Answers
The value of the equation is x = 4 and x = -5 ± √10i
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
( x - 4 ) / ( x + 5 ) + 9 / ( x² + 11x + 30 ) = 1/( x + 6 )
On simplifying the equation , we get
( x - 4 ) / ( x + 5 ) + 9 / ( x + 5 ) ( x + 6 ) = 1/( x + 6 )
Multiply the equation with the LCM , we get
( x - 4 ) ( x + 5 ) ( x + 6 ) + 9 ( x - 5 ) = ( x - 5 ) ( x + 5 )
x³ + 7x² - 14x - 120 + 9x - 45 = x² - 25
Subtracting x² on both sides of the equation , we get
x³+ 6x² - 5x - 165 = -25
Adding 25 on both sides of the equation , we get
x³+ 6x² - 5x - 140 = 0
Hence , the solution to the equation is x = 4 , -5 ± √10i
So , the larger solution is x = 4
And , the smaller solution is x = -5 ± √10i
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Related Questions
han types the letters a, s, d, f, and then repeats them over and over what is the fith letter diego will type
Answers
The fith letter Diego will type is the letter a
How to determine the fith letter diego will typeFrom the question, we have the following parameters that can be used in our computation:
Letters: a, s, d and f
When the letters are repeated, we have
a s d f a s d f a s d f a s d f a s d f......
using the above as a guide, we have the following:
Fifth letter = a
Hence. the fifth letter is a
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Find the point slope form of a line with Slope: 6/7 that passes through (-5,4)
Answers
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 6/7. Then the equation is given as,
y = (6/7)x + c
The equation passes through (-5, 4). Then we have
4 = (6/7) (-5) + c
4 = -30/7 + c
c = 58 / 7
Then the equation is given as,
y = (6/7)x + 58/7
7y = 6x + 58
The equation of the line with Slope: 6/7 that passes through (-5,4) will be 7y = 6x + 58.
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Question 1(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of center should the charity use to accurately represent the data? Explain your answer.
The median of 22.7 is the most accurate to use to show that they have plenty of money.
The mean of 20 is the most accurate to use to show that they need more money.
The median of 20 is the most accurate to use, since the data is skewed.
The mean of 22.7 is the most accurate to use, since the data is skewed.
Question 2(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
Question 3(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 11, with tick marks every one unit up to 25. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 20 on the number line. A line in the box is at 19. The lines outside the box end at 12 and 24.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 3.
The range is the best measure of variability, and it equals 12.
The IQR is the best measure of variability, and it equals 12.
The range is the best measure of variability, and it equals 3.
Question 4(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
2 0, 1, 3, 5, 7
3 2, 5, 7, 9
4
5 1
6 5
Key: 2|7 means 27
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 16.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 16.
Question 5(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The table shows the number of goals made by two hockey players.
Player A Player B
2, 3, 1, 3, 2, 2, 1, 3, 6 1, 4, 5, 1, 2, 4, 5, 5, 11
Find the best measure of variability for the data and determine which player was more consistent.
Player B is the most consistent, with an IQR of 3.5.
Player B is the most consistent, with a range of 10.
Player A is the most consistent, with an IQR of 1.5.
Player A is the most consistent, with a range of 5.
Question 6(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the cost of used books in dollars.
A horizontal line starting at 1 with tick marks every one unit up to 9. The line is labeled Cost in Dollars, and the graph is titled Cost of Used Books. There are two dots above 1, 2, 3, 5, and 6. There are four dots above 7.
Which measure of center is most appropriate to represent the data in the graph, and why?
The median is the best measure of center because there are no outliers present.
The median is the best measure of center because there are outliers present.
The mean is the best measure of center because there are no outliers present.
The mean is the best measure of center because there are outliers present.
Question 7(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of center for the data, and what is its value?
The median is the best measure of center, and it equals 6.5.
The mean is the best measure of center, and it equals 7.
The median is the best measure of center, and it equals 7.
The mean is the best measure of center, and it equals 6.5.
Answers
The median of 20 is the most accurate to use since the data is skewed.
Option C is the correct answer.
What is a histogram?A histogram is a representation of the distribution of data with intervals.
We have,
The data given shows a histogram that is skewed to the right.
Now,
Since the data is skewed.
The median is a better measure of the center of data than the mean.
Now,
Arrange the data in order:
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
Median = middle value.
Median = 20
Thus,
The median of 20 is the most accurate to use since the data is skewed.
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Answer:
your question is a bit confusing...
Step-by-step explanation:
Which of the following would NOT be an example of a boogie-woogie bass line?
A. F-A-C-D-Eb-D-C-A
B. G-B-D-E-F-E-D-B
C. C-D-E-F-G-F-E-D
D. C-E-G-A-Bb-A-G-E
Answers
Answer: Option D, "C-E-G-A-Bb-A-G-E" is not an example of a boogie-woogie bass line. Boogie-woogie is a genre of blues music that is characterized by a repetitive bass pattern that usually consists of 8th notes. The bass line is usually made up of the root note, fifth note, and octave of a chord, and it is played in a swung or shuffle rhythm. The most common boogie-woogie bass line consists of the notes of a I-IV-V chord progression in a 12-bar blues structure. Option D deviates from this typical pattern and therefore would not be considered a boogie-woogie bass line.
Step-by-step explanation:
College level
Attached photo.
Answers
The value of b form the logarithmic equation [tex]log_b}3=0.7925[/tex] is 3.9998688.
What are logarithms?In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.
Given that, [tex]log_b}25=2.3219[/tex] and [tex]log_b}3=0.7925[/tex].
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
We know that, logₐN=x is written exponential form as aˣ=N
Here, [tex]b^{2.3219}=25[/tex]
b=4.00006709
[tex]b^{0.7925}=3[/tex]
b=3.9998688
Therefore, the value of b is 3.9998688.
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What is the conjugate? x-\sqrt(2)
Answers
Answer:
[tex]x+\sqrt{2}[/tex]
Step-by-step explanation:
The conjugate of [tex]x-\sqrt{2}[/tex] would simply be [tex]x+\sqrt{2}[/tex]. All you have to do is simply change the sign to its opposite.
100 POINTS HELPWhich column on an accounting worksheet may not balance at the end of an accounting period?
A. The Adjusted Trial Balance
B. The Trial Balance
D. The Adjustments
C. The Income Statement
Answers
Answer: C
Step-by-step explanation:
The column on an accounting worksheet that may not balance at the end of an accounting period is the Adjustments column.
The Adjustments column on an accounting worksheet includes all the adjusting entries that are needed to update the accounts before the financial statements are prepared. These adjustments can include accruals, deferrals, depreciation, and other adjustments that need to be made to the accounts to accurately reflect the financial position of the company.
Since the Adjustments column is used to record these adjusting entries, it is possible that this column may not balance at the end of the accounting period, as the adjustments may not perfectly offset each other. However, this is not a problem, as the purpose of the worksheet is to help prepare the financial statements, not to balance each individual column.
Therefore, the correct answer is option D, the Adjustments column.
Answer:
C. The Income Statement
Step-by-step explanation:
The Income Statement column on an accounting worksheet may not balance at the end of an accounting period.
An accounting worksheet is a tool used by accountants to help organize and summarize financial information and to prepare financial statements. The worksheet is typically a multi-column form that includes columns for the unadjusted trial balance, adjustments, adjusted trial balance, income statement, and balance sheet.
The Adjustments column is used to record adjusting entries and to update the account balances to reflect accruals, deferrals, and other accounting adjustments. The Adjusted Trial Balance column is the result of the adjustments made in the Adjustments column and should include all the account balances that will be used to prepare the financial statements.
I need help with this please!
Answers
Answer:
d<0Step-by-step explanation:
3+d<3-d
3+d<3-dcancel equal terms
3+d<3-dcancel equal termsd<-d
3+d<3-dcancel equal termsd<-dMove the variable to the left
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0divide both sides
3+d<3-dcancel equal termsd<-dMove the variable to the leftd+d<0collect like terms2d<0divide both sidesd<0
CAN SOMEONE HELP WITH THIS?✨
Answers
The population of the town is 2564 people after 4 years.
What is Exponential Growth?An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.
y = a(1+r)ˣ,
where a is the initial population and r is the rate in decimals and x is the time period.
Given:
The initial population of the town is 1652 people.
And the town's population is tripling every 10 years.
Let y₀ be the initial population, r be the growth rate and t be the time.
So,
y = y₀(e[tex])^{rt}[/tex]
Substituting the values to the function,
y = 1652(e[tex])^{rt}[/tex]
In 10 years,
3y₀= y₀(e[tex])^{rt}[/tex]
r = log(3)/10
Now, the population of town after 4 years is,
y = 1652(e[tex])^{{ln(3)/10} \cdot {t}}[/tex]
y = 2563.64
y ≈ 2564 people.
Therefore, the population is y ≈ 2564, people.
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You are examining the data with a stem-and-leaf plot. Here is the start of the plot. Finish the plot.
Answers
The stem-and-leaf plot is finished as follows:
4| 1 3 7.
What is a stem-and-leaf plot?The stem-and-leaf plot lists all the measures in a data-set, with the first number as the key, for example:
4|5 = 45.
To complete the stem-and-leaf plot, we must obtain the measures above 40 from the table, which are given as follows:
41, 43 and 47.
Considering the format of the plot, the plot is completed as follows:
4| 1 3 7.
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Out of 10,551 passing attempts, Drew Brees
completed 7,142
What is the completion percentage for
Drew Brees? Show or explain how you got
your answer.
Answers
Answer: 67.69%
Step-by-step explanation:
To calculate the completion percentage,
Divide the completed passes by the total passing attempts.
> 7142/10551
Then, multiply that answer by 100 to get the percentage.
> 67.69%
Suppose that So, S1, S2,... is a sequence of subsets of N. Which one of the following sets is guaranteed to be different from all sets in the sequence? (a) S = {n | n & Sn²} (b) S = {n | n² & Sn²} (c) S = {n²| n & Sn²} (d) S = {n² | n² & Sn} (e) S = {n² | n & Sn} Explain why your chosen set is guaranteed not to be in the sequence So, S1, S2, ...
Answers
Suppose that So, S1, S2,... is a sequence of subsets of N the following sets is guaranteed to be different from all sets in the sequence is S = {n² | n² & Sn}.
Subsets are a part of the mathematical concept of sets. A set is anything that is wrapped in curly braces, such as "a,b,c,d." If set A is a collection of even integers and set B is composed of the numbers 2, 4, and 6, then set A is the superset of set B and set B is said to be a subset of set A. Review Sets Subset and Superset for further details.
Set A is referred to as a subset of Set B if each element of Set A is also present in Set B. In other words, Set B includes Set A.
As an illustration, if set A has the elements X, Y, and set B contains the elements X, Y, and Z, then set A is the subset of set B.
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a home with a swimming pool recently sold in the area for 250,000 another home in the same area that does not have a swimming pool but is similar in all other respects sold recently for 230,000 what can you assume from this information.a. All swimming pools cost $20.000b. The aproximate value of pool in that area is $20.000c. No home without a pool in that area will sell for more than $230.000d. Homes without a pool will sell faster in that area than homes with a pool
Answers
The correct answer is option b.The approximate value of pool in that area is $20.000c.
What is approximate value?A value that is similar to another value but not exactly equal to it is referred to as an approximation number. When the outcomes of the numerical calculations are unknown, the approximation is applied. They are typically used when greater place value decimal numbers emerge as a result.
Approximate value of a pool in the area = Value of home with a swimming pool in the area - Value of home without a swimming pool in the same area.
Value of home with a swimming pool in the area = $250,000
Value of home without a swimming pool in the same area = $230,000.
The approximate value of pool in the area = 250000 - 230000 = 20000.
Hence, the correct answer is option b. The approximate value of pool in that area is $20.000c.
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A wildlife biologist captured and released 34 trouts from two different lakes and measured them to the nearest inch. She captured 17 of the fish from Fralest Lake and 17 of the fish from Lake Reverwalk. She then calculated the following statistical information.
Based on these samples, what generalization can be made?
A. At least half of the trout in Lake Reverwalk measure between 12 and 18 inches.
B. At least half of the trout in both lakes measure between 12 and 18 inches.
C. Not enough information is provided to draw any of these conclusions.
D. At least half of the trout in Fralest Lake measure between 12 and 18 inches.
Answers
The requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
Interquartile range (IQR), The IQR is the range of the middle 50% of values in a data set. To calculate the IQR, we first need to find the quartiles of the data set.
In the given question we have 3 IQR data sets that jointly vary from 10 to 17 by this we can conclude that, at least half of the trout in both lakes measure between 12 and 18 inches.
Thus, the requried generalization that can be made is at least half of the trout in both lakes measure between 12 and 18 inches. Option B is correct.
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Simplify the following union and or intersection. [2,3] ∪ (3,∞)
Answers
The union of the set elements is [2, ∞)
How to determine the union or the intersectionFrom the question, we have the following parameters that can be used in our computation:
[2,3] ∪ (3,∞)
The above is a union set
The definition of the union set is that we write out all the elements in the set
Using the above as a guide, we have the following:
[2,3] ∪ (3,∞) = [2, ∞)
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use the midpoint rule with the given value of n to approximate the integral. round the answer to four decimal places. integral 48 0 sin Vx dx, n=4
Answers
By using the midpoint rule, the value of n to approximate the integral is 9.24.
The integral of a function is a measure of the total area under the curve of the function over a given interval. The Midpoint Rule is a method used to approximate the value of an integral by dividing the interval into smaller subintervals, finding the midpoint of each subinterval, and using the height of the function at the midpoint to estimate the area of the subinterval.
In this specific problem, we are asked to approximate the integral of the function f(x) = sin root x from x = 0 to x = 48, using the Midpoint Rule with n = 4 subintervals. To do this, we divide the interval [0,48] into 4 equal subintervals of width
=> (48-0)/4 = 12.
The midpoint of each subinterval is calculated as follows:
1st subinterval: (0 + 12)/2 = 6
2nd subinterval: (12 + 24)/2 = 18
3rd subinterval: (24 + 36)/2 = 30
4th subinterval: (36 + 48)/2 = 42
Next, we find the height of the function f(x) = sin root x at each of these midpoints.
1st subinterval: sin root 6 = 0.77
2nd subinterval: sin root 18 = 0.97
3rd subinterval: sin root 30 = 0.87
4th subinterval: sin root 42 = 0.71
Finally, we multiply each height by the width of the subinterval to find the estimated area of each subinterval, and add up these areas to obtain the final estimate of the integral:
(0.77 * 12) + (0.97 * 12) + (0.87 * 12) + (0.71 * 12) = 9.24
So, our final estimate of the integral of f(x) = sin root x from x = 0 to x = 48 using the Midpoint Rule with n = 4 is 9.24. Rounding to 4 decimal places, our answer is 9.2400.
Complete Question:
Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to four decimal places.
∫0 to 48 sin √x dx, n=4
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Use the cross products property to solve the proportion.9/10=d/6.4
Answers
Using the cross product property, the value of d is 5.76.
What is Proportion?Proportions are defined as the concept where two or more ratios are set to be equal to each other.
Suppose we have two ratio p : q and r : s.
If both these ratios are proportional, then we can write it as p : q = r : s or p/q = r/s
Given proportional relation is,
9 / 10=d / 6.4
Doing the cross multiplication,
9 × 6.4 = 10 × d
57.6 = 10d
d = 57.6 / 10
d = 5.76
Hence the solution of the proportion is d = 5.76.
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50
Question 10
A diagram has circles such that the area represents the populations of various
countries in the world. The circle for United States has a radius of 4.2 cm and the circle
for India has a radius of 8.7 cm. If 4% of the world's population is in United States, what
percentage of the world's population is in India? Round to the nearest percent.
Answers
Answer: 17%
Step-by-step explanation:
So, the formula to get the area of a circle is [tex]\pi r^{2}[/tex].
USA: [tex]4.2^{2} \pi[/tex] = 55.42cm
India: [tex]8.7^2\pi[/tex] = 237.79cm
From this, we can divide India by USA:
237.79 / 55.42 = 4.291
Then, with that we can multiply our 4% by 4.291:
4 * 4.291 = 17.16400
Rounded to the nearest percent is 17%
Complete the sentence below.
The time shown is
15:40
past/to
in the morning/afternoon
Answers
Answer:
uajajjahajajaaajjsjaja
The time shown is 15:40, which indicates that it is 20 minutes to 4 o'clock in the afternoon.
How to complete the statementThe time displayed is 15:40, which is consistent with a 24-hour clock. It indicates that there are now 20 minutes left until 6:00.
The time 15:40 is in the afternoon because the afternoon begins at 12:00 and lasts until 18:00.
The 24-hour clock format avoids any doubt regarding AM (morning) or PM (afternoon/evening), it is vital to highlight.
As a result, 15:40 specifies that it is in the afternoon and that there are still 20 minutes until 4 o'clock.
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In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse. If a = 5.7 meters and c = 9.6 meters, what is b? If necessary, round to the nearest tenth.
Answers
Answer:
[tex]b[/tex] ≈ [tex]7.7[/tex]
Step-by-step explanation:
We need to use the Pythagorean Theorem: [tex]a^2+b^2=c^2[/tex]
In this case we have a and c. So let's plug those into the equation:
[tex](5.7)^2+b^2=(9.6)^2[/tex]
Solve:
[tex]32.49+b^2=92.16[/tex]
Round to the nearest tenth:
[tex]32.5+b^2=92.2[/tex]
Subtract 32.5
[tex]b^2=59.7[/tex]
Find 'b'
[tex]b=\sqrt{59.7}[/tex]
[tex]b[/tex] ≈ [tex]7.7[/tex]
I hope this helped you!
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Use the method for solving Bernoulli equations to solve the following differential equation. dy dx **=6x?y? Ignoring lost solutions, if any, the general solution is y= (Type an expression using x as the variable.)
Answers
The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex] the final solution is [tex]y = x^3 + 1[/tex].
The Bernoulli equation for this particular differential equation is [tex]dy/dx = 6x(y-1)[/tex]. To solve the equation, we first use the substitution u = y – 1. This substitution simplifies the equation to [tex]dy/dx = 6xu[/tex], which is a first-order linear equation with constant coefficients. Now we can use the method for solving Bernoulli equations to find the solution.
We first find the integrating factor, which is [tex]I(x) = exp(∫6xdx)= exp(3x^2)[/tex]. Then we multiply both sides of the equation by I(x) to get [tex]I(x)dy/dx = 6xI(x)u[/tex]. We can now integrate both sides with respect to x and get the general solution of [tex]y = u + 1 = (1/I(x))∫6xI(x)dx + 1[/tex]. After calculating the integral, the final solution is [tex]y = x^3 + 1[/tex].
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Find the volume of the figure. Express the answer in terms of pi and then round to the nearest whole number.
Answers
Answer:
5025π m³
Step-by-step explanation:
the figure consists of two figures;
a cone and phere
volume of a cone=1/3πr²h
volume of hemisphere=2/3πr³
1/3×π×15×15×37=2775π
2/3×π×15×15×15=2250π
sum up the volumes
2775π+2250π
=5025π m³
Rehan proved by mathematical induction that for all the positive integers,
is divisible by 3. Can you find an integer counterexample to show that this statement is not true? Explain.
Answers
A counterexample that shows that all the integers are not divisible by 3 is given as follows:
2.
How to obtain the counterexample?The statement for this problem is given as follows:
"All the positive integers are divisible by 3".
The statement is false, as only numbers whose sum of the digits is a multiple of 3 are divisible by 3, hence for example, the number 2 is not divisible by 3.
The counterexample is the statement that proves that a conjecture(another statement) is false, hence the number 2 is the counterexample showing that not all positive statements are divisible by 3.
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A credit sale of $2700 is made on July 15, terms 2/10, n/30, on which a return of $300 is granted on July 18. What amount is received as payment in full on July 24?
Answers
Answer:
$2,450
Step-by-step explanation:
2/10, n/30 = discounts of 2%
Credit sale = $2,700
Sale return = $200
Net Receivable =$ 2,700 - $ 200 = $2,500
Discount = 2,500 x %2 = 50
Payment Receipt = $2,500 - $50 = $2,450
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Which two integers is /80
[tex] \sqrt{80} [/tex]
between? (A) 9 and 10 B) 7 and 8 8 and 9 D 11 and 12
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prime factorization of 756
Answers
The solution is, prime factorization of 756 = 3*2*3*2*3*7
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
here, we have,
756
we know,
756 = 6*6*21
=3*2*3*2*3*7
as, we know, 2,3,7 all are prime.
so, prime factorization of 756 = 3*2*3*2*3*7
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Rewrite 5^(2 .)5^(4) using a single exponent
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A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (*)A Bernoulli differential equation is one of the form dy/dx+P(x)y=Q(x)y^n (*). Observe that, if n=0 or 1 , the Bernoulli equation is linear. For other values of n , the substitution u=y^(1-n) transforms the Bernoulli equation into the linear equation du/dx + (1-n)P(x)u=(1-n)Q(x).Consider the initial value problemxy'+y=3xy^2, y(1)=-3(a) This differential equation can be written in the form (*) withP(x)=?Q(x)=?n=?(b) The substitution u=BLANK will transform it into the linear equation du=dx+ BLANK u=BLANK(c)Using the substitution in part (b), we rewrite the initial condition in terms of x and uu(1)=?(d) Now solve the linear equation in part (b), and find the solution that satisfies the initial condition in part (c).u(x)=?(e)(e) Finally, solve for yy(x0=?
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The solution of the the linear equation is y = 3/(x - 9xlnx)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
xy' + y = 3xy², y(1) = -3
This is Bernoulli equation: y' + (1/x)y = 3y²;
Let u = y^(1 - 2) = 1/y is new function.
Then u' = - y'/y
or
y' = -u'/u²;
y = 1/u.
Substitute all this in our ODE: - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.
we get linear, 1st order not homogenies ODE:
integrated factor:
μ = e∫(-1/x)dx = e-lnx = 1/x²
u'·1/x - 1/x2 = -3/x;
(u/x)' = - 3/x; u/x
= ∫(-3/x)dx;
u/x = -3lnx + C;
u = - 3xlnx + Cx;
y =1/u = 1/(- 3xlnx + Cx)
To get C ,use initial conditions:
y(1) = 3;
3 = 1/(-3·1·ln1 + C);
C = 1/3;
y = 3/(x - 9xlnx)
The solution of the the linear equation is y = 3/(x - 9xlnx)
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The solution of the the linear equation is y = 3/(x - 9xlnx)
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
xy' + y = 3xy², y(1) = -3
This is Bernoulli equation: y' + (1/x)y = 3y²;
Let u = y¹⁻² = 1/y is new function.
Then u' = - y'/y
or
y' = -u'/u²;
y = 1/u.
Substitute all this in our ODE: - u'/u² +(1/x)/u = 3/u², or u' - (1/x)u = -3.
we get linear, 1st order not homogenies ODE:
integrated factor:
μ = e∫(-1/x)dx = e-lnx = 1/x²
u'·1/x - 1/x2 = -3/x;
(u/x)' = - 3/x; u/x
= ∫(-3/x)dx;
u/x = -3lnx + C;
u = - 3xlnx + Cx;
y =1/u = 1/(- 3xlnx + Cx)
To get C ,use initial conditions:
y(1) = 3;
3 = 1/(-3·1·ln1 + C);
C = 1/3;
y = 3/(x - 9xlnx)
The solution of the the linear equation is y = 3/(x - 9xlnx)
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Please help due tonight
Answers
Answer:
x = 24, y = 12
Step-by-step explanation:
We can use the law of sines to solve for x
The law of sines says the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides (and angles)
In this triangle
the side with length 12√3 is opposite 60°
the side with length x is opposite 90°
Using the law of sines,
[tex]\dfrac{12\sqrt{3}}{\sin60}=\dfrac{x}{\sin 90}\\[/tex]
sin 60 = [tex]\dfrac{\sqrt{3}}{2}[/tex]
sin 90 = 1
[tex]\rightarrow \dfrac{12\sqrt{3}}{\dfrac{\sqrt{3}}{2}}=\dfrac{x}{1}\\\\\\x = 12\sqrt{3} \div \dfrac{\sqrt{3}}{2}}\\\\\textrm{When dividing fractions, flip the divisor and multiply}\\\\\rightarrow 12\sqrt{3} \times \dfrac{2}{\sqrt{3}}\\\\\textrm{$\sqrt{3}$ cancels out from numerator and denominator}:\\\\\\\rightarrow x = 12 \times 2 = \boxed{24}\\\\\\[/tex]
To solve for y we can again use the law of sines
[tex]\dfrac{y}{\sin 30} = \dfrac{x}{\sin 90}\\\\\textrm{again, as before $\sin 90$ is 1}\\\\\rightarrow \dfrac{y}{\sin 30} = x\\\\\rightarrow x = \dfrac{y}{\sin 30}\\\\\rightarrow y = x \sin 30\\\\\sin30 = \dfrac{1}{2}[/tex]
So y = x/2 = 24/ 2 = 12
ans:
x = 24, y = 12
Note
Another way to solve this question is to first recognize the triangle as a 30-60-90 right triangle
In a triangle of this kind, if the longest side side is a, the shortest side is a/2, and the third side is √3/2a
We could have solved this in this manner also
Here longest side = x, shortest side is y
The other side is 12√3 = x √3/2
So x = 12√3 ÷ √3/2 = 24 (as in the first method)
y = x/2 = 12
This approach is ok too, I find it less intuitive and we have to remember the ratios
If 12 subtracted from 7 time a number is equal to five times the sum of the number and 2,find the number.
Answers
Answer:
7-12=x
5(x+2)
7-12=-5
5(-5+2)
5(-3)
-15Step-by-step explanation: