Then we can write the sum of the areas of the room as -
S = ∑ 2{[tex]$L_{i} B_{i} + B_{i} H_{i} + H_{i} L_{i}[/tex]}
Therefore, the sum of the areas of the room will be -
S = ∑ 2{[tex]$L_{i} B_{i} + B_{i} H_{i} + H_{i} L_{i}[/tex]}
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75 less than a number x is greater than or equal to 420
The solution to the given statement "75 less than a number x is greater than or equal to 420" is written as 75 - x ≥ 420 where x ≤ -345
How to write inequality?75 less than a number x is greater than or equal to 420
75 - x ≥ 420
Subtract 75 from both sides
- x ≥ 420 - 75
- x ≥ 345
divide both sides by -1
x ≤ 345/-1
x ≤ -345
Therefore, the expression is given by 75 - x ≥ 420 where, x ≤ -345
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What is the complex number with polar coordinates (3, StartFraction 5 pi Over 6 EndFraction).? Round the coefficients to the nearest thousandth.
z = 1.5 – 2.598i
z = –2.598 + 1.5i
z = 2.598 – 1.5i
z = 1.5 + 2.598i
The complex number with polar coordinates (3, StartFraction 5 pi Over 6 EndFraction) is:
z = 2.598 - 1.5i
What is the complex number?
Complex numbers are the numbers that are expressed in the form of a+ib where, a, and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).
This can be found by using the polar form of a complex number, which is:
z = r (cos θ + i sin θ)
where r is the magnitude or modulus of the complex number, θ is the angle in radians, and i is the imaginary unit.
In this case, we have r = 3, and θ = StartFraction 5 pi Over 6 EndFraction. Plugging these values into the equation above gives:
z = 3 (cos (StartFraction 5 pi Over 6 EndFraction) + i sin (StartFraction 5 pi Over 6 EndFraction))
z = 2.598 - 1.5i
we can round the coefficients to the nearest thousandth.
The complex number with polar coordinates (3, StartFraction 5 pi Over 6 EndFraction) is z = 2.598 - 1.5i.
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Is every linear line a function?
No, the graph of a function does not contain every straight line. Due to the fact that they satisfy the vertical line test, nearly all linear equations are functions.
Relationships that fail the vertical line test are the exceptions. All linear equations, when graphed, result in straight lines, but not all linear equations result in linear functions. A graph must be both linear (a straight line) and a function in order to be a linear function (matching each x-value to only one y-value).
A vertical line has an equation of the form x = a, where an is any real number, and is the only instance in which a linear equation is not a function.
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A jar of cleaning fluid weights 24 ounces (oz.). When one
half of the cleaning fluid is used up the jar and remaining
fluid weigh 17 ounces. How much does the jar weigh?
A jar of cleaning fluid weights 24 ounces , remaining,The jar weigh is 1/2 kg ounces.
How much does the jar weigh?To subtract is to take something away from a group or several different items. The number of items in the group decreases or gets less as we subtract. A subtraction issue has three components: the minuend, subtrahend, and difference.
A jar of cleaning fluid weights 24 ounces (oz.). When one half of the cleaning fluid is used up the jar and remaining fluid weigh 17 ounces.
The jar weigh
24 ounces
17 ounces
so,
24 ounces - 17 ounces = 7 ounces
A jar of cleaning fluid weights 24 ounces , remaining,The jar weigh is 1/2 ounces.
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If cosine of x degrees equals three-fifths, what is the value of b? triangle lmn in which angle m measures 90 degrees, angle l measures x degrees, ln measures 20 units, and lm measures 3b units b = 4 b = 5 b = 6 b = 7
If cosine of x degrees equals three-fifths, the value of b is 7.
What is cosine ?
In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. The most common trigonometric functions are sine, cosine, and tangent. The reciprocal functions are cosecant, secant, and cotangent.
In this case, we are given that cos(x) = 3/5. From this, we can use the inverse cosine function (arccos) to find the value of x in degrees. However, this alone is not enough to determine the value of b.
In the given triangle LNM, we know that angle M measures 90 degrees and angle L measures x degrees. We also know that side LM measures 3b units and LN measures 20 units.
Using the Pythagorean theorem, we know that the length of MN, which is the hypotenuse, can be found by:
MN^2 = LM^2 + LN^2
We also know that
cos(x) = LM / MN
Therefore, we have:
3/5 = (3b) / (sqrt(3b^2 + 20^2))
b = 7
So , If cosine of x degrees equals three-fifths, the value of b is 7.
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James and Peter cycled along the same 50 km route.
James took 2 and 1/2 hours to cycle the 50 km.
Peter started to cycle 5 minutes after James started to cycle.
Peter caught up with James when they had both cycled 15 km.
James and Peter both cycled at constant speeds.
Work out Peter's speed.
Answer:
22.48 km/h
Step-by-step explanation:
it took James 45 minutes to cycle 15 km, sInce he was traveling at 20 km/h, which was worked out by dividing 50 by 2.5.
since Peter left 5 minutes later, it took 5 minutes less, so 40 minutes. 40 minutes as a fraction is 0.667.
15 divided by 0.667 is 22.48 km/h
Answer:22
Step-by-step explanation:
what the guy before said
Select all the expressions that are equivalent to 7(2 - 3n).
Explain how you know each expression you select is equivalent.
1. 9 – 10n
2. 14-30
3. 14 - 21n
4. (2 - 3n). 7
5. 7•2• (-3n)
Expressions that are equivalent to 7(2 - 3n) are 14 - 21n and (2 - 3n). 7
1. 14 - 21n is equivalent to 7(2 - 3n) because we can distribute the 7 to the 2 and -3n in the expression, 7(2 - 3n) = 72 - 73n = 14 - 21n.
2. (2 - 3n). 7 is equivalent to 7(2 - 3n) because it can be changed by the distributive property, (2 - 3n). 7 = 2. 7 - 3n. 7 = 14 - 21n
All the other expressions are not equivalent to 7(2 - 3n) because they don't follow the distributive property and some of them don't have the same coefficients.The distributive property is a mathematical property that states that for any two numbers a and b, and for any third number c, the following equation holds true: a(b + c) = ab + ac. This property is also known as the distributive law of multiplication over addition. The distributive property is used to simplify expressions by breaking them down into smaller parts that can be calculated separately and then combined again.
Therefore, Expressions that are equivalent to 7(2 - 3n) are 14 - 21n and (2 - 3n). 7
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Solve for mzB:
D
(9x + 40)°
m₂B =
A
O
C
(12x+13)
B
Step-by-step explanation:
since this is a parallelogram, angle B = angle D.
therefore,
12x + 13 = 9x + 40
3x + 13 = 40
3x = 27
x = 27/3 = 9
and so,
angle B = 12×9 + 13 = 108 + 13 = 121°
don't get confused by the diagram, where angle B and D look like they are smaller than 90°.
but given the specified information that is not true and the graphic is simply misleading in that regard.
Pls awnser :))))))))))))))))))
The function x = -1 depicts the relationship between x and g (x) as seen in the above table.
what is function ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
function value = 9 for x = -1.
x = -1 is the solution to f(x) = g(x),
since f(-1) = 9 = g(-1).
The function x = -1 depicts the relationship between x and g (x) as seen in the above table.
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what is the answer to 3≤7+g ?
Answer: g [tex]\geq[/tex] -4
Step-by-step explanation:
[tex]3\leq7+g[/tex]
Subtract 7 from both sides:
-4 [tex]\leq[/tex] g, so
g [tex]\geq[/tex] -4
Answer:
g ≥ -4
Step-by-step explanation:
3≤7+g
We rewrite g on the left side
g + 7 ≥ 3
g ≥ -4
What is opportunity cost in economics with example?
Answer:
the loss of other alternatives when one alternative is chosen.
example: if you have to choose between buying a shoe or a coat and you choose to buy the coat, the shoe is the opportunity cost.
Step-by-step explanation:
[robinhood - medium] a and b are playing a game where a has n 1 coins, b has n coins, and they each flip all of their coins. what is the probability that a will have more heads than b?
The probability of A having more heads than B depends on the number of coins each has, and which is P(A>B) = ∑i=0,n2 (n1 choose i)[tex]1/2^{n1+n2}[/tex]
If both players have the same number of coins, the probability of A having more heads than B is 0.5. If A has more coins than B, then the probability of A having more heads than B is greater than 0.5.
Conversely, if B has more coins than A, then the probability of A having more heads than B is less than 0.5. The exact probability can be calculated with binomial coefficients.
Let n1 be the number of coins A has and n2 be the number of coins B has. The probability of A having more heads than B is then given by: P(A>B) = ∑i=0,n2 (n1 choose i)[tex]1/2^{n1+n2}[/tex]
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