a) Find the general solution y=yc+yp of the differential equation
y'' + x^2 y' +2xy = 5-2x+10x^3
that consists of three power series centered at x =0. You can list the first five nonzero terms of each power
series.
b) Consider the initial value problem
y' = √1-y^2 y(0)=0
Show that y= sin x is the solution of the initial value problem (b).
c) Look for a solution of the initial value problem (b) in the form of a power series about x = 0. Find
the coefficients up to the term in x^7 in this series.
Answers
a) To find the general solution of the given differential equation, a power series centered at x=0 is used, and the first five nonzero terms of each power series are determined.
b) The solution to the initial value problem y' = √(1-y^2), y(0) = 0, is shown to be y = sin(x).
c) The coefficients up to the term in x^7 are found for a power series solution of the initial value problem y' = √(1-y^2), y(0) = 0.
a) To find the general solution y = yc + yp of the given differential equation:
y'' + x^2 y' + 2xy = 5 - 2x + 10x^3,
we can first find the complementary solution yc by assuming a power series of the form y = ∑(n=0 to ∞) a_n x^n. Substituting this series into the differential equation and equating coefficients of like powers of x, we can determine the values of the coefficients a_n. However, for simplicity, we will only consider the first five nonzero terms of the power series.
Let's write the power series for yc:
yc = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + ...
Differentiating twice with respect to x, we get:
y' = a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + ...
y'' = 2a_2 + 6a_3 x + 12a_4 x^2 + ...
Substituting these series into the differential equation, we have:
(2a_2 + 6a_3 x + 12a_4 x^2 + ...) + x^2(a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + ...) + 2x(a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + ...) = 5 - 2x + 10x^3
To equate coefficients, we match the powers of x on both sides of the equation:
For the term without x:
2a_2 + a_0 = 5
For the term with x:
6a_3 + 2a_2 + a_1 = -2
For the term with x^2:
12a_4 + 3a_3 + 2a_1 + a_2 = 0
For the term with x^3:
4a_4 + 4a_2 + a_3 = 10
For the term with x^4:
a_4 = 0 (no coefficient on the right-hand side)
Solving this system of equations will give us the values of a_0, a_1, a_2, a_3, and a_4. Since we are only interested in the first five nonzero terms of the power series, we will truncate the series at the fifth term.
b) To show that y = sin(x) is the solution to the initial value problem y' = √(1-y^2), y(0) = 0:
We can differentiate y = sin(x) to obtain y' = cos(x). Substituting this into the differential equation, we have:
cos(x) = √(1 - sin^2(x))
Using the trigonometric identity sin^2(x) + cos^2(x) = 1, we simplify the equation to:
cos(x) = √(cos^2(x))
Taking the positive square root, we have:
cos(x) = cos(x)
This confirms that y = sin(x) satisfies the differential equation y' = √(1-y^2).
c) To find a power series solution for the initial value problem y' = √(1-y^2), y(0) = 0, we assume a power series of the form y = ∑(n=0 to ∞) a_n x^n. Substituting this series into the differential equation and equating coefficients, we can determine the values of the coefficients a_n up to the term in x^7.
Let's write the power series for y:
y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + a_5 x^5 + a_6 x^6 + a_7 x^7 + ...
Differentiating y with respect to x, we get:
y' = a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + 5a_5 x^4 + 6a_6 x^5 + 7a_7 x^6 + ...
Substituting these series into the differential equation, we have:
a_1 + 2a_2 x + 3a_3 x^2 + 4a_4 x^3 + 5a_5 x^4 + 6a_6 x^5 + 7a_7 x^6 + ... = √(1 - (a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + a_5 x^5 + a_6 x^6 + a_7 x^7 + ...)^2)
Simplifying this equation and equating coefficients of like powers of x, we can determine the values of the coefficients a_n up to the term in x^7.
To find the coefficients up to the term in x^7, you will need to perform the substitution and equate coefficients. It will involve expanding the square root and equating coefficients of each power of x from 0 to 7 on both sides of the equation.
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Related Questions
Users can learn how to use a program by referring to the Blank______ feature within the application. quizlet
Answers
Users can learn how to use a program by referring to the interactive tutorial feature within the application, Quizlet.
Quizlet is a popular online learning platform that offers a variety of educational tools and resources, including interactive tutorials. These tutorials are designed to guide users through the process of using a particular program or application. By accessing the "Blank" feature within Quizlet, users can practice and familiarize themselves with the program's interface and functionality.
The "Blank" feature allows users to interact directly with the program by presenting them with a blank canvas or workspace where they can perform various tasks or exercises. This hands-on approach helps users develop practical skills and gain confidence in using the program effectively.
By following the step-by-step instructions provided within the interactive tutorial feature, users can learn how to navigate through the program's menus, understand its features and tools, and perform specific actions or tasks. The tutorial may include demonstrations, explanations, and interactive exercises that allow users to practice and reinforce their understanding.
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50 Points!!! Are collinear lines real? If so, explain.
Answers
Answer:
You may see many real-life examples of collinearity such as a group of students standing in a straight line, a bunch of apples kept in a row, next to each other, etc. In geometry, two or more points are said to be collinear, if they lie on the same line.
Step-by-step explanation:
Hope this helps!=D
Is 5cm 3cm 7cm is a sides of a triangle?.
Answers
Answer:
Yes! The sides 5,3 and 7 can create a triangle!
Step-by-step explanation:
It follows the rule:
a + b > c
a + c > b
c + b > a
Find the lateral area of this cone.
Answers
Step-by-step explanation:
lateral surface area here = πrl
r = 10
l = √h²+r²= √ 24²+ 10² = 26
lateral surface area = 10 × 26 × π
= 260π in²
hope this will be helpful to you .
plz mark my answer as brainlist if you find it useful.
Answer:
The lateral area of cone is 260π in².
Step-by-step explanation:
Given : \(\small\blue\bull\) Height of cone = 24 in.\(\small\blue\bull\) Radius of cone = 10 in.\(\begin{gathered}\end{gathered}\)
To Find : \(\small\blue\bull\) Slant height of cone \(\small\blue\bull\) Lateral surface area of cone\(\begin{gathered}\end{gathered}\)
Using Formulas :\(\star{\underline{\boxed{\sf{\purple{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}}}\)
\(\pink\star\) l = slant height \(\pink\star\) r = radius \(\pink\star\) h = height\(\star{\underline{\boxed{\sf{\purple{La_{(Cone)}= \pi r\ell}}}}}\)
\(\pink\star\) La = Lateral area\(\pink\star\) π = 3.14 \(\pink\star\) r = radius \(\pink\star\) l = slant height\(\begin{gathered}\end{gathered}\)
Solution :Finding the slant height of cone by substituting the values in the formula :
\(\begin{gathered} \qquad{\longrightarrow{\sf{\ell = \sqrt{{(r)}^{2} + {(h)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10)}^{2} + {(24)}^{2}}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{{(10 \times 10)} + {(24 \times 24)}}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{(100)+(576)}}}}\\\\\qquad{\longrightarrow{\sf{\ell = \sqrt{100 + 576}}}}\\\\\quad{\longrightarrow{\sf{\ell = \sqrt{676}}}}\\\\\quad{\longrightarrow{\sf{\ell = 26 \: in}}}\\\\\quad\star\underline{\boxed{\sf{\pink{\ell = 26 \: in}}}} \end{gathered}\)
Hence, the slant height of cone is 26 in.
\(\begin{gathered}\end{gathered}\)
Now, finding the lateral area of cone by substituting the values in the formula :
\(\begin{gathered} \qquad{\longrightarrow{\sf{La_{(Cone)} = \pi r \ell}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 10 \times 26}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = \pi \times 260}}}\\\\\qquad{\longrightarrow{\sf{La_{(Cone)} = 260\pi\: {in}^{2}}}}\\\\ \qquad{\star{\underline{\boxed{\sf{\pink{La_{(Cone)} = 260\pi \: {in}^{2}}}}}}}\end{gathered}\)
Therefore, the lateral area of cone is 260π in².
\(\rule{300}{2.5}\)
a family has a bill of 26 dollars and want to leave a 15% tip
Answers
Answer:
The 15% tip is $3.90
Step-by-step explanation:
To find 15% of $26, multiply .15 × 26
You get 3.9 that is $3.90. (If we aren't talking about dollars$, then sorry, but the numbers/math is the same)
If you're at the table and everyone's phone is dead (so no calculators), then find 10%:
10% of 26.00 is 2.60 (just move the decimal to the left one place)
Cut it in half to find 5%:
Half of 2.60 is 1.30
Add them together:
2.60 + 1.30 is 3.90
15% of 26 is 3.90
Please help me I will give you extra points and the crown
What is the special angle pair relationship between <1 and <3
Answers
From the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.
As given in the question,
From the given figure:
line l is parallel to line m.
t is the transversal of line l and m
Relationship between angles for the parallel lines
∠1 and ∠2 are straight angles and are supplementary
∠3 and ∠2 are interior angles and are supplementary
⇒m(∠1 + ∠2) = m(∠3+∠2)
⇒m∠1= m∠3
Therefore, from the given figure , the special angle pair relationship between ∠1 and ∠3 are known as corresponding angles and are congruent.
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Jesse and Mark are jogging along the route shown at a rate of 12 miles per hour. They start by jogging south along Capitol Street for 1 mile, then turn east on H Street and jog for 1.75 miles. At that point, Jesse is tired and decides to walk home along Florida Avenue at a rate of 5 miles per hour. Mark plans to jog back the way they came. Jesse wants to find out who will arrive home first and by how much time. Which statements should he consider when solving the problem? Check all that apply
Answers
Answer:
the answer is 1,2,4,5 and 7.
Answer: The answer is A,B,D,E,G
Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.
Jevonne is on his way home from a vacation. He is staring 818 miles from home and drives about 65 miles per hour. The function d=818-65h represents Jevonne's distance from home d after driving h hours. Part A: Describe an appropriate domain of this function, using x to represent time, given the context using inequality notation
Answers
The appropriate domain of the function, using h to represent time, is [0, ∞) or h ≥ 0, since Jevonne's distance from home can never be negative.
Since Jevonne's distance from home can never be negative, the domain of the function is restricted to non-negative values of h. Therefore, an appropriate domain of the function, using h to represent time, is:
h ≥ 0
Inequality notation can be used to express this domain as:
[0, ∞)
This means that h can take any non-negative value, including zero (which corresponds to the starting point of Jevonne's journey), and can increase without bound as Jevonne continues to drive further away from home.
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Solve 2(x+ 1) = 2x + 2
Answers
Answer:
2(x+1)
Step-by-step explanation:
I think it's work.
15/53
1
35%
White shapes and black shapes are used in a game.
Some of the shapes are circles.
All the other shapes are squares.
OD
The ratio of the number of white shapes to the number of black shapes is 5:11
The ratio of the number of white circles to the number of white squares is 3:7
The ratio of the number of black circles to the number of black squares is 3:8
Work out what fraction of all the shapes are circles
Answers
9/32 is fraction of all the shapes are circles .
What does a math ratio mean?
An ordered pair of numbers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls)Find the equivalent ratio for the total shapes:
Total Black Shapes : Total White Shapes = 5 : 11
Multiply by 2:
Total Black Shapes: Total White Shapes = 10 : 22
Find the ratio for the white shapes:
White circles : White squares = 3 : 7
Sum of the units = 3 + 7
Sum of the units = 10
Find the equivalent ratio for the total shapes:
Black circles : Black squares = 3 : 8
Multiply by 2:
Black circles : Black squares = 6 : 16
Sum of the units = 6 + 16
Sum of the units = 22
Combine the ratios:
white circles : white squares : black circles : black square = 3 : 7 : 6 : 16
Circles = 3 + 6
Circles = 9 units
Total = 3 + 7 + 6 + 16
Total = 32 units
Find the fraction of all the shapes that are circles:
Fraction = 9/32
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For a positively skewed distribution with a mode of x = 31 and a mean of 36, the median is most probably?
Answers
According to the question the median is most probably less than 36.
For a positively skewed distribution, the mode is the value that occurs most frequently, the mean is the average value, and the median is the middle value when the data is arranged in ascending order.
Given that the mode is \(\(x = 31\)\) and the mean is \(\(36\),\) we can infer that the majority of the data is clustered towards the left (lower values) and there are some relatively high values that pull the mean to the right.
Since the distribution is positively skewed, the median is expected to be lower than the mean. This is because the presence of outliers or higher values on the right side of the distribution affects the mean more than the median.
Therefore, the median is most probably less than 36.
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please hurry
Simplify: 14-30/ 2 (- 4)
Answers
Answer:
74
Step-by-step explanation:
PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. The value of the given expression (14-30)/2(-4) when simplified is 2.
What is PEMDAS?PEMDAS is an acronym that refers to the sequence of operations to be employed when solving equations with multiple operations. PEMDAS is an acronym that stands for P-Parenthesis, E-Exponents, M-Multiplication, D-Division, A-Addition, and S-Subtraction.
The given expression can be simplified as shown below.
(14 - 30)/ 2 (- 4)
Using the rule of PEMDAS, solving parenthesis first,
= (14-30) / (-8)
= (-16)/ (-8)
Solving the division,
= 2
Hence, The value of the given expression (14-30)/2(-4) when simplified is 2.
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why is pi divided by 2 irrational
Answers
Answer:
pi is an irrational number, so cannot be expressed as a fraction
I think this is what you mean but if it's not sorry
One gram of protein contains 4 calories. One gram of fat contains 9 calories. A snack has 60 calories from grams of protein and grams of fat.
The equation represents the relationship between these quantities.
Determine if each pair of values could be the number of grams of protein and fat in the snack. Be prepared to explain your reasoning.
5 grams of protein and 2 grams of fat
10.5 grams of protein and 2 grams of fat
8 grams of protein and 4 grams of fat
If there are 6 grams of fat in the snack, how many grams of protein are there? Show your reasoning.
In this situation, what does a solution to the equation tell us? Give an example of a solution.
Answers
10.5 grams of protein and 2 grams of fat are the possible values of protein and fat based on the given algebraic equation.
If there are 6 grams of fat in the snack, using the algebraic equation, there would be 1.5 grams of protein in the cracker.
How to Analyze Relationships Using Algebraic Equations?Given the algebraic equation that represents the relationship between the quantities of protein and fat contained in a snack as 4p + 9f = 60 , where f represents quantity of fat, and p represents the quantity of protein, to determine if each pair of values can be the number of protein and fat that are contained in the snack, substitute the given values into the algebraic equation.
If the right side of the equation and left side are equal, then the values for the number of grams for protein and fat are correct.
Given, p = 5, f = 2, substitute the values into 4p + 9f = 60:
4(5) + 9(2) = 60
38 ≠ 60 [not true]
Given, p = 10.5, f = 2, substitute the values into 4p + 9f = 60:
4(10.5) + 9(2) = 60
60 = 60 [true]
Given, p = 8, f = 4, substitute the values into 4p + 9f = 60:
4(8) + 9(4) = 60
68 ≠ 60 [not true]
Given, f = 6, substitute the value into 4p + 9f = 60 to find the grams of protein:
4p + 9(6) = 60
4p = 60 - 54
4p = 6
p = 1.5 grams of protein
This solution tells us that there are 1.5 grams of protein where you have 6 grams of fat in a cracker.
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Can u help me please
Answers
The slope of the line as shown in the diagram is 4/3.
What is slope?The slope of a line is the ratio of the amount that y increases as x increases some amount.
To calculate the slope from the diagram, we use the formula below.
Formula:
S = Δy/Δx........... Equation 1Where:
S = Slope.From the graph,
At x = 30, y = 20
And at x = 60, y = 60
Therefore,
Δy = 60-20 = 40Δx = 60-30 = 30Substitute these values into equation 1
S = 40/30S = 4/3Hence, the slope of the is 4/3.
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X^2 = 14
I need help answer asap
Answers
Answer:
x = ±sqrt(14)
Step-by-step explanation:
x^2 = 14
Take the square root of each side
sqrt(x^2) = ±sqrt(14)
x = ±sqrt(14)
18. John wants to have an interest income of $3,000 a year. How much must he invest for one
year at 8%?
Answers
Using simple interest, John must invest $37500 for one year at 8%
In this question we have been given John wants to have an interest income of $3,000 a year.
We need to find the amount of money he must invest for one year at 8%
We know that formula of simple interest is:
I = Prt
where P = Principal Amount
I = Interest Amount
r = Interest rate in decimal;
R = Interest rate as a percent; r = R/100
t = Time Periods
Given that Interest Amount per year I = $3000
Rate of interest R = 8%
r = 0.08
To find P = ?
P = I / rt
P = 3000 / (0.08 * 1)
P = $37500
Therefore, the amount of money he must invest for one year at 8% = $37500
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please help me I have to get this done before we go on break
Answers
Answer:
1st answer option
Step-by-step explanation:
6^(1/3) / 6^(1/4) = 6^(1/3) × 6^(-1/4) = 6^(1/3 - 1/4) =
= 6^(4/12 - 3/12) = 6^(1/12)
use laplace transforms to solve the initual value problem y'-4y =f(x), y(0)=0 2 0<=x and x<4
Answers
The solution to the initial value problem y'-4y=f(x), y(0)=0 for 0<=x<4 is given by:
y(x) = F(-4)e^(-4x)
The Laplace transform of the differential equation y'-4y=f(x) is given by:
sY(s) - y(0) - 4Y(s) = F(s)
where Y(s) and F(s) are the Laplace transforms of y(x) and f(x), respectively.
Substituting the initial condition y(0)=0 and rearranging, we get:
Y(s) = F(s)/(s+4)
Now we need to find the inverse Laplace transform of Y(s) to obtain the solution y(x). Using the partial fraction decomposition method, we can write:
Y(s) = A/(s+4) + B
where A and B are constants to be determined.
Multiplying both sides by (s+4), we get:
F(s) = A + B(s+4)
Setting s=-4, we get:
A = F(-4)
Setting s=0, we get:
B = Y(0) = y(0) = 0
Therefore, the partial fraction decomposition of Y(s) is given by:
Y(s) = F(-4)/(s+4)
Taking the inverse Laplace transform of Y(s), we get:
y(x) = L^-1{F(-4)/(s+4)} = F(-4)L^-1{1/(s+4)}
Using the table of Laplace transforms, we find that the inverse Laplace transform of 1/(s+4) is e^(-4x). Therefore, the solution to the initial value problem is given by:
y(x) = F(-4)e^(-4x)
where F(-4) is the value of the Laplace transform of f(x) evaluated at s=-4.
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What is the measure of z? X 4 Z 9 z= [?]V Give your answer in simplest form.
![What is the measure of z? X 4 Z 9 z= [?]V Give your answer in simplest form.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/78Sr9AV5atRLFFx0j7jTPbHBO91KKQcS.jpeg)
Answers
Answer:
3√13
Step-by-step explanation:
4 : y = y = 9
y^2 = 36
y = 6
z = \(\sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}\)
117 = 3^2 * 13
\(\sqrt{117} = \sqrt{3^2 * 13} = 3\sqrt{13\)
Convert \(\frac{7\pi }{4}\) to degrees.
![Convert [tex]\frac{7\pi }{4}[/tex] to degrees.](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/OraDkuCHmYj4QdVxaqErC1sjFrZaZltG.png)
Answers
To explain
7pi 180°
—— * ——-
4 pi
The pi cancels out because they are across from eachother
Which leaves
7/4 and 180
We divide 180 by 4=45°
And now 45° multiplied by 7 is equal to 315°
The spring dance committee has a budget of $125 to decorate the gym for the spring dance. They have already spent $65. Some members want to buy helium balloons that cost $.80 each right and solve an inequality to show the number of balloons that the dance committee could buy.
Answers
The inequality representing the number of balloons the dance committee could buy is x ≤ 75. This means that the committee can buy up to 75 balloons with the remaining budget of $60.
To solve the inequality representing the number of balloons the dance committee could buy, let's denote the number of balloons as "x." Since each balloon costs $0.80, the total cost of the balloons can be calculated by multiplying the cost per balloon with the number of balloons:
Total cost of balloons =\($0.80 \times x\)
The committee has a budget of $125, and they have already spent $65. Therefore, the amount of money remaining for buying balloons can be determined by subtracting the amount spent from the total budget:
Money remaining = Budget - Amount spent
Money remaining = $125 - $65
Money remaining = $60
The total cost of the balloons should not exceed the money remaining in the budget. Hence, we can set up the inequality:
$0.80 \(\times x\) ≤ $60
To isolate x, we divide both sides of the inequality by $0.80:
x ≤ $60 / $0.80
x ≤ 75
Its important to note that the inequality assumes that the committee wants to use the entire remaining budget for buying balloons. If they want to allocate some of the remaining money for other decorations or expenses, the maximum number of balloons they can buy may be less than 75
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Can someone help with this problem
Answers
Answer:
Step-by-step explanation:
The answer is C. 5x + 15 because the 5 outside the parentheses () is supposed to multiply by what's inside the parentheses. So multiply 5 and x and 5 and 3 (5 * X = 5x) (5 * 3 = 15).
Which equation describes a circle with a radius of 4 and a center located at (-5, 2)?
A. (1 – 5)2 + (y + 2)2 = 4
B. (1 – 5)2 + (y + 2)2 = 16
C. (1 + 5)2 + (y - 2)2 = 4
D. (1 + 5)2 + (y - 2)2 = 16
Answers
B is the answer. It makes perfect sense
TRUE or FALSE: -5 < 3
Answers
Answer:
true
Step-by-step explanation:
Algebraic Proof
Match the justification to each step of the deductive reasoning about this picture. Please Help!
Answers
The following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
3. 3x + 15 = 6x (Combining like terms)
4. 15 = 3x (Subtraction Property of Equality)
5. x = 5 (Division Property of Equality)
6. CE = 6(5) (Substitution)
Recall:
The Segment Addition Postulate states that when a point lies between two endpoints on a line segment, the length of the larger segment equals the sum of the lengths of the two smaller segments formed.Thus, the following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
Rationale: Plug in the values of CD, DE and CE3. 3x + 15 = 6x (Combining like terms)
Rationale: Add 8 and 7 together4. 15 = 3x (Subtraction Property of Equality)
Rationale: Subtract 3x from each side of the equation.5. x = 5 (Division Property of Equality)
Rationale: Divide each side of the equation by 3).6. CE = 6(5) (Substitution)
Rationale: Plugging in the value of x into "6x"Learn more about Segment Addition Postulate on:
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You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you
decide to swim 15 minutes longer than she does one day at practice.
Write an equation for the number of minutes you swim, y, when your friend swims 2 number of minutes.
You swim 55 minutes.
How many minutes did your friend swim?
minutes
Answers
Answer:
40 minutes
Step-by-step explanation:
Answer:
Y = X + 15*D
Step-by-step explanation:
Y = Person Swims During Practice
X = Frien Swims During Practice
D = number of Days both Practice
its given that daily 15 minutes longer swim then Friend
Hence
Y = X + 15*D
Question 38.
Write the first six terms of the arithmetic sequence with the first term, a1 = 240, and common difference, d= 24.
The first six terms are a1 = ,a3= , a4= ,a5= , and a6= .
Answers
\(a(1) = 240 \\ a(2) = a(1) + d = 240 + 24 = 264 \\ a(3) = a(2) + d = 264 + 24 = 288 \\ a(4) = a(3) + d = 288 + 24 = 312 \\ a(5) = a(4) + d = 312 + 24 = 336 \\ a(6) = a(5) + d = 336 + 24 = 360\)
There are 12 eggs in a dozen. Write an algebraic expression for the number of eggs in d dozen.
Answers
Answer:
4d=48
Step-by-step explanation:
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
9
72
36
27
81
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
O The college will have about 640 students who prefer cookies.
O The college will have about 1,280 students who prefer cookies.
O The college will have about 1,440 students who prefer cookies.
Answers
Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:
D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.
What is an inferential statistic?An inferential statistic is one that makes inference or predictions about a population based on a sample.
From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:
D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.
More can be learned about inferential statistics at brainly.com/question/13852073
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