The solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is y=[tex]-x^{2} +1[/tex].
Given a differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex].
We are required to find the solution of the differential equation when y(0)=1.
dy/dx=[tex]2xy/(x^{2} -1)[/tex]
Taking y to left side and dx to right side.
1/y dy=2x/[tex](x^{2} -1)[/tex] dx
Integrating both sides.
[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]----------1
log y=[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]
Solving right side.
[tex]\int\limits {2x/(x^{2} -1)} \, dx[/tex]
let [tex]x^{2} -1[/tex]=z
differentiating both sides with respect to x.
2x=dz/dx
2x dx=dz
Put 2x dx=dz in 1.
[tex]\int\limits {1/y} \, dy[/tex]=[tex]\int\limits {1/z } \, dz[/tex]
log y=log z+log c
Put z=[tex]x^{2} -1[/tex]
log y=log([tex]x^{2} -1[/tex])+log c
log y=log [{[tex]x^{2} -1[/tex])c]
y=([tex]x^{2} -1[/tex])c------------2
Put x=0 and y=1
1=(0-1)c
1=-c
c=-1
Put c=-1 in 2 to get the solution.
y=-1([tex]x^{2} -1[/tex])
y=[tex]-x^{2} +1[/tex]
Hence the solution of the differential equation dy/dx=[tex]2xy/(x^{2} -1)[/tex] is
y=[tex]-x^{2} +1[/tex].
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(THIS IS DUE TMRW!!)
Explain how to get the Unit Rate for Amount of Miles Ran per Minute for #18. Jaime ran 6 miles in 60 minutes. How far does Jaime run (in miles) per minute? Show all work and then write an explanation.
A mile is 5,280 feet long and an hour is 3,600 seconds long, thus 60 miles per hour is 60 x 5,280 / 3,600 = 88 feet per second.
What is the unit rate formula?How Do I Determine the Unit Rate? The denominator of a unit rate is always 1. To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.
Miles per hour is a relatively typical example of a unit rate that we face on a daily basis. This rate is a unit rate since it describes the number of miles in one hour.
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Solve for x round to the nearest tenth 33 27
Select the reason why these triangles are
similar. If they are not, select "Not similar."
A. AA
C. SAS
60°
/60°
B. SSS
D. Not similar
The reason why these triangles are similar is A. AA.
What is similar triangle?A similar triangle is a triangle in which the corresponding angles are congruent (equal in measure) and the corresponding sides are in proportion. This means that the corresponding sides of two similar triangles are in the same ratio, but the triangles may be different sizes.
What is triangle?A triangle is a three-sided polygon. It is defined by three points in a plane, called its vertices, and the straight lines connecting each pair of these points, called its sides. The three angles of a triangle always add up to 180 degrees.
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if each quadrilateral below is a kite, find the missing measures
please hurry
A quadrilateral shape called a trapezoid that has exactly one set of parallel sides. Isosceles Trapezoid: A trapezoid with congruent non-parallel sides.
What are angles in a quadrilateral?A quadrilateral is a polygon with four vertices, four sides, and four angles, all of which add up to 360 degrees. The quadrilateral is formed by two triangles when the diagonals are drawn. The angle total for these two triangles is 180°. As a result, the quadrilateral has a 360° total angle.
With four sides, four vertices, and four angles, a quadrilateral is a closed shape and a specific kind of polygon. A quadrilateral's internal angles add up to 360 degrees in all cases. The four angles found at each vertex of a four-sided form are referred to as the interior angles of a quadrilateral and are the only angles in a quadrilateral. Every quadrilateral's internal angles add up to 360 degrees.
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The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
If the equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books. The number of books is 4.
How to find the number of books?Given data:
Equation: 3.95m + 8.95b = 47.65
Where:
Magazine, m = 3
Now let find the number of book by using the equation to solve for b
3.95(3) + 8.95b = 47.65
11.85 + 8.95b = 47.65
Collect like terms
8.95b = 35.8
Divide both side by 8.95b
b = 35.8/8.95
b = 4 books
Therefore we can conclude that the number of books is 4.
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The complete question is;
Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.
Select all the equations that are equivalent to y - 4 = (x - 1).
It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.
How to determine the equivalent equation?
To determine if two equations are equivalent, you can check if they represent the same line in the cartesian plane. The following methods can be used to determine equivalent equations:
Graph the equations: You can graph the equations on the same coordinate plane and see if they produce the same line. If they do, the equations are equivalent.Check for the same slope and y-intercept: You can check if the equations have the same slope and y-intercept. If they do, the equations are equivalent.Solving for y: You can put the equation in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, if the slope and y-intercept are the same for both equations, the equations are equivalent.The following equations are equivalent to y - 4 = (x - 1):
y = x - 1 + 4
y = x + 3
y - 4 = x - 1 + 4
y - 4 = x + 3 - 4
(y - 4) + 4 = (x - 1) + 4
y = x - 1 + 4
All of the above equations have the same slope and y-intercept, which means they represent the same line in the cartesian plane.
It's important to note that equation y = x - 1 + 4 and y = x + 3 are in slope-intercept form, which is a common way to write linear equations.
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Which expression renames 3/4−7/10 using common denominators?
3/4 and 9/10 using the least common denominator is 15/20 and 18/20.
What is LCM?LCM of two or more than two given numbers is the smallest common multiple that is divisible by two or more than two given numbers.
Given, are two fractions 3/4 and 7/10 we know the LCM of 4 and 10 is 20.
∴ (3×5)/(4×5) and (7×2)/(10×2).
(we have to multiply same constant to the fraction to retain it's original value).
So, 3/4 and 4/10 using the least common denominator is 15/20 and 14/20.
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Shawn has 22 boxes of golf balls. Each box has three golf balls.
Look at each equation below. Decide if it can be used to find the total number of golf balls?
(SCREENSHOT BELOW)
Answer:
1) can 2) can’t 3) can’t 4) can
Step-by-step explanation:
There are 66 golf balls in total 1 and 4 are the only equations that equal 66
Which graph represents the inequality y is less than negative one-third times x plus 1?
A graph which represents the inequality y is less than negative one-third times x plus 1 is shown in the image below.
What is an inequality?In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:
Less than or equal to (≤).Greater than (>).Greater than or equal to (≥).Less than (<).How to determine the graph which represents the inequality?In order to determine and plot the graph which represents the inequality, we would first of all translate the word problem into an algebraic equation as follows;
y is less than or equal to one-third times x plus 1 ⇒ y < x/3 + 1.
Next, we would use an online graphing calculator to graphically solve the given inequality.
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Answer:
B
Step-by-step explanation:
The graph shows the answer accurately
Eric ran 3 kilometers in 20 minutes.
Taylor ran 2,550 meters in 17 minutes. Was one person faster than the other or were they running at the same rate?
Answer:It is not possible to answer this question without knowing the rate at which the other person was running.
Step-by-step explanation:
SOMEONE HELP ME PLEASE DUE TONIGHT
HI is 7 because all sides are equal. K is 100 because J is 40 and L is also 40 because they are equal. All triangles are equal to 180. 40+40+100=180
Your math teacher tells you that the next week's test is worth 100 points and contains 28 problems. Each problem is worth either 5 or 3 points. How many of each type of problem are on the test?
Therefore , equation problem answer is there will be six 5 mark problem and twenty two 3 mark problem.
How do you quickly solve equations?Remove parentheses from each side of the equation and combine similar terms to make it simpler. To separate the variable term on one side of the equation, use addition or subtraction. To find the variable, use division or multiplication.
Here,
Given :
Since the total number of points is 28, we can create the Let Statements:
Let x= one type of question
Let 28-x= the other type of questions
Create an equation to relate the number of questions to the price
100=5x+3(28-x) Distribute
100=5x+82-3x Subtract 76 from both sides of the equation
100-82=5x-3x Combine like terms
18=3x Divide both sides by 3
x=6
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How do you convert base 10 to base E?
To convert from base 10 to base e, we need to split down a number in base e into the powers of e.
When we convert from base 10 to base e, the pattern will be exactly the same. It will be just with e instead of 10.
For example, to see how many digits (before the decimal point) of ln(12) = 2.4849...
It means that the first digit will be on the e^2 position. Now lets find:
12 / e^2 = 1.624…
So, there will only be a 1 in the e^2 position. The remaining is 12 – e^2. The next position is e^1 position. To find out what’s on this position, we need to do the following calculation:
(12 – e^2) / e = 1.696…
The next digit will also be a 1.
Now we do the 1’s position:
(12 – e^2 – e) / 1 = 1.892…
Next digit’s a 1.
We can continue for a few more decimal places:
(12 – e^2 – e – 1) / e – 1 = 2.426…
Next digit’s a 2.
(12 – e^2 – e – 1 – 2 * e – 1) / e – 2 = 1.159…
Next’s digit a 1.
So, 12 in base e is 111.21…
Since e is irrational and 12 is not, this will be never ending. But there will only can be 0’s, 1’s, and 2’s, since e is less than 3.
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i cant figure this out
Answer:
4^2 or 16
Step by step explanation:
4^5 = 4x4x4x4x4
4^3 = 4x4x4
4^5 ÷ 4^3 = 4x4x4x4x4 ÷ 4x4x4 = 4x4
4x4 = 4^2 = 16
Find the length of the indicated
side of the similar figure.
12
X
x = [?]
X
8
4
The length of the side indicated in the similar figure can be found using the concept of similarity.
Find the length of the indicated side?The length of the side indicated in the similar figure can be found using the concept of similarity.When two figures are similar, the corresponding sides are proportional.In this case, the side indicated in the figure is 8, and the side we are looking for is X.To find the length of X, we can set up a proportion and solve for X. The proportion would be 8/X = 12/8, which simplifies to X = 12.Therefore, the length of the side indicated in the similar figure is 12.The length of the indicated side of the similar figure is 4.This is because the two figures are similar, meaning they have the same shape and ratio of sides.This means that if one side is 8, the other will be 4, since 8/4 = 2.This theory is called the Proportionality Rule and states that if two figures are similar, the corresponding sides are proportional.To learn more about Proportionality Rule refer to:
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Select the correct answer!!!
By which postulate or theorem is ∠3 ≅ ∠6?
Answer:
B) Alternate Interior Angles Theorem
Step-by-step explanation:
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. In the above diagram, m∠3 ≅ m∠6
The balance on a credit card, that charges a 10.5% APR interest rate, over a 1 month period is given in the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily balance, for this card over this 1 month period?
finance charge = $[?]
Round to the nearest hundredth.
The finance charge on the average daily balance for the one month is $2.07.
What is the finance charge?The finance charge is the interest and other fees charged on a credit facility.
To compute the finance charge, we apply the annual percentage rate (APR) on the Average Daily Balance, multiplied by the number of days in the billing cycle, and divided by 365.
Days 1-3: $200 (initial balance) $600 ($200 x 3)
Days 4-20: $300 ($100 purchase) $5,100 ($300 x 17)
Days 21-30: $150 ($150 payment) $1,500 ($150 x 10)
Total = $7,200
Average Daily Balance = $240 ($7,200/30)
APR interest rate = 10.5%
MPR interest rate = 0.875% (10.5%/12)
Finance Charge = $2.07 ($240 x 10.5% x 30/365)
Or $ ($240 x 0.875%)
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Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct ? Why or why not
It is possible that Lance ay that 2,376 ÷10 by the power of 2 i the ame a 2,376 x 0. 1 i he correct
The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example the little "2" says to use 8 two times in a multiplication: 82 = 8 × 8 = 64.
What are powers?
A power is the product of multiplying a number by itself. Usually, a power is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.
Since 2376÷10
It will give us
237.6
So to convert to standard form it will be
2376×10^-1
How
Since the point has been shifted to the right side
And it will definitely give us 2376.0
But the point zero is not necessary
10^1 also means 0.1
So it is possible
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There are 8 squares and 2 triangles. What is the simplest ratio of triangles to total shapes?
Answer:
2:10 or 1:5
Step-by-step explanation:
Answer: 4 squares to 1 triangle
Step-by-step explanation: both can be divided by two and that is the largest number they can be divided into
What is an exponential function called?
An exponential function is a function in which the variable appears in an exponent.
The most common form of an exponential function is f(x) = aˣ, where a is a positive constant, known as the base of the function, and x is the variable. The variable x is called the exponent of the function.
The base, a, determines the growth rate of the function. If the base is greater than 1, the function will increase rapidly as x increases. If the base is between 0 and 1, the function will decrease rapidly as x increases.
Exponential functions can also be written in the form y = a×bˣ, where a and b are constants, b is the base and x is the exponent. In this form, a represents the y-intercept of the function, which is the point where the function crosses the y-axis.
An exponential function can be recognize by the presence of the variable in an exponent and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.
In conclusion, an exponential function is a function in which the variable appears in an exponent and is defined as f(x) = aˣ or y = a×bˣ, where a is the base of the function and x is the exponent.
The base determines the growth rate of the function and the graph of an exponential function is a curve that goes up and to the right if the base is greater than 1, and goes down and to the right if the base is between 0 and 1.
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1. Which polygon or polygons are regular? (2 points)
Answer:
the first and the third
Step-by-step explanation:
Is it possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm Why or why not?
We cannot construct a triangle with side lengths 3.5 cm, 9.2 cm and 5.3 cm. So it is not possible to construct a triangle whose sides are 3.5 cm 9.2 cm and 5.3 cm. This is because these lengths does not follow triangle inequality theorem.
It is not possible to construct a triangle using the given side lengths of 3.5 cm, 9.2 cm, and 5.3 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, if we take 3.5 cm and 5.3 cm as two sides, the sum of their lengths is 8.8 cm. But the length of the third side (9.2 cm) is greater than 8.8 cm, so these three side lengths cannot form a triangle.
It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle.
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help me pleaseeeeeeee dont guess
The inequalities given are 9) "And inequality, 10) "Or" inequality.
What are Compound Inequalities?Compound inequalities are inequalities which consist of two or more simple inequalities.
"And" compound inequality has both the inequalities true.
"Or" compound inequalities have any one of them as true.
9. |5 + m| < 13
This can be written as,
-13 < 5 + m < 13
-13 - 5 < m < 13 - 5
-18 < m < 8
This is an "and" inequality. Because m can lie between -18 and 8.
10. 4 |y + 6| ≥ 3
|y + 6| ≥ 3/4
-3/4 ≥ y + 6 ≥ 3/4
-3/4 - 6 ≥ y ≥ 3/4 - 6
-6.75 ≥ y ≥ -5.25
The value of y can be either ≤ -6.75 or y ≥ -5.25. y cannot be both.
So this is an "or" inequality.
Hence the first one is and inequality and the second one is or inequality.
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what is the measure of the length of a rectangle with a perimeter of 10 inches and a width of 2 inches?
Answer:
3 inches
Step-by-step explanation:
The perimeter is the sum of all the sides of a shape. A rectangle has 4 sides.
2 * 2 = 4
One side is 2 in., so the parallel side is also 2 in.
10 - 4 = 6
Subtract the sum from the perimeter.
6 / 2 = 3
Since there are two sides left, divide by 2.
I'LL GIVE BRAINIEST TO WHOEVER ANSWERS THIS CORRECTLY
3. The function represents the number of specialty items produced at the old factory w weeks after a change in management. The graph represents the number of specialty items produced at the new factory during the same time period.
(a) During Week 0, how many more specialty items were produced at the old factory than at the new factory? Explain.
(b) Find and compare the growth rates in the weekly number of specialty items produced at each factory. Show your work.
(c) When does the weekly number of specialty items produced at the new factory exceed the weekly number of specialty items produced at the old factory? Explain.
Answer:
The correct answer is A
I hope that helped.
Step-by-step explanation:
PLEASE HELP
calculate (30m) (2.01m). Use the correct number of significant digits in the answer
The expression 30m × 2.01m will be 60.3m²
How to illustrate the expression?In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.
The value of the expression will be:
= 30m × 2.01m
= 60.3m²
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Five Smithtown High School students are saving up to buy their first cars. They all have after-school jobs, and their weekly sala-ries are listed in the table. (Table: Emily $110, Sam $145, Danielle $130, Katie $160, Stephanie $400)
a. What is the mean weekly salary for these students?
b. What is the median salary?
c. Whose salary would you consider to be an outlier?
d. Which number do you think is better representative of the data, the mean or the median?
e. Explain your answer to part d.
Answer:
A. $189.
B. $130.
C. Stephanie's.
D. The Mean.
E. The mean is the average of the data. The Median is just the middle number which doesn't reveal all that much about the data.
Answer:
A.) $189
B.) $145✔️ | *(not $130❌)*
C.) Stephanie's
D.) Median✔️ | *(not "mean"❌)
E.) Because there is an outlier, the median is better representative than the mean.
Which description best compares the graphs of the two functions below?
A description which best compares the graphs of the two functions above include the following: B. The line for function A is steeper.
How to compare the two functions?In order to compare the two functions, we would have to find the slope of function B based on the data points contained in the table by using the slope formula.
Mathematically, the slope of a straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Substituting the given points into the slope formula, we have the following;
Slope, m = (-1 - (-2))/(3 - 0)
Slope, m = (-1 + 2)/3
Slope, m =1/3
From function A y = 3x - 2, the slope is equal to 3. Consequently, we can logically deduce that the line representing function A is steeper than the line representing function B because its slope is bigger i.e 3 > 1/3.
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
Answer: It is C I got it right on the exam
Step-by-step explanation: