The value of the given expression increases, because as x decreases, 5/x increases
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given that, what happens to the value of the expression 5/x+5 as x decreases from a large positive number to a small positive number,
We know that, If the denominator of the fraction is decreased, the value of a fraction is increased while the numerator remains unchanged.
Therefore, if the value of x in the given starts decreasing the value of the whole fraction will start increasing.
Hence, the value of the expression increases, because as x decreases, 5/x increases
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mike painted 1/3 of his room using 2/5 of a can of paint. how much paint will it take to paint the whole room
Answer:
He will need 6/5 cans of paint.
The answer could also be written as 1 1/5 cans of paint or 1.2 cans of paint.
Step-by-step explanation:
Since 2/5 filled 1/3 of the room, he will need 3 times that amount.
2/5 * 3/1 = 6/5
Using the the interior angle measure 150 degrees find the exterior measure.someone please help
Answer:
30 degrees.
Step-by-step explanation:
Angles must add up to 180 so,
180 - 150 = 30.
How will you calculate marginal utility?
To calculate marginal utility, you need to determine the additional utility that a consumer derives from consuming an additional unit of a good or service. This involves finding the difference in total utility before and after consuming the additional unit.
Marginal utility is the additional utility (or satisfaction) that a consumer derives from consuming an additional unit of a good or service. To calculate marginal utility, you can follow these steps:
1. Determine the total utility that a consumer derives from consuming a certain amount of a good or service.
2. Increase the amount consumed by one unit.
3. Determine the new total utility that the consumer derives from consuming the additional unit.
4. Subtract the initial total utility from the new total utility to obtain the marginal utility of the additional unit.
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Question 3 3.1.1. Express the following as single trigonometry ratio: 3.1.1. Cos2x · Cos3x - Sinax. Sin3x 2 B12. Sinzx Cosx+Cosex Sinx 3.2. Determine the value of the following without using a calcula 3.2.1. Sın 85° Cos25°- Cos 85°. Sin 25° 322 Cos 160°. Cos10° + Sin160°. Sin 10° 44
Using trigonometric identity, the value of the expressions are (Cosx + Cos5x)/2 + Sin3x.Cosx, √3/2, √3/2 and -√3/2
What is the expression of the trigonometric identityTo solve this problem, we need to apply trigonometric identity;
1.
Cos2x · Cos3x - Sinax. Sin3x:
Using the identity Cos(A - B) = CosA.CosB + SinA.SinB, we can write:
Cos2x · Cos3x = (Cos(2x - 3x) + Cos(2x + 3x))/2 = (Cos(-x) + Cos(5x))/2 = (Cosx + Cos5x)/2
So the expression becomes:
(Cosx + Cos5x)/2 - Sinax. Sin3x
Using the identity Sin(A - B) = SinA.CosB - CosA.SinB, we can write:
Sinax. Sin3x = (Sin(ax - 3x) - Sin(ax + 3x))/2 = (Sin(-2x) - Sin(4x))/2 = (-Sin2x - Sin4x)/2
So the expression becomes:
(Cosx + Cos5x)/2 + (Sin2x + Sin4x)/2
Using the identity SinA + SinB = 2.Sin((A+B)/2).Cos((A-B)/2), we get:
(Sin2x + Sin4x)/2 = Sin3x.Cosx
Therefore, the expression simplifies to:
(Cosx + Cos5x)/2 + Sin3x.Cosx
2.
Sinzx Cosx+Cosex Sinx:
Using the identity Sin(A + B) = SinA.CosB + CosA.SinB, we can write:
Sinzx Cosx+Cosex Sinx = Sin(x + z)
So the expression is equivalent to Sin(x + z).
3.
Sın 85° Cos25°- Cos 85°. Sin 25°:
We can use the identity Sin(A - B) = SinA.CosB - CosA.SinB:
Sin 85° Cos25°- Cos 85°. Sin 25° = Sin(85° - 25°) = Sin60° = √3/2
4.
Cos 160°. Cos10° + Sin160°. Sin10°:
We can use the identity Cos(A - B) = CosA.CosB + SinA.SinB:
Cos 160°. Cos10° + Sin160°. Sin10° = Cos(160° - 10°) = Cos150° = -√3/2
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Max organized a community toy drive for the holidays. He asked each family to donate a total of 2 gifts. Eighteen families participated in the toy drive. Write and solve an equation that represents how many gifts were donated.
g + 2 = 18; g = 16 gifts
g − 2 = 18; g = 20 gifts
g divided by 18 equals 2; g = 36 gifts
2g = 18; g = 9 gifts
Answer: 36
Step-by-step explanation:
g divided by 18 equals 2; g = 36 gifts.
The correct option is (3).
What is Arithmetic?The fundamental ideas in number theory, measurement, and calculation are frequently referred to as "arithmetic" (which is derived from the Greek word "arithmos," "number"). (that is, the processes of addition, subtraction, multiplication, division, raising to powers, and extraction of roots).
As per the given data:
A community toy drive for holidays was organized my Max.
Each family has to donate a total of 2 gifts.
Total number of families were equal to 18.
Let's assume the total number of gifts from all the families is g.
For finding the equation to find the total number of gifts given by all the families:
g = Gifts given by each family × Number of families
g = 18 × 2
∴ g divided by 18 equals 2; g = 36 gifts.
Hence, g divided by 18 equals 2; g = 36 gifts.
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Is the number 1 prime? Explain why or why not.
Please explain why.
1 can only be divided by one other integer except1, hence it is not a prime number.
The reason why 1 is not a prime number.Any natural number higher than 1 that is not the sum of two smaller natural numbers is referred to be a prime number. A composite number is a natural number greater than one that is not prime.
Given this definition, 1 is not a prime number because it can only be divided by one other integer, which is 1 itself.
Based on the explanation above, we can then conclude that 1 is not a prime number.
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Javier is standing at a distance from a flagpole. He sights the bottom of the flagpole at a 4°
angle of depression and the top of the flagpole at a 25°
angle of elevation. If Javier is 6 feet tall, what is the total height, to the nearest foot, of the flagpole?
Answer: To find the height of the flagpole, we can use the fact that the angles of depression and elevation are complementary angles, meaning that they add up to 90°.
Let's call the height of the flagpole "h". Then, we have:
h - 6 = h * tan(4°) (the height difference between Javier and the bottom of the flagpole)
and
h = 6 + h * tan(25°) (the height of the top of the flagpole as seen by Javier).
By substituting the first equation into the second, we can find h:
h = 6 + h * tan(25°)
h = 6 + h / tan(65°)
h * tan(65°) = 6 + h
h * tan(65°) - h = 6
h = 6 / (tan(65°) - 1)
Using a calculator, we find that h = approximately 43.3 feet. Rounding to the nearest foot, the height of the flagpole is 43 feet.
Step-by-step explanation:
Find the solution to the
system 2x + 3y = 6 and
-2/3x
Answer:
I got 7 as the answer
Step-by-step explanation:
I hope this helps!!
2x − 5y + 3x = 8
3x − y + 4z=7
x+3y + 2x = -3
Answer:=3
Step-by-step explanation: For 2x-5y=3 substitute
does any1 know the answer to this?
Answer:
Check below under ‘explanation’
Step-by-step explanation:
5 Units up means every point will move 5 units in the upward direction along the y- axis. Therefore the x- coordinates of every point will remain the same and only their y-coordinates will change:
Q’ = [tex](-8, -4)[/tex]
R’ = [tex](-2, -4)[/tex]
S’ = [tex](-2, 4)[/tex]
T’ = [tex](-8, 4)[/tex]
Given the following historical demand and forecast, calculate the Tracking Signal in Week 3:
Week 1 Demand: 50 Forecast: 49
Week 2 Demand: 54 Forecast: 56
Week 3 Demand: 58 Forecast: 60
The Tracking Signal in Week 3 is -1.8.
The Tracking Signal in Week 3 can be calculated by using the following formula:
Tracking Signal = (Sum of Forecast Errors) / (Mean Absolute Deviation)
First, we need to calculate the forecast errors for each week:
Week 1 Forecast Error = Actual Demand - Forecast = 50 - 49 = 1
Week 2 Forecast Error = Actual Demand - Forecast = 54 - 56 = -2
Week 3 Forecast Error = Actual Demand - Forecast = 58 - 60 = -2
Next, we need to calculate the Mean Absolute Deviation (MAD):
MAD = (|1| + |-2| + |-2|) / 3 = (1 + 2 + 2) / 3 = 5 / 3 = 1.67
Finally, we can calculate the Tracking Signal:
Tracking Signal = (1 + -2 + -2) / 1.67 = -3 / 1.67 = -1.8
Therefore, the Tracking Signal in Week 3 is -1.8.
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The cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for 4 tickets
What is the slope
Is it positive negative zero or undefined
The slope is 1/19.5 and it is positive slope.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
Given that, the cost of tickets to the amusement park is $19.50 for 1 ticket and $78 for 4 tickets.
Here, the coordinates are (19.50, 1) and (78, 4)
Now, the slope = (4-1)/(78-19.50)
= 3/58.5
= 1/19.5
Therefore, the slope is 1/19.5 and it is positive slope.
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Gregory is six years younger than Janet. 7 years ago, Janet was thrice as old as Gregory. How old are they know?
The ages of Gregory and Janet are 10 and 16 years respectively.
How to find there ages?Gregory is six years younger than Janet. 7 years ago, Janet was thrice as old as Gregory. Therefore, the ages of Gregory and Janet are as follows:
Let
x = age of Janet
Gregory age = x - 6
x - 7 = 3(x - 6 - 7)
Hence,
x - 7 = 3(x - 13)
x - 7 = 3x - 39
x - 3x = -39 + 7
-2x = -32
divide both sides by -2
x = -32 / -2
x = 16 years
Therefore,
Janet age = 16 years
Gregory's age = 16 - 6 = 10 years
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Janet's current age is 16 and Gregory's current age is 10
How to determine how old they are know?Let's start by using algebra to represent the information in the problem.
Let's assume that Janet's current age is "J" and Gregory's current age is "G".
From the first sentence, we know that:
G = J - 6
From the second sentence, we know that 7 years ago, Janet was thrice as old as Gregory.
J - 7 = 3(G - 7)
So, we have
J - 7 = 3(J - 6 - 7)
This gives
J - 7 = 3J - 39
So, we have
2J = 32
This gives
J = 16
This also means that
G = 16 - 6
G = 10
Hence, Gregory's age is 10
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How to solve 400 divided by 1,600
Answer:
1/4
Step-by-step explanation:
400 divided by 1600 = [tex]\frac{400}{1600}[/tex]
We simplify by 400, and get the answer
1/4
Answer:
0.25 or 1/4
Step-by-step explanation:
1600/400
1600 cant go into 400 so you start with zero, add a decimal next to your zero, and carry down a 1. That then becomes 1600/4000 divide that and drop the decimal to equal 0.25.
What is an important first step when building a theory?
\
Overall, building a theory is a complex process that requires careful planning, attention to detail, and a willingness to remain open to alternative explanations and interpretations.
An important first step when building a theory is to formulate a clear and testable research question or hypothesis. A research question or hypothesis is a statement that suggests a relationship between two or more variables, and it guides the development of the theory. The research question or hypothesis should be specific, measurable, and falsifiable, meaning that it can be tested and potentially proven false through empirical research. Once a clear research question or hypothesis has been formulated, the researcher can then begin to gather and analyze data to support or refute the theory.
Another important first step when building a theory is to conduct a comprehensive review of existing literature and research in the field. This review helps the researcher to identify gaps or inconsistencies in current knowledge and to develop a clear understanding of the state of the field. This step can also help the researcher to refine their research question or hypothesis, as well as to identify potential variables and relationships that may be relevant to the theory.
Another important step when building a theory is to select an appropriate research design and methodology that will allow for the systematic collection and analysis of data. The research design should be aligned with the research question or hypothesis, and should enable the researcher to collect high-quality data that can be analyzed using appropriate statistical or qualitative methods.
In addition, it is important to be mindful of potential biases that can impact the development of a theory, such as confirmation bias or researcher bias. It is important for the researcher to be objective and to consider all possible explanations for their data, rather than solely seeking out evidence that supports their hypothesis or preconceived ideas.
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Charlie reads quickly. He reads
1
3
7
1
7
3
1, start fraction, 3, divided by, 7, end fraction pages every
2
3
3
2
start fraction, 2, divided by, 3, end fraction minutes. Charlie reads at a constant rate.
Charlie reads [tex]2\frac{1}{7}[/tex] pages per minute.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, Charlie reads [tex]1\frac{3}{7}[/tex] pages every [tex]\frac{2}{3}[/tex] minute.
Therefore, His unit rate can be obtained by dividing the number of pages by the amount of time which is,
= [tex]\frac{1\frac{3}{7}}{\frac{2}{3}}[/tex] pages per minute.
= (10/7)×(3/2) pages per minute.
= 30/14 pages per minute.
= 15/7 pages per minute.
= [tex]2\frac{1}{7}[/tex] pages per minute.
Q. Charlie reads quickly he reads [tex]1\frac{3}{7}[/tex] pages every [tex]\frac{2}{3}[/tex] minute, His unit rate of page per minute would be?
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Raju used a piece of wire to make shape
(p +10)
(p+10) 25 cm
a) what was the original length of the piece of wire?
b) given that p=6 find the perimeter of the figure
What’s the value of x?
Answer:
The value of [tex]x[/tex] is [tex]55\textdegree[/tex].
Step-by-step explanation:
A straight line is equal to 180 degrees.
So any angles that forms on the same side of a straight line always add to 180 degrees.
We are given an angle of [tex]130\textdegree[/tex] on the exterior of the triangle.
Lets call the angle next to that [tex]\angle B[/tex].
We can conclude that
[tex]\angle B+130=180[/tex]
[tex]\angle B=180-130[/tex]
[tex]\angle B=50[/tex]
The sum of the interior angles in a triangle is 180 degrees. This is because a triangle is a polygon with three sides and three angles, and the sum of the angles in any polygon can be found by using the formula:
sum of interior angles = (n - 2) x 180 degrees
Note: n is the number of sides.
A triangle has 3 sides. So substituting 3 in for n gives us
(3 - 2) x 180 degrees = 180 degrees
So the sum of the interior angles in a triangle is always 180 degrees.
[tex]x\textdegree=180\textdegree-75\textdegree-50\textdegree\\x\textdegree=55\textdegree[/tex]
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How much is 10 mL in teaspoons or tablespoons?
10 mL is equal to 2 teaspoons or 0.67 tablespoons. One teaspoon is equal to 5 mL, so to convert 10 mL to teaspoons, divide 10 by 5. One tablespoon is equal to 15 mL, so to convert 10 mL to tablespoons, divide 10 by 15.
10 mL is equal to 2 teaspoons (tsp) or 0.67 tablespoons (tbsp).
One teaspoon is equal to 5 mL, so to convert 10 mL to teaspoons, you can divide 10 by 5, which gives:
10 mL / 5 mL/tsp = 2 tsp
Therefore, 10 mL is equal to 2 teaspoons.
One tablespoon is equal to 15 mL, so to convert 10 mL to tablespoons, you can divide 10 by 15, which gives:
10 mL / 15 mL/tbsp = 0.67 tbsp
Therefore, 10 mL is equal to approximately 0.67 tablespoons.
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What is the mean of this set 0,3,6,9,11,13,14
Answer:
8
Step-by-step explanation:
0+3+6+9+11+13+14 = 56
56/7 = 8
Find the radius of each circle. Use calculators value of pie. Round answer to the nearest tenth
area=153.9cm2
The radius of the circle is 7 centimeter.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
We have to find the radius r of the circle when area is 153.9 square centimeter.
A=πr²
153.9=3.14r²
Divide both sides by 3.14
153.9/3.14=r²
49.01=r²
Take square root on both sides
r=7
Hence, the radius of the circle is 7 centimeter.
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solve for solutions 18. y = -6x-2
12x + 2y = -6
The solution to the system of equations:
y = -6x - 2
12x + 2y = -6
This is an inconsistent system of equations
What is an Equation ?
An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.
For example, 3x+2y=0.
Types of equation
1. Linear Equation
2. Quadratic Equation
3. Cubic Equation
we can substitute the value of y from the first equation into the second equation:
12x + 2(-6x - 2) = -6
12x + -12x - 4 = -6
0x - 4 = -6
-4 = -6
This is an inconsistent system of equations, which means that there are no real solutions that satisfy both equations.
This means that there is no point at which both lines intersect and that the two lines are parallel, never meeting.
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What is the sum of the following temeratures? -10°C; 24 °C; -12°C;8°C; -1 °C
The sum of the given temperature measures as required is; -9°C.
What is the value of the addition of the give temperatures;It follows from the task content that the sum of the given temperature measures is to be determined.
Since the given temperatures are; -10°C; 24 °C; -12°C; 8°C; -1 °C.
Therefore, the sum of the temperatures can be determined as follows;
-10°C + 24 °C + -12°C + 8°C + -1 °C
= 9°C.
Ultimately, the sum of the given temperatures is; 9°C.
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Does anyone have the answers to the first part of UNIT 3 Polynomials and Factoring LESSON 9 Polynomials and Factoring Unit Test Connexus
A polynomial is an expression consisting of variables and coefficients and factoring is the process of breaking down a polynomial into simpler units
A polynomial is an expression consisting of variables and coefficients, which are combined using only addition, subtraction, and multiplication. For example, 3x^2 + 2x - 1 is a polynomial, where x is the variable, 3 and 2 are coefficients, and ^2 and ^1 are exponents.
Factoring is the process of breaking down a polynomial into simpler units, which can be multiplied together to obtain the original polynomial. The simplest units are usually linear expressions, which have the form ax + b, where a and b are coefficients. For example, the polynomial 3x^2 + 2x - 1 can be factored into (3x - 1)(x + 1) by identifying two linear expressions that when multiplied together produce the original polynomial.
Factoring is an important tool in algebra, as it can help to simplify expressions, solve equations, and identify the roots of a polynomial.
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What is the area of this figure?
Please hurry!
Answer: 89 mm^2; Option 1
Step-by-step explanation: Solve the area of the largest rectangle by multiplying 7 and 8. That equals 56. Then do 4 times six to get the area of the medium rectangle and thats 24. Do the same thing with the small square and you get nine. Add them up to get 89.
You have cubes with edge lengths of 1/4 inch, 1/3 inch, and
1/2 inch. If you only use ONE size of cube, which can you use to fill the container? Explain your reasoning.
The size of the cube that can be used to fill the [tex]1\frac{2}{3}[/tex] inches, [tex]\frac{2}{3}[/tex] inch, [tex]2\frac{1}{3}[/tex] inches is the cube with edge length of 1/3 inches
What is a cube?A cube is a three dimensional solid with six congruent square faces.
The expression the height and length dimensions of the rectangular prism as improper fractions, indicates that we get;
Height = (1 2/3) cm = (3 × 1 + 2)/3 cm = 5/3 cm
Length = (2 1/3) cm = (3 × 2 + 1)/3 cm = 7/3 cm
The denominators of the dimensions of the height, length and width of the rectangular prism are equivalent to 3. The edge length of the cube that can be used to fill the container should have a denominator that is a factor of 3.
The size of the cube that can be used to fill the container is therefore the cube with side length of 1/3 inches
The volume of the container = (5/3) in × (2/3) in × (7/3) in = 70/27 in³
The volume of the (1/3) inch cube = (1/3) in ×(1/3) in ×(1/3) in = 1/27 in³
The number of 1/3 inch cubes that fills the container = (70/27)/(1/27) = 70
The possible dimensions of the rectangular prism container in the question obtained from a similar question posted online are;
Height = (1 2/3) centimeters
Width = (2/3) centimeters
Length = (2 1/3) centimeters
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base area 42 m height 8 m
Where may you be going with this?
please help hurry i need help hurry calculating slope
The slopes for the given pairs of points are:
015/14-2/5-25/21014How to find the slopesTo find the slope of a line passing through two points (x1, y1) and (x2, y2), we use the formula:
slope = (y2 - y1) / (x2 - x1)
Using this formula for each pair of points, we get:
(19, 3), (20, 3)
slope = (3 - 3) / (20 - 19) = 0/1 = 0
(3,0), (-11, -15)
slope = (-15 - 0) / (-11 - 3) = -15 / -14 = 15/14
(19,-2), (-11, 10)
slope = (10 - (-2)) / (-11 - 19) = 12 / (-30) = -2/5
(6, -10), (-15, 15)
slope = (15 - (-10)) / (-15 - 6) = 25 / (-21) = -25/21
(12,-18), (-15, -18)
slope = (-18 - (-18)) / (-15 - 12) = 0 / (-27) = 0
(3,-20), (5, 8)
slope = (8 - (-20)) / (5 - 3) = 28 / 2 = 14
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how do i do this please
If FG is parallel to KL , then the ratio of FJ to KJ must be equal to GJ to JL. Therefore FG is not parallel to KL
What are similar triangles?Two objects are similar if they have the same shape, or if one has the same shape as the mirror image of the other. More precisely, one can be obtained from the other by uniformly scaling, possibly with additional translation, rotation and reflection.
The ratio of corresponding sides of Similar triangles are equal.
This means that 32/72 must be equal to 48/64
32/72 = 8/18 = 4/9
48/64 = 12/16 = 3/4
Since the ratio of the corresponding sides are not
equal ∆FGJ is not similar to JKL and thus FG is not parallel to KL
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Find & particular solution Yp of the following equation using the Method of Undetermined Coefficients. Primes denote the derivatives with respect to x
y" -y' - 2y = 8x + 5 A particular solution is Yp(x) = ?
(a) The particular solution, y_p is 7
(b) y_p is -4x
(c) y_p is -4x + 7
(d) y_p is 8x + (7/2)
To find a particular solution to a differential equation by inspection - is to assume a trial function that looks like the non-homogeneous part of the differential equation.
(a) Given y'' + 2y = 14.
Because the no non-homogeneous part of the differential equation, 14 is a constant, our trial function will be a constant too.
Let A be our trial function:
We need our trial differential equation y''_p + 2y_p = 14
Now, we differentiate y_p = A twice, to obtain y'_p and y''_p that will be substituted into the differential equation.
y'_p = 0
y''_p = 0
Substitution into the trial differential equation, we have.
0 + 2A = 14
A = 6/2 = 7
Therefore, the particular solution, y_p = A is 7
(b) y'' + 2y = −8x
Let y_p = Ax + B
y'_p = A
y''_p = 0
0 + 2(Ax + B) = -8x
2Ax + 2B = -8x
By inspection,
2B = 0 => B = 0
2A = -8 => A = -8/2 = -4
The particular solution y_p = Ax + B
is -4x
(c) y'' + 2y = −8x + 14
Let y_p = Ax + B
y'_p = A
y''_p = 0
0 + 2(Ax + B) = -8x + 14
2Ax + 2B = -8x + 14
By inspection,
2B = 14 => B = 14/2 = 7
2A = -8 => A = -8/2 = -4
The particular solution y_p = Ax + B
is -4x + 7
(d) Find a particular solution of y'' + 2y = 16x + 7
Let y_p = Ax + B
y'_p = A
y''_p = 0
0 + 2(Ax + B) = 16x + 7
2Ax + 2B = 16x + 7
By inspection,
2B = 7 => B = 7/2
2A = 16 => A = 16/2 = 8
The particular solution y_p = Ax + B
is 8x + (7/2)
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