The indicated function y1(x) is a solution of the given differential equation. use reduction of order or formula (5) in section 4.2, y2 = y1(x) e−∫p(x) dx y 2 1 (x) dx (5) as instructed, to find a second solution y2(x). 9y'' − 12y' + 4y = 0; y1 = e2x/3

Answers

Answer 1

Given that [tex]y_1=e^{2x/3}[/tex], we can use reduction of order to find a solution [tex]y_2=v(x)y_1=ve^{2x/3}[/tex].

[tex]\implies {y_2}'=\dfrac23ve^{2x/3}+v'e^{2x/3}=\left(\dfrac23v+v'\right)e^{2x/3}[/tex]
[tex]\implies{y_2}''=\dfrac23\left(\dfrac23v+v'\right)e^{2x/3}+v''e^{2x/3}=\left(\dfrac49v+v'+v''\right)e^{2x/3}[/tex]

[tex]\implies9y''-12y'+4y=0[/tex]
[tex]\implies 9\left(\dfrac49v+v'+v''\right)e^{2x/3}-12\left(\dfrac23v+v'\right)e^{2x/3}+4ve^{2x/3}=0[/tex]
[tex]\implies9v''-3v'=0[/tex]

Let [tex]u=v'[/tex], so that

[tex]9u'-3u=0\implies 3u'-u=0\implies u'-\dfrac13u=0[/tex]
[tex]e^{-x/3}u'-\dfrac13e^{-x/3}u=0[/tex]
[tex]\left(e^{-x/3}u\right)'=0[/tex]
[tex]e^{-x/3}u=C_1[/tex]
[tex]u=C_1e^{x/3}[/tex]

[tex]\implies v'=C_1e^{x/3}[/tex]
[tex]\implies v=3C_1e^{x/3}+C_2[/tex]

[tex]\implies y_2=\left(3C_1e^{x/3}+C_2\right)e^{2x/3}[/tex]
[tex]\implies y_2=3C_1e^x+C_2e^{2x/3}[/tex]

Since [tex]y_1[/tex] already accounts for the [tex]e^{2x/3}[/tex] term, we end up with

[tex]y_2=e^x[/tex]

as the remaining fundamental solution to the ODE.

Answer 2

The indicated function y1(x) is a solution of the given differential equation.The general solution is [tex]y = c_1 e^{2x}- c_2e^{-6x}/8[/tex]

What is a differential equation?

An equation containing derivatives of a variable with respect to some other variable quantity is called differential equations.

The derivatives might be of any order, some terms might contain the product of derivatives and the variable itself, or with derivatives themselves. They can also be for multiple variables.

Given differential equation is

y''-4y'+4y=0

and

[tex]y_1(x) = e^{2x}[/tex]

[tex]y_2(x) = y_1(x) \int\limits^a_b {e^{\int pdx} \, / y_1 ^2(x)dx[/tex]

The general form of equation

y''+P(x)y'+Q(x)y=0

Comparing both the equation

So, P(x)= - 4

[tex]y_2(x) = y_1(x) \int\limits^a_b {e^{\int pdx} \, / y_1 ^2(x)dx\\\\\\[/tex]

[tex]y_2(x) = e^{2x}\int e^{-4x} \, / e^{4x}dx[/tex]

[tex]y_2(x) = e^{2x}\int e^{-8x}dx\\\\y_2(x) = -e^{-6x}/8[/tex]

The general solution is

[tex]y = c_1 e^{2x}- c_2e^{-6x}/8[/tex]

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Related Questions

help find the answer to this question

Answers

First, find the area of the entire traingle using the formula bh/2.
18*9/2=81 cm^2
Then subtract the area of the smaller triangle within the larger one (white triangle). It has the same base but a height of only 4.
18*4/2=36 cm^2
81-36=45
Final answer: 45 cm^2

The circumference of a circle is 6.28. What is the area of the circle.

Answers

Hello there! Thank you for asking your question here at Brainly. I will be assisting you today with how to handle this problem, and will teach you how to handle it on your own in the future.

First, let's evaluate the question.
"The circumference of a circle is 6.28. What is the area of a circle?"

Now, let's remember the different formulas for area and circumference.
The circumference is "2•3.14•r", while the area is "3.14•r•r".

We have our circumference, 6.28.
However, we are looking for the area. Since we have the circumference, we need to narrow down to the radius (so we can solve for the area).
Let's set this up as an equation;
C = 2 • 3.14 • r
Plug in the value for our circumference.
6.28 = 2 • 3.14 • r
Multiply 2 by 3.14 and r to simplify the right side of the equation.
2 • 3.14 • r = 6.28 • r = 6.28r

We're now left with:
6.28 = 6.28r
Divide both sides by 6.28 to solve for r.
6.28 / 6.28 = 1
6.28r / 6.28 = r

We are now left with the radius:
R = 1.

Now, we can solve for the area.
Remember our formula for the area.
A = r • r • 3.14.
Plug in 1 for r.
A = 1 • 1 • 3.14
A = 3.14.

Your area is 3.14 units^2.

I hope this helps, and has prepared you for your future problems in relation to this topic!

Circumfrence= πd
6.28=3.14*d
6.28/3.14=d
D=2
Area= πr*r
=3.14*1*1
=3.14

Describe the relationship between the similarity ratio of two triangles and the ratio of their areas.

Answers

[tex]\bf \textit{let's say the sides ratio is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{s_1}{s_2} \\\\\\ \textit{then the ratio of their areas is }\cfrac{\bigtriangleup_1}{\bigtriangleup_2}\qquad \cfrac{(s_1)^2}{(s_2)^2}\\\\ -------------------------------\\\\[/tex]

[tex]\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------\\\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}[/tex]

Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. (remember, m is a factor of n if m divides n evenly.)

Answers

This is the following condition in order to get the specific output for this specific problem: if is_a_prime(n): is_prime = True Now all you have to do is write is_a_prime().

For the hard code for this problem:

if n == 2:
is_prime = True
elif n % 2 == 0:
is_prime = False
else:
is_prime = True
for m in range (3, int (n * 0.5) + 1, 2):
if n % m == 0:
is_prime = False
break.

To add, a high-level programming language that is widely used for general-purpose programming, created by Guido van Rossum and first released in 1991 is called Python.

Below is the solution of assign true to is_prime if n has no factors other than 1 and itself.

Further explanation

Python is an interpreted, high-level, general-purpose programming language. Python is created by Guido van Rossum and first released in 1991. Its design philosophy emphasizes code readability. Python is a more productive language than Java because it is an interpretive language which is accompanied by elegant syntax and it makes an excellent choice for scripting and rapid application development in many areas. Python is a general-purpose, versatile and popular because it is concise and easy to read, and it is also a good language to have in any programmer’s stack as it can be used for everything such as web development, software development, data science applications.

Given a positive integer n, assign true to is_prime if n has no factors other than 1 and itself. And remember, m is a factor of n if m divides n evenly. So:

if n == 2:

is_prime = True

elif n % 2 == 0:

is_prime = False

else:

is_prime = True

for m in range (3, int(n**0.5)+1, 2):

if n % m == 0:

is_prime = False

Learn moreLearn more about python https://brainly.com/question/4331067Learn more about python IDLE or similar environment https://brainly.com/question/6280029Learn more about python function https://brainly.com/question/9806744

Answer details

Grade: 9

Subject: mathematics

Chapter: python

Keywords: python, integer, factors, python IDLE, is_prime

Say a certain manufacturing industry has 63.1 thousand jobs in 2008, but is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018. Assuming this holds true, what will be this industry’s percent change from 2008 to 2018? a. 70% b. -27% c. -17% d. -75%

Answers

Using linear function concepts, it is found that the industry’s percent change from 2008 to 2018 will be of:

b. -27%

What is a linear function?

A linear function is modeled by:

[tex]y = mx + b[/tex]

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0.

In this problem:

The industry had 63.1 thousand jobs in 2008, hence b = 63.1.This number is expected to decline at an average annual rate of 1.7 thousand jobs per year from 2008 to 2018, hence m = -1.7.

Thus, the function is:

y = -1.7x + 63.1.

In 2018, which is 10 years after 2008, the value of the function is:

y(10) = -1.7(10) + 63.1 = 46.1.

The percent change is given by the change divided by the initial value, hence:

(46.1 - 63.1)/63.1 = -27%

Hence option b is correct.

More can be learned about linear function concepts at https://brainly.com/question/24808124

The correct answer is b. -27%.

To solve this problem, we need to find the number of jobs in 2018 and then calculate the percent change from 2008 to 2018.

Given information:

- Number of jobs in 2008: 63.1 thousand

- Average annual rate of decline: 1.7 thousand jobs per year

- Time period: 2008 to 2018 (10 years)

Step 1: Find the total decline in jobs from 2008 to 2018.

Total decline in jobs = Average annual rate of decline × Number of years

Total decline in jobs = 1.7 thousand × 10 years = 17 thousand jobs

Step 2: Find the number of jobs in 2018.

Number of jobs in 2018 = Number of jobs in 2008 - Total decline in jobs

Number of jobs in 2018 = 63.1 thousand - 17 thousand = 46.1 thousand jobs

Step 3: Calculate the percent change from 2008 to 2018.

Percent change = (Change in value / Original value) × 100%

Percent change = ((46.1 - 63.1) / 63.1) × 100%

Percent change = (-17 / 63.1) × 100%

Percent change ≈ -27%

Therefore, the industry's percent change from 2008 to 2018 is approximately -27%.

Number of jobs in 2018 = [tex]46.1\text{ thousand} \\[/tex]

Percent change from 2008 to 2018 = [tex]-27\%[/tex]

Each of a certain type of tire on a 4 wheel car lasts exactly 10,000 miles. How many spare tires of this same variety must carried so that a trip of 15,000 miles can just be completed.

Answers

3 spare tires are needed. This works if you rotate the tires every 5,000 miles.

Tire A, B, C, D (and spare is E F G)
first 5,000 miles you use tire A B C D
second 5000 miles you use tire B C D E
third 5000 miles you use A E F G

Each tires is used no more than twice (10,000 miles).

Find the number of permutations of 8 things taken 5 at a time. 40,320 6,720 336

Answers

In probability, the number of ways of arranging objects could be done in combinations and permutations. The only difference between them is if you arrange them with or without repetition. If you choose permutation, then the arrangement should have no repetition. Thus, for permutation, the number of ways of arranging 'r' things out of a total of 'n' objects is:

P = n!/(n-r)!, where the term '!' is called factorial

For example, when you say 8!, that would mean 8×7×6×5×4×3×2×1 = 40,320. Substituting the values:

P = 8!/(8-5)! = 6,720 ways

Final answer:

The number of permutations of 8 things taken 5 at a time is calculated using the formula P(n, k) = n! / (n-k)!, resulting in 6,720 possible permutations.

Explanation:

To find the number of permutations of 8 things taken 5 at a time, we use the formula for permutations, which is:

P(n, k) = n! / (n-k)! where n is the total number of items, and k is the number of items to be chosen.

In this case, n=8 and k=5. Using the formula, we get:

P(8, 5) = 8! / (8-5)! = 8! / 3! = (8 × 7 × 6 × 5 × 4) / (3 × 2 × 1) = 6720.

So, the number of permutations of 8 things taken 5 at a time is 6,720.

What is the solution to the equation 0.8m − 4 = −0.8m?

Answers

m= 2.5 that's the solution for m for them to be equal

0.8m − 4 = −0.8m
0.8m + 0.8m = 4
1.6m = 4
m = 4 /1.6
m = 2.5

What is the probability that a person who is older than 35 years has a hemoglobin level between 9 and 11

Answers

Answer:

1. The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is 0.284.

2. The probability that a person who is older than 35 years has a hemoglobin level of 9 and above is 0.531.

Step-by-step explanation:

Let the number of person who is older than 35 years has a hemoglobin level between 9 and 11 be x.

From the given table it is clear that the total number of person who is older than 35 years is 162.

[tex]76+x+40=162[/tex]

[tex]x+116=162[/tex]

[tex]x=162-116[/tex]

[tex]x=46[/tex]

The number of person who is older than 35 years has a hemoglobin level between 9 and 11 is 46.

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is

[tex]P=\frac{\text{Person who is older than 35 years has a hemoglobin level between 9 and 11}}{\text{Person who is older than 35 years}}[/tex]

[tex]P=\frac{46}{162}\approx 0.284[/tex]

The probability that a person who is older than 35 years has a hemoglobin level between 9 and 11 is 0.284.

Person who is older than 35 years has a hemoglobin level of 9 and above is

[tex]46+40=86[/tex]

The probability that a person who is older than 35 years has a hemoglobin level of 9 and above is

[tex]P=\frac{\text{Person who is older than 35 years has a hemoglobin level of 9 and above}}{\text{Person who is older than 35 years}}[/tex]

[tex]P=\frac{86}{162}\approx 0.531[/tex]

The probability that a person who is older than 35 years has a hemoglobin level of 9 and above is 0.531.

Answer:

.531

Step-by-step explanation:

Plato

Suppose that an individual has a body fat percentage of 17.9% and weighs 132 pounds. How many pounds of her weight is made up of fat? Round your answer to the nearest tenth.

Answers

f=132(17.9/100)

f=2362.8/100

f=23.628

f≈23.6 pounds (to nearest tenth of a pound)

Here are the scores of 17 students on a history test. 62, 65, 66, 67, 67, 76, 77, 78, 79, 80, 86, 88, 88, 89, 90, 91, 92 Notice that the scores are ordered from least to greatest. Make a box-and-whisker plot for the data.

Answers

I added a picture with it for you. I suggest that before this becomes an issue you take some time and study box and whisker plots, because they tend to show up on a lot of standardized math tests.

Coffee with sugar and milk added to it can contain up to calories. To consume a maximum of 600 mg if caffeine per day, how many full eight-ounce servings of a name-brand coffee with 330 mg of caffeine per 16-ounce serving could someone drink in a day and still stay below this limit? full 8-ounce servings

Answers

We know there is 330 mg of caffeine per 16-ounce serving. So if we want 8-ounce servings:
330 mg : 2 = 165 mg
Also we have to consume a maximum of 600 mg.
165 mg * 3 = 495 mg < 600 mg
165 mg * 4 = 660 mg > 600 mg
Answer: Someone could drink 3 full 8-ounce servings in a day and still stay below the limit.

Answer:

A) 500

B) 3

Right on edge

Step-by-step explanation:

Find the value of x
A 41
B 44
C 46
D 36

Answers

This time it's cosine.

Cosine is the adjacent/hypotenuse. In this case, the adjacent is 15 and hypotenuse is 21.

15/21, or like 5/7.

Now put that into a fancy calculator with the [tex]cos^{-1} [/tex] thing or something like that and then you have the answer, or around 44 degrees.

How do you convert numbers to percents

Answers

To convert numbers to percentage, just multiply the 100%.
Example: 23 (×100) = 2300%
0.23 (×100) = 23%

Hope it helped!

PLEASE HELP !!! HURRY!! Given m || n, find x.

Answers

4x+35 + 5x-8 = 180

9x +27 =180

9x =153

x=153/9 = 17

x = 17

The answer is x=9x+27

Question help a robotic rover on mars finds a spherical rock with a diameter of 1313 centimeters. the rover picks up the rock and lifts it 1515 centimeters straight up. the rock has a specific gravity of 5.255.25. the gravitational acceleration on mars is 3.73.7 meters per second squared. if the robot's lifting arm has an efficiency of 3535% and required 1212 seconds to raise the rock 1515 centimeters, how much power (in watts) did the arm use?

Answers

Due to apparent doubling of numbers in the question, assume
diameter=13 cm/2=0.065m
h=15 cm=0.15m
rho=5.25*1000=5250 kg/m^3
eta=35%=0.35 [efficiency]
t=12 s
g=3.7 m/s^2

mass, m=rho*V=rho*(4pi/3)(r^3)
=5250 kg/m^3 * (4pi/3)(0.065)^3 m^3
=1.922 kg

Work done in lifting h=0.15m
W=mgh
=1.922pi kg * 3.7 m/s^2 * 0.15 m
=1.067pi kg (m/s)^2
=1.067pi J

Average power required, with efficiency eta=0.35
P=(W/t)/eta
=(1.067pi J )/ (12 s) /0.35
=0.254pi J/s
=0.798W (approx.)

If 2m = 4x and 2w = 8x, what is m in terms of w?

Answers

2^m=2^n take the natural log of both sides

m*ln2=n*ln2 divide both sides by ln2

m=n

you can simply divide the eqution or you substitute the value of x in any equation.

D=6.3cm what is the circumference and area of the circle

Answers

Circumference = 2pir
=2×pi×1.6
=10.05

Area= pir^d
=pi × 6.3
=19.79

Solve the equation. 5x + 6 = 2(2x – 3)

Answers

Isolate the variable on one side of the equation and everything else to the opposite side of the variable.

You can isolate the variable by undoing the operations done to the variable.
For example, if we added 5 to x (x + 5) then we would need to undo that operation. We would need to use the inverse of addition. Which is subtraction.

5x + 6 = 2(2x - 3)
5x + 6 = 4x - 6 <-- Distribute the 2
x + 6 = -6 <-- Subtract 4x from each side
x = -12 <-- Subtract 6 from each side

So, x is equal to -12.

The solution to the equation 5x + 6 = 2(2x – 3) is x = -12

The given equation is:

5x + 6 = 2(2x - 3)

Expand the right hand side of the equation using distributive rule

5x + 6 = 4x - 6

Collect like terms

5x - 4x = -6 - 6

Simplify the equation above

x = -12

Therefore, the solution to the equation 5x + 6 = 2(2x – 3) is x = -12

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Suppose a tax is added to each flight. dollars is added to every flight, no matter how long it is. the table shows the new data. what happens to the correlation coefficient when a constant is added to each number?

Answers

The correlation coefficient is unchanged. The attached graphs show how. On the left is the regression line for some made-up data. On the right is the regression line for data made by adding 3 to each of the first data points.

The correlation coefficient in both cases is 0.961.

In a certain company, 74 employees were hired in the last 5 years. If
this represents 43% of the current number of employees, then how
many current employees does the company have?

- list the steps please & thank you!

Answers

You have to be able to take the written words and turn them into a workable equation. 74 employees is 43% of the current number, which you don't know. The word "is" means = , the 43% is written as .43, the word "of" means to multiply and the current number of employees, what you're looking for, is your unknown x. So translating those words into an equation looks like this:
74 = .43x. And dividing both sides by .43 you get that the current number of employees is 172.09, or just 172

Final answer:

To find the total number of employees in the company, set up and solve the equation, 0.43 * X = 74. Solving this provides approximately 172 employees

Explanation:

In order to answer this question, we need to use the concept of percentages. Here are the steps:

Since we know 74 employees represent 43% of all employees, we set up the equation: 0.43 * X = 74, where X is the total number of employees in the company. Solving the equation for X leads us to the answer. We divide both sides of the equation by 0.43, which gives us X = 74/0.43. Calculating the right side of the equation, we find X is approximately 172, so there are approximately 172 employees in the company.

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Which is the graph of 2x – 4y > 6?

Answers

Answer:

Its the last graph

The graph of 2x – 4y > 6 is in the far-right graphic image.

Further explanation

Let us first arrange the equation of the line followed by making a graph of a linear inequality.

Step-1: the x-intercept and the y-intercept

2x - 4y = 6

For y = 0, we get the x-intercept.

2x - 4(0) = 6

2x = 6, and then divide by two on both sides.

Hence, the x-intercept is [tex]\boxed{x = 3} \rightarrow \boxed{ \ (3, 0) \ }[/tex]

For x = 0, we get the y-intercept.

2(0) - 4y = 6

-4y = 6, and then divide by -4 on both sides.

Hence, the y-intercept is [tex]\boxed{y = -1\frac{1}{2}} \rightarrow \boxed{ \ (0, -1\frac{1}{2}) \ }[/tex]

Step-2: graph the inequality

2x - 4y = 6 is the boundary line and we draw the line dashed since the equality symbol is " > ".Test the point (0, 0), as origin, in 2x - 4y > 6, i.e., [tex]\boxed{2(0) - 4(0) > 6} \rightarrow \boxed{ \ 0 > 6, false \ }[/tex]So we shade the region which does not contain the test point.- - - - - - - - - -

Notes:

To graph a linear equality in two variables, follow the steps.

Draw the boundary line using a dashed line if the inequality symbol is " < or > ", or a solid line if the inequality symbol is " ≤ or ≥ ".Choose a test point which is not on the boundary line and substitute it into the equality.Shade the region which includes the test point if the resulting inequality is true, and shades the region which does not contain the test point if the resulting inequality is false.Learn moreFinding the equation, in slope-intercept form, of the line that is parallel to the given line and passes through a point brainly.com/question/1473992Which of the following is the correct graph of the solution to the inequality −8 greater than or equal to −5x + 2 > −38? https://brainly.com/question/1626676 When the x-axis and y-axis have different units of measure the slope can be interpreted as a rate https://brainly.com/question/4858319

Keywords: linear inequality, the equation of the line, shaded region, x-intercept, test the point, the line dashed

A sofa is on sale for 26% off. The sale price is $629 . What is the regular price?

Answers

100% - 26% = 74%

74% ..............$629
100% ..............?

629 x 100/74 = 850

answer
regular price is $850

The regular price is $850 hope this helped

The radius of the circle whose equation is (x + 4)² + (y - 2)² = 36 is 36 18 6

Answers

[tex]36=r^2\\r=6[/tex]

The equation of a circles is:

(x-h)^2+(y-k)^2+r^2, where (h,k) is the center of the circle and r is the radius

r^2=36

r=√36

r=6

The social studies teacher is giving a test worth 80 points, and containing 34 questions. There are 2 point and 4 point questions on the test. How many of each type of question are on the test? Show your work. A. List the two equations B. Find each type of question

Answers

x is 2 pt questions
y is 4 pt questions
x+y=34
2x+4y=80
Multiply the top equation by -2 to use elimination technique
-2x-2y=-68
Then combine the two equations (x is cancelled out)
2y=12
y=6
If there are 6 four point questions, there must be 28 two point questions to get a total of 34 questions.

Breanna works in the mall and her hours increase during busy shopping times of the year. Breanna has a plan to save $25 each week for 5 weeks, and then increase that amount by $20 for the next 7 weeks during the busy time, then go back to $25 per week. If Breanna’s plan is to save $540, how many weeks total will she need to save?
a.
11 weeks
b.
16 weeks
c.
22 weeks
d.
23 weeks

Answers

The math I used is probably not the quickest way, but for me, the easiest.
25*5=125 25+20=45 45*7=315 125+315=440 25*4=100 440+100=540 5+7+4=16
B is your answer.

Answer:

Number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

Step-by-step explanation:

As given

Breanna works in the mall and her hours increase during busy shopping times of the year.

Breanna has a plan to save $25 each week for 5 weeks.

Thus

Breanna saves in first 5 weeks = Amount saves per weeks in next 5 weeks × Number of weeks .

= $25 × 5

= $ 125

Increase that amount by $20 for the next 7 weeks during the busy time.

Thus

Amount saves per weeks for next 7 weeks = Amount saves per weeks in first 5 weeks + Increase in amount .

= $25 +$ 20

= $ 45

Breanna saves in next 7 weeks = Amount saves per week× Number of weeks .

Put all the values in the above

= $45 × 7

= $ 315

As given

Breanna saves $25 per week.

If Breanna’s plan is to save $540 .

Let us assume last weeks in which Breanna saves $25 per weeks be x .

Breanna saves in last x weeks = Amount saves for next x weeks × Number of weeks .

= 25 × x

= 25x

Equation becomes

Breanna saves in first 5 weeks + Breanna saves in next 7 weeks + Breanna saves in last x weeks = Total saving amount .

125 + 315 + 25x = 540

440 + 25x = 540

25x = 540 - 440

25x = 100

[tex]x = \frac{100}{25}[/tex]

x = 4 weeks

Thus

Total number of weeks Breanna saves = 5 weeks + 7 weeks + 4 weeks

= 16 weeks

Therefore the number of weeks Breanna saves are 16 weeks .

Option (b) is correct .

What is the future value of $845 a year for seven years at an interest rate of 11.3 percent? $6,683.95 $6,075.69 $8,343.51 $8,001.38 $8,801.91?

Answers

the future value of cash whose initial value is $845, at the rate of 11.3% for 7 years will be calculated using the compound interest rate, that is:
A=p(1+r/100)^n
where:
A=future amount
r=rate=11.3%=0.113
time=7 years
thus the future value of our cash will be:
A=845(1+0.113)^7
A=845(1.113)^7
A=$1,787.82

In 7 years, you will have $1,787.82

One weekend, a newsstand sold twice as many Sunday papers as Friday papers. The Sunday paper costs $1.50, and the Friday paper costs $0.75. How many Sunday papers were sold if the newsstand took in $116.25?

Answers

1.50s + 0.75f = 116.25
2f = s

1.50(2f) + 0.75f = 116.25
3f + 0.75f = 116.25
3.75f = 116.25
f = 116.25/3.75
f = 31...31 friday papers

2f = s
2(31) = s
62 = s <=== 62 sunday papers

Answer:

Step-by-step explanation:

simplify the expression by using a double angle formula

cos^2 4theta-sin^2 4theta

Answers

Double angle formula for cos(2x) is
cos(2x)=cos^2(x)-sin^2(x)

Substitute x=4theta, then
cos(8theta)=cos^2(4theta)-sin^2(4theta)
=>
cos^2(4theta)-sin^2(4theta) = cos(8theta)

Help Please question in the file.

Answers

check the picture below.

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