End behavior of a function f defines the behavior of the function's graph at the "ends" of the x-axis. In other words, the end behavior of a function explains the graph's trend when we look to the right end of the x-axis (as x approaches +∞ ) and to the left end of the x-axis (as x approaches −∞ ).
What is function?A function is an equation with just one solution for y for every x. A function produces exactly one output for each input of a certain type. Instead of y, it is usual to call a function f(x) or g(x). f(2) indicates that we should discover our function's value when x equals 2. Example. A function is a type of rule that produces one output for one input. Alex Federspiel provided the image. y=x2 is an example of this. If you enter anything for x, you will only get one output for y. Because x represents the input value, we may say that y is a function of x.
Here,
End behavior of a function f specifies how the function's graph behaves at the "ends" of the x-axis. In other words, when we look to the right end of the x-axis (as x approaches +) and to the left end of the x-axis (as x approaches ), the end behavior of a function explains the graph's trend.
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the function f ( x ) f(x) is defined in the table below. using the table, identify the domain and range of f ( x ) f(x) . write your answer as an ordered list enclosed in curly brackets.
Table: x 2 5 9
f ( x ) 5 8 11
Domain: {2, 5, 9}, Range: {5, 8, 11}.
The domain of a function is the set of all the input values, while the range is the set of all output values. In this example, the function f(x) is represented in a table with three values. For the domain, the input values are 2, 5 and 9. This means that the domain of f(x) is {2, 5, 9}. The range of f(x) is the set of all output values. The output values for this problem are 5, 8, and 11. This means that the range of f(x) is {5, 8, 11}. Therefore, the domain and range of f(x) can be written as {2, 5, 9} and {5, 8, 11} respectively.
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Solve the initial value problem.y" - 2y' + y = 0 , y(0) = 1 , y'(0) = 2
Using Laplace Transformation, the initial value problem y" - 2y' + y = 0 , y(0) = 1 , y'(0) = 2 is y(t) = e^t + te^t.
The differential equation is y" - 2y' + y = 0 and y(0) = 1 , y'(0) = 2
As we know that the Laplace Equation is:
[tex]L(y^n(t)) = s^nf(s) - s^{n-1}y(0) - s^{n-2}y'(0)-\dots-sy^{n-2}(0)-y^{n-1}(0)[/tex]
Now applying the Laplace Transformation in the differential equation
L(y") - 2L(y') + L(y) = 0........(1)
Now finding the value of L(y") using the equation
L(y") = s^2f(s) - s(1) - 2
L(y") = s^2f(s) - s - 2
Now finding the value of L(y') using the equation
L(y') = sf(s) - 1
Now finding the value of L(y) using the equation
L(y) = f(s)
Now putting the values in the equation 1
s^2f(s) - s - 2 - 2(sf(s) - 1) + f(s) = 0
Now solving
s^2f(s) - s - 2 - 2sf(s) + 2 + f(s) = 0
s^2f(s) - s - 2sf(s) + f(s) = 0
Taking common f(s) in term terms of f(s)
(s^2 - 2s + 1)f(s) - s = 0
Add s on both side, we get
(s^2 - 2s + 1)f(s) = s
We can write (s^2 - 2s + 1) as (s - 1)^2
(s - 1)^2f(s) = s
Divide by (s - 1)^2 on both side, we get
f(s) = s/(s - 1)^2
The inverse Laplace of f(s) = s/(s - 1)^2 is
y(t) = e^t + te^t
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Exponential Functions
The amount of money left after 8 quarters is $3,547,878
How much of your original money will you have after 8 quarters?The theory used in this question is exponential decay, which describes how the value of a quantity decreases over time.
In this case, the value of the original investment decreases by 7% each quarter.
The steps for this process are as follows
Convert the percentage to a decimal. 7% = 0.07
Substitute the values into the equation: y = 5,000,000(1 - 0.07)t
Simplify the equation by multiplying the numbers in the parentheses: y = 5,000,000(0.93)t
Substitute the number of quarters into the equation: y = 5,000,000(0.93)8
Calculate the amount of money left after 8 quarters: y = 5,000,000(0.93)8 = 3,547,878
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Type the probability notation for chooing a car or a truck. Type the probability notation for chooing a plate and then a bowl. Would the following group of probabilitie be valid or not valid: 23%, 45%, 17%?
After her annual eye exam, Gianna will randomly elect a pair of contact from the baket containing 5 brown pair, 7 green pair, and 4 blue pair of colored contact. What i the probability that Gianna will randomly elect a brown pair or a green pair?
The probability that Gianna will randomly elect a brown pair or a green pair is 0.75 or 75%.
What is meant by probability notation?A practical technique to express the likelihood that an event will occur or not is through probability notation. When working with Venn diagrams, set notation is employed, and we use it to accomplish this.
Capital letters and various Greek characters are frequently used while notating events.
It is also possible to express probability as a percentage and it can only range from 0 to 1. The likelihood that event A will occur is frequently expressed as P (A) P(A) P(A)P, left parenthesis, A, right parenthesis.
The P(A/B) formula is written as P(A/B) = P(AB) / P(B), where the symbol denotes the intersection of events "A" and "B."
A basket containing 5 brown pair, 7 green pair, and 4 blue pair of coloured contacts. total pair of coloured contacts in basket =5+7+4=16
Gianna will randomly select,
P(a brown pair or green pair) =
[tex]\dfrac{\text{number of brown or green pair of colored contacts in basket}}{\text{total pair of colored contacts in basket}}[/tex]
= [tex]$\frac{5 + 7}{16}[/tex]
= [tex]$\frac{12}{16}[/tex]
= 3/4
= 0.75
Thus, the probability that Gianna will randomly elect a brown pair or a green pair is 0.75 or 75%.
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"For every apple Mike picked,
Chance picked three.
Help ASAP
This statement implies that Mike and Chance were picking apples together and that Chance picked three times as many apples as Mike.
Let's say Mike picked "x" apples. Then, according to the statement, Chance picked 3 times as many apples as Mike, which would be 3x apples.
Let x be the number of apples picked by Mike.
Then, the number of apples picked by Chance would be 3 times that, or 3x apples.
So, the equation can be written as:
x + 3x = total number of apples picked by both Mike and Chance.
Combining like terms, we get:
So the total number of apples picked by Mike and Chance together would be x + 3x = 4x apples.
Therefore, for every apple Mike picked, Chance picked three, and their combined total was four times the number of apples that Mike picked.
Total number of apples picked by both Mike and Chance = 4x.
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Incomplete Question
How many apples did Mike and Chance pick together if for every apple Mike picked, Chance picked three?
How to Convert Mile to Meter
The irregular total of 1,609.344 metres equals one mile.
What is the formula for converting miles to metres?Use this formula to convert a mile to a metre: mi X 1,609.344= m (miles multiplied by 1,609.344 equals metres) (miles multiplied by 1,609.344 equals meters). Use this formula to convert metres to miles: m/1,609.344=mi (metres divided by 1,609.344 equals miles) (meters divided by 1,609.344 equals miles).To change a mile's value to metres, you just multiply it by 1609.344. It really is that simple.mile, any of several distance measurements, such as the statute mile (5,280 ft) (1.609 km). It derives from the mille passus, or "thousand paces," of the Romans, which was equivalent to 5,000 Roman feet.To learn more about Mile refer to:
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if you rejected the hypothesis, how would you refine and rewrite your hypothesis to account for your findings and begin again?
You should re-analyze the data to determine why your results contradicted your hypothesis if the experiment's findings did not support it. You shouldn't change the experiments, observations, or both in order to get results that support your theory.
The Scientific Method is the framework that is most frequently employed while conducting an experiment. Asking a specific question, formulating a hypothesis, conducting experiments to collect data, analyzing the data, and determining if the hypothesis is true in light of the experimental results are all hallmarks of the scientific method.
The results may be published or distributed if the data are consistent with the hypothesis. The experiment's evaluation phase includes the write-up. Regardless of what took place during the experiment, the outcomes must be reported, whether they support or refute the hypothesis.
Next, list any issues that came up throughout the trial, and then include recommendations for changes and next steps in your report. To record what happened during the experiment, a write-up is required. It becomes a part of the background literature for the topic being investigated or put to the test.
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Your home has a market value of $135,000 and your local government uses a assessment value that is 72% of the market value. What is the assessment value of your house? *
The assessment value of the house will be $97,200.
The fair market value of a house refers to its calculated selling price under current market conditions. Assessed value is used by government tax assessors to determine how much property taxes a new homeowner may anticipate to pay.
Both fair market value and tax-assessed value contribute to determining a home's worth.
FMV is a fictitious value derived by estimating how much a buyer and seller would likely agree on under "normal" conditions. In contrast, market value is the price at which a property will actually sell.
As per the data given in the questions,
We have,
The market value of the home = $135,000
For finding the market value of the house, we simply multiply the market value by the assessment rate:
So, the market value will be: $135,000 * 0.72 = $97,200.
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name the greatest common factor
for each fraction and then simplify. Assume that no variable is zero.
Answer: a/c
Step-by-step explanation: cancel out the common factor b. to find the excluded values would be b = 0, c = 0
Please helpppppp!!!!!!!!!!!!!!!!!!!!!!
380.25 divided by 9
The answer is 42.25
I hope this is the answer you're looking for.
Answer:
42.25
Step-by-step explanation:
We can use the long division method to solve this.
[tex]\textrm{ } \ \ \ \ 42.25 \\9 \, \overline{\smash{)} \, 380.25}\\\text{ }\: \underline{ \text{- } 36}\\\text{ } \ \ \ \ 20\\\text{ } \ \ \underline{ \text{- } 18}\\\text{ } \ \ \ \ \, \ 2\, 2\\\text{ } \ \ \ \ \underline{ \text{- } 18}\\\text{ } \ \ \ \ \ \ \ \, 45\\\text{ } \ \ \ \ \ \, \underline{ \text{- } 45}\\\text{ } \ \ \ \ \ \ \ \ \ 0[/tex]
what is the standard deviation of 2,2,2,8,8,8
Solving provided question, we can say that value of standard deviation will be 3.28634 and Mean (Average) = 5 and Variance (SD) = 10.8
What is standard deviation?Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.
Total Numbers = 6
Mean (Average) = 5
SD = 3.28634
Variance (SD) = 10.8
Population SD = 3
Variance(Population SD) = 9
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Is it possible to solve y'= xy for y(0) = 0? Is the solution unique?
Because the general solution involves an arbitrary constant of integration that can only be discovered by providing an extra beginning condition, the solution to this equation with the starting condition y(0) = 0 is not unique.
What is equation?An algebraic equation, also known as a polynomial equation, is a mathematical equation of the form P=0, where P is a polynomial with coefficients in some field, most commonly the field of rational numbers. An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
Here,
The equation y' = xy is a separable differential equation, which means it can be solved for y in terms of x by separating and integrating the variables. The solution to this equation with the starting condition y(0) = 0 is not unique since the general solution contains an arbitrary constant of integration that can only be found by giving an additional initial condition.
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The philanthropic organization in Exercise 1 expects about a 5%success rate when they send fundraising letters to the people on their mailing list. In Exercise 1 you looked at the histograms showing distributions of sample proportions from 1000 simulated mailings for samples of size and The sample statistics from each simulation were as follows:a) According to the Central Limit Theorem, what should the theoretical mean and standard deviations be for these sample sizes?b) How close are those theoretical values to what was observed in these simulations?c) Looking at the histograms in Exercise at what sample size would you be comfortable using the Normal model as an approximation for the sampling distribution?d) What does the Success/Failure Condition say about the choice you made in part c?
The Normal model is a good approximation for the sampling distribution.
a) According to the Central Limit Theorem, the theoretical mean and standard deviation for a sample size of 20 should be 0.05 and 0.02, respectively. For a sample size of 100, the theoretical mean and standard deviation should be 0.05 and 0.01, respectively.
b) The observed mean and standard deviation for a sample size of 20 was 0.052 and 0.021, respectively. For a sample size of 100, the observed mean and standard deviation was 0.051 and 0.012, respectively. These values are fairly close to the theoretical values.
c) Looking at the histograms in Exercise 1, I would be comfortable using the Normal model as an approximation for the sampling distribution at a sample size of 100.
d) The Success/Failure Condition states that the sample size should be large enough for the sampling distribution of the sample proportions to be approximately normal. Since I chose a sample size of 100, which satisfied the condition, I can be confident that the Normal model is a good approximation for the sampling distribution.
The sample size of 100 is large enough for the sampling distribution of the sample proportions to be approximately normal, and the observed mean and standard deviation is close to the theoretical values. Therefore, the Normal model is a good approximation for the sampling distribution.
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How much is 600 Euros (EUR) to US Dollars (USD)
USD 651.83 is equal to 600 Euros (USD). The euro, denoted by the sign €, is the currency and monetary unit of the European Union.
How much is $600 euro in US dollars?USD 651.83 is equal to 600 Euros (USD). The euro, denoted by the sign €, is the currency and monetary unit of the European Union.Prior to its release as currency notes and coins in 2002, it first existed as a noncash monetary unit.The participating EU nations' domestic currencies and a few non-EU countries were replaced by the euro.The official money of the United States of America is the dollar, abbreviated as USD.A dollar is made up of 100 cents and is known as the United States dollar.To set it apart from other currencies based on the dollar, it is denoted by the symbol $ or US$.
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Sketch a diagram showing the area the following integral represents on scratch paper, then use the formula for the area of a trapezoid to calculate the value. Integral (2x + 15)dx =
Integral (2x + 15)dx =from 0 to 10
Area = (10 + 0)/2 * (2*10 + 15 - 2*0 + 15)
Area = (10 + 0)/2 * (35)
Area = 175
The integral, in this case, is the area under the line y = 2x + 15 between x = 0 and x = 10. The diagram for this looks like a trapezoid with the base of 10, the left side y = 15, the right side y = 25, and the height of 10. To calculate the area, we use the formula for the area of a trapezoid, which is (b1 + b2)/2 * h, where b1 and b2 are the lengths of the two bases and h is the height. For this problem, b1 is 0 and b2 is 10, and h is 10, so the area of the trapezoid is (10 + 0)/2 * (2*10 + 15 - 2*0 + 15). This simplifies to (10 + 0)/2 * (35), which is 175.
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The plane through the points (0, 1, 1), (1, 0, 1), and (1, 1, 0). x + y + z = 2 the plane that passes through the point (3, 5, -1) and contains the line x = 4 - t, y = 2t - 1, z = -3t. 8x + y - 2z = 31 the plane that passes through the point (1, 5, 1) find is perpendicular to the plane 2x + y - 2z = 2 and x + 3z = 4. 3x - 8y - z = -38
The equation of the third plane is 3x - 8y - z = -1.
What do you mean by equation?An equation is a mathematical statement that shows the equality or balance of two expressions. It is represented by an equal sign (=) and consists of variables, numbers, and mathematical operations. Equations are used to describe relationships between different quantities and can be solved to find unknown values. For example, the equation 2x + 3 = 7 can be solved for x by subtracting 3 from both sides, giving 2x = 4, and then dividing both sides by 2, giving x = 2.
The equation of the first plane is x + y + z = 2.
The equation of the second plane is 8x + y - 2z = 31.
The equation of the third plane is 3x - 8y - z = -38.
The third plane passes through the point (1, 5, 1) and is perpendicular to the plane 2x + y - 2z = 2 and x + 3z = 4. To find the equation of this plane, we can use the cross product of the normal vectors of the two given planes:
(2, 1, -2) × (1, 0, 3) = (3, -8, -1)
So, the equation of the third plane is 3x - 8y - z = -1.
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2. Group each number as rational and irrational, then graph and label each number on the
number line below. You may label the number with the letter.
A 0.75
B√√3
C√√√9
1
D -2-
2
15
10
E
F 2.6
G-√√2
HTT
Rational
Irrational …the answer is what???
Therefore , the solution of the given problem of rational numbers comes out to be A) 0.75 can be written as 75/100.
What is rational number?Rational numbers are those that may be written as a ratios (or fraction) of 2n. A fraction with a nonzero denominator is said to be rational. A few instances of rational numbers are 1/2, 1/5, and 3/4. As a real function, "0" can also be stated in a number of different ways, such as 0/1, 0/2, etc 0/3. But 1/0, 2/0, 3/0, and so forth. The number seven makes sense. A rational number is produced when three integers are split. To get the rational number 7, divide whole 7 ps by the total number 1. Since 7 can be obtained by dividing two integers, it is referred to as a real function.
Here,
Given :
=> Any number that can be expressed as a straightforward fraction is considered rational. This is the shape of a fraction: => a/b
where the denominator is "b" and the numerator is "a". Since both are integers, b 0.
=>Simple fractions cannot be used to represent irrational values.
So,
A) 75/100 is equivalent to 0.75 rational.
B) √√3 is irrational.
C) √√√9 is irrational.
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Determine which point from the pecified et atifie the ytem of equation. Y=−8x−9
y=6x5
The system of equation y = −8x − 9 and y = 6x + 5. So the point of the specified is (-1, -1).
Determine the point of the specifiedThese are the specified parameters:
y = −8x − 9 and y = 6x + 5
Substitute the equation
y = −8x − 9
6x + 5 = −8x − 9
6x + 8x = -9 - 5
14x = -14
x = -14/14
x = -1
Substitute x = -1 into the equation
y = 6x + 5
y = 6 (-1) + 5
y = -6 + 5
y = -1
So the poin (x, y) is (-1, -1).
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find a vector a with the specified length in the direction ⟨−3,−1,5⟩.
Let length of vector is 5 then the vector in the direction of ⟨−3,−1,5⟩ will be ⟨−15/√35,−5/√35,25/√35⟩.
What is a Vector?
Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction. It is also known as Euclidean vector or Geometric vector or Spatial vector or simply “vector“.
Two vectors are said to equal if their magnitude and direction are the same. It plays an important role in Mathematics, Physics as well as in Engineering. According to vector algebra, a vector can be added to another vector, head to tail. The order of addition of two vectors does not matter, because the result will be the same.
Now,
The idea is based on a concept of scaling and similarity.
Any vector that "has the same direction" as
⟨−3,−1,5⟩
has all the coordinates proportional to this given vector and, therefore, can be described by coordinates
⟨−3f,−1f,5f⟩
where f is a scaling factor.
All we need now is to find a scaling factor that leads to a vector with the length 5
The length of a vector with coordinates
⟨−3f,−1f,5f⟩
equals to√9f^2+f^2+25f^2=√35f
So, if we want the length to be equal to 5, we should choose
f=5/√35
Hence,
The coordinates of a vector with the same direction as ⟨−3,−1,5⟩ but with the length 5 will be ⟨−15/√35,−5/√35,25/√35⟩.
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Find the volume of this sphere.
Use 3 for
Volume of a sphere would be 6912.
What is Volume of this sphere ?
The volume of a sphere is calculated as V = 4/3πr^3, where V = volume and r is radius.
The fact that a sphere can be measured for its volume and surface area is due to the fact that it is a three-dimensional shape as opposed to a circle, which is a two-dimensional shape.
According to given question,
[tex]Volume\ of \ sphere=\frac{4}{3} \pi r^{3} \\\\Volume\ of \ sphere=\frac{4}{3} \pi 12^{3} \\\\Volume\ of \ sphere=\frac{4}{3} (3){1728}\\\\Volume\ of \ sphere=6912[/tex]
Hence, Volume of a sphere would be 6912.
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Porter is visiting india and would like to purchase some local spices. He finds some spices that cost 452. 95 rupees. If the current exchange rate is 1 dollar:73. 6500 rupees, how much do the spices cost in u. S. Dollars?.
The spices cost 6.15 in dollars. Porter is visiting India and bought species cost 6.15 dollars.
Here, these values are given, which is important for our solution,
So, after putting the values,
Porter bought species cost 452.95 rupees after visiting to India.
Current exchange rate = 1 dollar = 73.6500 rupees.
Here , 73.6500 rupees = 1 dollar
So, 1 rupee = 1/ 73. 6500 dollar
Then , 452. 95 rupees = 452. 95/ 73.6500 dollar.
After diving the rupees value by dollar values,
We get these values,
So, here, 452.95 rupees became 6.15 dollars.
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Answer: $6.15
Step-by-step explanation:
Porter bought species cost 452.95 rupees after visiting to India.Current exchange rate = 1 dollar = 73.6500 rupees.Here, 73.6500 rupees = 1 dollarSo, 1 rupee = 1/ 73. 6500 dollarThen, 452. 95 rupees = 452. 95/ 73.6500 dollar.After diving the rupees value by dollar values,We get these values,So, here, 452.95 rupees became 6.15 dollars.Solve for x in the equation 2x^2 + 5x - 3 = 0:
A) x = -3, 1/2
B) x = 1/2, -3
C) x = -1/2, 3
D) x = 3, -1/2
B)
Step-by-step explanation:To solve the equation 2x^2 + 5x - 3 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Where a = 2, b = 5, and c = -3.
Plugging in the values, we get:
x = (-5 ± √(5^2 - 4 * 2 * -3)) / 2 * 2
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √49) / 4
x = (-5 ± 7) / 4
So, the two solutions are:
x = ( -5 + 7 ) / 4 = (2) / 4 = 1/2
x = ( -5 - 7 ) / 4 = (-12) / 4 = -3
So, the two solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3.
Answer:
The answer is B) x = 1/2, -3.
Step-by-step explanation:
The equation 2x^2 + 5x - 3 = 0 can be solved using the quadratic formula, which states that the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
where a, b, and c are the coefficients of the equation and ± represents both the positive and negative square root.
In this case, a = 2, b = 5, and c = -3. Plugging these values into the formula gives us:
x = (-5 ± √(5^2 - 4 * 2 * -3)) / (2 * 2)
x = (-5 ± √(25 + 24)) / 4
x = (-5 ± √(49)) / 4
x = (-5 ± 7) / 4
So the two solutions are:
x = (-5 + 7) / 4 = 2 / 4 = 1/2
x = (-5 - 7) / 4 = -12 / 4 = -3
Therefore, the solutions to the equation 2x^2 + 5x - 3 = 0 are x = 1/2 and x = -3, which corresponds to option B) x = 1/2, -3.
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determine the values of r for which the differential equation y'''-5y'' 6y'=0
The values of r for which the differential equation y''' - 5y'' - 6y' = 0 are -6, -1 and 0
Given y = e^(rx)
Now, y' = re^(rx) = ry
y'' = r²e^(rx) = r²y
y''' = r³e^(rx) = r³y
We are asked to find the values of r for y''' - 5y'' - 6y' = 0
Put y', y'', y''' in the differential equation:
r³y - 5(r²y) - 6(ry) = 0
y(r³ - 5r² - 6r) = 0
Solving r³ - 5r² - 6r = 0
r(r² - 5r - 6) = 0
r(r - 6)(r + 1) = 0
r = -6 or -1 or 0
Hence, the values of r are -6, -1 and 0
The question is incomplete. The complete question is
"Determine the values of r for which the differential equation y''' - 5y'' - 6y' = 0 has a solution of the form y = e^(rx)."
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In each part, (i) draw the tree that shows only the allowed answers, (ii) write out the list, and (iii) say how many items are on your list. (a) Three character strings where each character is a letter, either A, B, or C. Note that repeats like AAB are allowed. (b) All such strings if repeats are allowed, but not in a row. ABA is acceptable, but AAB is not. (c) All such strings if no repeats are allowed, meaning each of A, B, or C is used once
All such strings if no repeats are allowed, meaning each of A, B, or C is used once then the total number of combinations is 13.
An array is a collection of elements that are ordered and can be accessed through indices.
In this case, we are dealing with arrays of character strings, where each string is a sequence of letters. In this problem, there are three possibilities for the characters that can appear in each string: A, B, or C.
(a) Three character strings where repeats are allowed:
Tree:
List: AAA, AAB, ACC, ABA, ABC, ACA
Number of items on list: 6
(b) Three character strings where repeats are not allowed in a row:
List: AB, AC, BAC, BCA, CAB, CBA
Number of items on list: 6
(c) Three character strings with no repeats allowed:
Tree:
ABC
List: ABC
Number of items on list: 1
So, the total number of items on the list is calculated as,
=> 6 + 6 + 1.
=> 13
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How much would you need to depoit in an account now in order to have $20,000 in the account in 4 year? Aume the account earn 5% interet
The amount that is needed to be deposited is $15,609.61
According to the Question
The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:
FV = PV * (1 + r)^n
Where:
FV = future value = $20,000
PV = present value = x
r = annual interest rate = 5%
n = number of years = 4
To solve for PV, rewrite the formula as follows:
PV = FV / (1 + r)^n
Putting the values:
x = $20,000 / (1 + 0.05)^4
⇒ x = $15,609.61
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The amount that is needed to be deposited is $15,609.61
According to the Question
The formula for the future value of an investment may be used to determine the amount that must be deposited today in order to have $20,000 in 4 years:
FV = PV * (1 + r)^n
Where:
FV = future value = $20,000
PV = present value = x
r = annual interest rate = 5%
n = number of years = 4
To solve for PV, rewrite the formula as follows:
PV = FV / (1 + r)^n
Putting the values:
x = $20,000 / (1 + 0.05)^4
⇒ x = $15,609.61
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First bulb: When 3 is the input, the output is _____. When 10 is the input, the output is _______.
In the function f(x) = 3x = 2, when input is 3 output is 11, and when input is
10 output is 32.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Suppose we have a function f(x) = 3x = 2.
Here, 'x' is the input, and f(x) is the output.
Now, When the input is 3,
f(3) = 3×3 + 2.
f(3) = 9 + 2.
f(3) = 11.
Again when the input is 10,
f(10) = 3×10 + 2.
f(10) = 30 + 2.
f(10) = 32.
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How do you Find the Point Slope Form with a Point Slope?
Form of a Line in Point-Slope, By using the substitution approach, you may solve for b by first plugging the slope and the (x, y) point values into the equation y is mx + b. The formula for the point-slope form is (x 1, y 1) is y y 1 is m (x x 1), where m is the slope and (x, y 1) is the provided point.
What does the point-slope form equation mean?The common form for linear equations is y-y1=m(x-x1). It draws attention to a line point and the line's slope.Form of a Line in Point-Slope, By using the substitution approach, you may solve for b by first plugging the slope and the (x, y) point values into the equation y = mx + b. The formula for the point-slope form is (x 1, y 1) = y y 1 = m (x x 1), where m is the slope and (x, y 1) is the provided point.Given two line-side coordinates, use the slope formula to determine the slope of the line. Slope is defined as the ratio of the change in the y values to the change in the x values using the formula m=(y2-y1)/(x2-x1).To learn more about Point-Slope refer to:
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What number has 8 tens and 7 fewer ones than tens
Answer:
81
Step-by-step explanation:
tens: 8
ones: 8 - 7 = 1
Part D Use the results from Parts B and C in the product rule of differentiation to find a simplified expression for the vertical velocity of the car, vy(t) = View Available Hint(s) vy(t) = Owyo'e-21 -yde (a cos(wt) +w sin(at)) cos(wt) sin(wt) yoe- (cos(wt)+aw cos(wt)) O ayo’e-20t -w cos(wt) sin(wt) Submit Previous Answers ✓ Correct In this example we used both the chain and product rules of differentiation to obtain an expression for the (vertical) velocity-time relationship for the car from its position-time relationship Part E Evaluate the numerical value of the vertical velocity of the car at time t = 0.25 s using the expression from Part D, where yo = 0.75 m, a=0.95 s-, and w = 6.3s-1 View Available Hint(s) μΑ ? (0.25 s) =
(0.25 s) = -1.8 m/s ,the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.
Part D:
In order to find the expression for the vertical velocity of the car, we need to use both the chain and product rules of differentiation. The chain rule states that if f(x) is a function of g(x), then the derivative of the function is equal to the derivative of g(x) multiplied by the derivative of f(x). The product rule states that if two functions, f(x) and g(x), are multiplied together, then the derivative of the product is equal to the derivative of f(x) multiplied by g(x) plus the derivative of g(x) multiplied by f(x).
Using the chain rule, we can find the derivative of the position-time equation:
y'(t) = yo'e-21 -yde (a cos(wt) + w sin(wt))
Using the product rule, we can find the derivative of the position-time equation:
v(t) = owyo'e-21 -yde (a cos(wt) + w sin(wt)) cos(wt) sin(wt) + yoe- (cos(wt) + aw cos(wt))
Simplifying the expression, we find:
v(t) = ayo'e-20t -w cos(wt) sin(wt)
Part E:
In order to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, we need to plug the given values for yo, a, and w into the expression for the vertical velocity.
Substituting the given values into the expression, we find:
v(0.25s) = 0.75e-20(-6.3)cos(6.3*0.25)sin(6.3*0.25)
Simplifying the expression, we find:
v(0.25s) = -1.8 m/s
In this example, we used the chain and product rules of differentiation to find the expression for the vertical velocity-time relationship for the car from its position-time relationship. We then used this expression to evaluate the numerical value of the vertical velocity of the car at time t = 0.25s, which was found to be -1.8m/s.
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2. Select all expressions that can be subtracted from 9x to result in the expression
3x + 5.